Which rational x makes 3x^2-7x an integer?
lemm...@my-deja.com
so far:
------
For which rational numbers x is 3x^2 - 7x an integer? Find necessary and
sufficient conditions.
------
I've tried all manner of substitutions and manipulations for x, but I
think my best progress has been made by supposing we have 3x^2-7x=c
where c is an integer and then using the quadradic formula to obtain
x = (7 +/- sqrt(49+12c)) / 6
x will be rational as long as sqrt(49+12c) is rational. This happens iff
49+12c is a perfect square, or
49+12c=m^2
Where m is an integer. Experimentally, I've found this equation always
has a solution for c if m is coprime to 12. In fact, I've found
experimentally that I can replace the 49=7^2 with any other square
coprime to 12 and still find a solution for c.
Anyways, I'm unable to move pass this point, and I'm not sure if being
able to explain this phenomenon will yield a satisfactory answer to the
problem. Even if the right answer to the problem has nothing to do with
the 49+12c=m^2 equation, I'd still like to know more about this
equation, if possible, and why it has the above mentioned property.
Sent via Deja.com http://www.deja.com/
Before you buy.
Pax
but I've noticed that if you designate x as 1, then x=x+1, the
resulting string of increasing differences will, at the second
subtractive reduction between the differences, always yield a
span of 18 between them.
Is that encrypted up there in what you've said somewhere? :)
Be well - Pax
---
The purpose of Light is to fill the darkness and travel on;
the purpose of Life is to find the Light and travel with it. - Pax
-----------------------------------------------------------
Got questions? Get answers over the phone at Keen.com.
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hka...@datacomm.ch
Hallo :
3 x^2 - 7 x equals an integer y if and only if
(1) 3 x^2 - 7 x - y = 0 .
The roots of (1) are rational if and only if the discriminant
d := 49 - 12 y is the square of a natural number z :
(2) z^2 = 49 + 12 y = 1 + 12(y + 4) = 1 + 12m , m integer
or
(3) z^2 congruent 1 (mod 12)
The solutions of (3) are (check !)
(4) z congruent 1 , 5 , 7 , 11 (mod 12)
i.e. z = 1 + 12 n , n natural, etc. x is then found using the
quadratic formula.
Kind regards
Hans
Iain Davidson
<lemm...@my-deja.com> wrote in message news:8ks1l3$mfu$1...@nnrp1.deja.com...
> Okay, stumped on another one. First, the problem, and then my work on it
> so far:
>
> ------
> For which rational numbers x is 3x^2 - 7x an integer? Find necessary and
> sufficient conditions.
When x is an integer, the expression is an integer, so you can assume that
x = p/q where q >1 and p/q is in its lowest terms.
3(p/q)^2 -7(p/q) = C
3p^2 -7pq -Cq^2 = 0
If P is a prime that divides q then
3p^2 = 0 mod P
If P divides 3p^2 it must divide either 3 or p^2.
If it divides p^2 it divides p but by assumption there is
no prime that divides both p and q.
P divides 3 and is therefore equal to 3
So q = 3.
3p^2 -7p*3 -9C =0
p^2 -7p -3c = 0
p(p-7) = 3c
3 cannot divide p as then 3 would divide both p and q
So 3 divides p-7 and p is of the form 3m+1
So x must be an integer or of the form (3m+1)/3
Pax
>In article <018ab450...@usw-ex0103-024.remarq.com>,
> Pax <pax1NO...@whitesweb.com.invalid> wrote:
>> lemm...@my-deja.com wrote:
>> work on it
>> >so far:
>> >
>> >------
>> >For which rational numbers x is 3x^2 - 7x an integer? Find
>> necessary and
>> >sufficient conditions.
>> >
>> >
>> but I've noticed that if you designate x as 1, then x=x+1, the
>> resulting string of increasing differences will, at the second
>> subtractive reduction between the differences, always yield a
>> span of 18 between them.
>>
>> Is that encrypted up there in what you've said somewhere? :)
>>
>>
Hello :)
>
>3 x^2 - 7 x equals an integer y if and only if
>
>(1) 3 x^2 - 7 x - y = 0 .
>
>The roots of (1) are rational if and only if the discriminant
>d := 49 - 12 y is the square of a natural number z :
>
>(2) z^2 = 49 + 12 y = 1 + 12(y + 4) = 1 + 12m , m
integer
>
>or
>
>(3) z^2 congruent 1 (mod 12)
>
>The solutions of (3) are (check !)
>
>(4) z congruent 1 , 5 , 7 , 11 (mod 12)
>
>i.e. z = 1 + 12 n , n natural, etc. x is then found using
the
>quadratic formula.
>
>Kind regards
>Hans
>
>
>
Then guess what I discovered was just a strange coincidence.
Not surprised, it was just the first thing to hit me when I
looked at the equation using simple, in-my-head math. :)
3x^2-7x=y
(where x = 1 through 10)
9-7=2
36-14=22
81-21=60
144-28=116
225-35=190
324-42=282
441-49=392
576-56=520
729-63=666
900-70=830
..
Neatly, the 2nd reduction always seems to yield 18. :) :)
2, 22, 60,116,190,282,392,520,666,830
__\-| \-| \-| \-| \-| \-| \-| \-| \-| 1st reduction
___20, 38, 56, 74, 92,110,128,146,164
______\-| \-| \-| \-| \-| \-| \-| \-| 2nd reduction
_______18, 18, 18, 18, 18, 18, 18, 18
Seeing that was fun, will have to leave the calculus to you for
the time-being. :)
Virgil
>(3) z^2 congruent 1 (mod 12)
>
>The solutions of (3) are (check !)
>
>(4) z congruent 1 , 5 , 7 , 11 (mod 12)
>
>i.e. z = 1 + 12 n , n natural, etc.
Note that z == 1 or 5 or 7 or 11 (mod 12) is equivalent to
z == 1 or 5 (mod 6)
--
Virgil
vm...@frii.com
Doug Magnoli
Pax wrote:
> >(3) z^2 congruent 1 (mod 12)
> >
> >The solutions of (3) are (check !)
> >
> >(4) z congruent 1 , 5 , 7 , 11 (mod 12)
> >
> >i.e. z = 1 + 12 n , n natural, etc. x is then found using
> the
> >quadratic formula.
> >
> >Kind regards
> >Hans
> >
> >
> >
> Then guess what I discovered was just a strange coincidence.
> Not surprised, it was just the first thing to hit me when I
> looked at the equation using simple, in-my-head math. :)
>
> 3x^2-7x=y
> (where x = 1 through 10)
>
> 9-7=2
> 36-14=22
> 81-21=60
> 144-28=116
> 225-35=190
> 324-42=282
> 441-49=392
> 576-56=520
> 729-63=666
> 900-70=830
> ..
>
Looks like you're using 9x^2-7x instead of 3x^2-7x.
>
> Neatly, the 2nd reduction always seems to yield 18. :) :)
>
> 2, 22, 60,116,190,282,392,520,666,830
> __\-| \-| \-| \-| \-| \-| \-| \-| \-| 1st reduction
> ___20, 38, 56, 74, 92,110,128,146,164
> ______\-| \-| \-| \-| \-| \-| \-| \-| 2nd reduction
> _______18, 18, 18, 18, 18, 18, 18, 18
That's because the second reduction (as you call it) of a quadratic
divided by 2! will yield the coefficient of the x-squared term, which,
as you did it, was 9. If you repeat it with 3x^2-7x, you'll find your
reduction to be 6.
-Doug Magnoli
Pax
If x=1:
then what is 3 times x (3*1), isn't it 3?
Then what is 3 squared (3*3), isn't it 9?
What is 7 times x (7*1), isn't it 7?
What is 9 - 7, isn't it 2?
Now, perhaps I made an error by considering 3x to be the term to
be squared. If the way the problem is written should indicate
that, then I missed it.
Where x=1, 9x^2-7x would yield 81-7, as far as I can see. 3(x^2)
yields 3, where x=1. Then, the first subtraction would be 3-7,
leaving us with -4 as the difference. Is that what you're
saying?
It seems you're saying (3*1)*2, not "^2", which gives us 6.
Pax
To both Hans and Doug, if you gentlemen would be so kind. :) :)
"Pax" <pax1NO...@whitesweb.com.invalid> wrote in message
news:065df2dc...@usw-ex0103-023.remarq.com...
Hello again, Hans, :)
Guess you're saying by this that y has to be a positive integer?
Have I've misread the equation? Think I may be having a bracket problem. :)
Could you restate it as above, but using exhaustive bracketing? Where should
brackets be placed?
Exhaustively (as I have read the equation "3x^2-7x"), where x = 1
((3*x)^2) - (7*x) = y
((3*1)^2) - (7*1) = y
(3^2) - 7 = y
9 - 7 = 2
Should it be read as
(3*(x^2)) - (7*x) = y
or
3*((x^2) - (7*x)) = y
or
(3*x)^(2 - (7*x)) = y
or some other way I'm not catching?
Hello, Doug, :)
Why would you say that? Where did that "9x" come from according to your
interpretation of what I did?
The first numbers up there... (9 through 900)... are the first part of the
equation. 9 will go into all of the results of the first part of the equation,
but that's due to the 3 in 3x^2, 3 squared is 9. Someone might break the first
part into (3^2)*(x^2) and come out with the same result... but after that
computation, you still have the subtraction of the "7x" part of the equation to
consider... (7 through 70).
> >>
> >> Neatly, the 2nd reduction always seems to yield 18. :) :)
> >>
> >> 2, 22, 60,116,190,282,392,520,666,830
> >> __\-|_\-|_\-|_\-|__\-|__\-|__\-|__\-|__\-|___1st reduction
> >> __20, 38, 56, 74, 92,110,128,146,164
> >> _____\-|_\-|_\-|_\-|_\-|__\-|__\-|__\-|_____2nd reduction
> >> _____18, 18, 18, 18, 18, 18, 18, 18
> >
> >That's because the second reduction (as you call it) of a
> quadratic
> >divided by 2! will yield the coefficient of the x-squared term,
> which,
> >as you did it, was 9. If you repeat it with 3x^2-7x, you'll
> find your
> >reduction to be 6.
> >
> >-Doug Magnoli
> >
I didn't "divide" anything when I reduced, Doug, I only used subtraction.
First reduction:
22-2=2
60-22=38
116-60=56
190-116=74
282-190=92
392-282=110
520-392=128
666-520=146
830-666=164
Second reduction:
38-20=18
56-38=18
74-56=18
92-74=18
110-92=18
128-110=18
146-128=18
164-146=18
No further reduction is possible through this simple method I was using. Guess
you could then divide 18 by 3 and get 6, but seems as if you should do a set of
possible divisors/quotients instead... {1,2,3,6,9,18}... if you were going that
route.
So, whatever you're talking about... guess it's over my head if it's past my
simple interpretation of the original equation under question, which is:
((3x)^2) - (7x) = y
but I assumed that it was probably over my head when I replied. :)
May both of you be well - Pax
o~O~oo~O~oo~O~oo~O~oo~O~oo~O~oo~O~oo~O~oo~O~oo~O~oo~O~oo~O~o
As Pogo said: "We has met thu enuhmy 'n' he is US!"
David C. Ullrich
<pax1NO...@whitesweb.com.invalid> wrote:
>Doug Magnoli <dmag...@home.com> wrote:
>>
>>
[...]
>>
>>Looks like you're using 9x^2-7x instead of 3x^2-7x.
>>
[...]
>
>Now, perhaps I made an error by considering 3x to be the term to
>be squared. If the way the problem is written should indicate
>that, then I missed it.
If you actually do want to learn some mathematics
then when someone who sounds like he might know what
he's talking about makes a correction like this you should
try to figure out whether he's right and if so why.
You seem to realize that the notation 3x^2
could be read in two different ways. One of those
readings is the standard interpretation - all you
have to do is find a book somewhere and look it
up: 3x^2 means 3*(x^2). If a person wants to
write (3x)^2 the parentheses are required.
Pax
post which asked that exact question. Typical.
cmd...@usit.net
Am I missing something here? Set the expression equal to n (an
integer) and use the quadratic formula to solve for x.
Clyde Davenport
"Pax" <pa...@whitesweb.com> wrote:
>> >Looks like you're using 9x^2-7x instead of 3x^2-7x.
>
>
Pax
I DID say thank you. Don't you see it at the first of my reply
below?
His reply was in the form of an insult, as has been usual from
the first time he ever replied to me on anything.
[Quoting D. Ullrich]
If you actually do want to learn some mathematics then when
someone who sounds like he might know what he's talking about
makes a correction like this you should try to figure out
whether he's right and if so why.
You seem to realize that the notation 3x^2 could be read in two
different ways. One of those readings is the standard
interpretation - all you have to do is find a book somewhere and
look it up: 3x^2 means 3*(x^2). If a person wants to write (3x)
^2 the parentheses are required.
[Close quote]
My reply was not immediately after either Hans' or Doug's reply
to me. I did research. The notation was NOT clear TO ME. The
standard way of reading it Algebraically is all I had to go
by... which is (3x)^2, since x is usually the term being worked
upon/with, the 3 being a multiplier of x, the ^2 being another.
I proceeded to work the equation from left to right, as I was
taught.
http://www.algebrahelp.com/simpoops.htm
[Open quote]
Parenthesis and Brackets -- Simplify the inside of parenthesis
and brackets before you deal with the exponent (if any) of the
parenthesis or remove the parenthesis.
Exponents -- Simplify the exponent of a number or of a
parenthesis before you multiply, divide, add, or subtract it.
[**PLEASE NOTE**]
**Multiplication and Division** -- Simplify multiplication and
division in the order they appear from left to right.
Addition and Subtraction -- Simplify addition and subtraction in
the order they appear from left to right.
[Close quote]
What he calls the "standard interpretation" is NOT the standard
algebraic interpretation. However, I did not question his
different interpretation, as I did not question the
interpretation of the others. I was MERELY showing what
resulted from my OWN, SIMPLE algebraic interpretation of the
equation... while NEVER assuming my interpretation was the
correct one... in fact, my assumption was just the opposite,
that my interpretation was NOT correct... which I stated and
restated with every post of mine.
You don't approve my dislike of him? I'm sorry, but that's just
the way it is. I didn't set the rules with him, he did. I
don't care if he ever replies to me on ANYthing.
Regards - Pax
----- Original Message -----
From: "Wiener, Matthew" <MWi...@m-s-g.com>
To: <pa...@whitesweb.com>
Sent: Tuesday, July 18, 2000 2:33 PM
Subject: Re: Which rational x makes 3x^2-7x an integer?
>Thank you. Guess you didn't bother to read the ENTIRETY of my
>post which asked that exact question.
Uh, what are you talking about????
You asked a question, David *answered* that exact question, and
then you insult him, saying he hadn't noticed that you asked
that exact question??? How else could he answer it? Why don't
you say thank you, or whatnot?
Sheesh, that doesn't even make any sense.
--
-Matthew P Wiener (mwi...@m-s-g.com)
Pax
>
>Am I missing something here? Set the expression equal to n (an
>integer) and use the quadratic formula to solve for x.
>
>Clyde Davenport
>
Hi, Clyde, :)
I NEVER said I was doing it properly, all I had the misfortune
of doing in my credulous simplicity was showing what in-my-head
algebra came up with when I first looked at the problem, working
it simply from left to right, as standard Algebra dictates. It
never crossed my mind that what I saw was the proper way to work
the problem. ALL I was doing was showing something interesting
(to me) I happened to notice.
It IS still math, and it IS still a valid form of math... it's
just not the form that's required to solve this apparently. I
have no problem with that. Why should anyone have a problem
with the simple pattern I happened to notice? Primes make a
pattern when they're mapped if you stand back and look at a huge
field of them. Does it matter? Probably not. It's just
interesting.
Kind regards - Pax
Virgil
Is there any rational but non-integer value besides x = 7/3 for which
3*(x^2) - 7*x is an integer? If there is, could someone give a specific
example of such a rational number?
--
Virgil
vm...@frii.com
Ed Hook
Pax <pax1NO...@whitesweb.com.invalid> writes:
|> I DID say thank you. Don't you see it at the first of my reply
|> below?
|> His reply was in the form of an insult, as has been usual from
|> the first time he ever replied to me on anything.
There's just the slightest possibility that
you're a bit too sensitive. I'd read what
Prof. Ullrich posted as simply some good advice.
After all, if you _are_ traversing unfamiliar
territory and you happen upon someone who
seems to know something more about it than you
do, why would you _not_ try to understand
what he was telling you ??
|> [Quoting D. Ullrich]
|> If you actually do want to learn some mathematics then when
|> someone who sounds like he might know what he's talking about
|> makes a correction like this you should try to figure out
|> whether he's right and if so why.
|> You seem to realize that the notation 3x^2 could be read in two
|> different ways. One of those readings is the standard
|> interpretation - all you have to do is find a book somewhere and
|> look it up: 3x^2 means 3*(x^2). If a person wants to write (3x)
|> ^2 the parentheses are required.
|> [Close quote]
|> My reply was not immediately after either Hans' or Doug's reply
|> to me. I did research. The notation was NOT clear TO ME. The
|> standard way of reading it Algebraically is all I had to go
See, that (in fact) is _not_ the "standard
way of reading it". The *standard* way interprets
"3x^2" as "3 times the square of x". This actually
follows from the stuff that you quoted next ..
|> by... which is (3x)^2, since x is usually the term being worked
|> upon/with, the 3 being a multiplier of x, the ^2 being another.
|> I proceeded to work the equation from left to right, as I was
|> taught.
|> http://www.algebrahelp.com/simpoops.htm
|> [Open quote]
|> Parenthesis and Brackets -- Simplify the inside of parenthesis
|> and brackets before you deal with the exponent (if any) of the
|> parenthesis or remove the parenthesis.
|> Exponents -- Simplify the exponent of a number or of a
|> parenthesis before you multiply, divide, add, or subtract it.
|> [**PLEASE NOTE**]
|> **Multiplication and Division** -- Simplify multiplication and
|> division in the order they appear from left to right.
|> Addition and Subtraction -- Simplify addition and subtraction in
|> the order they appear from left to right.
|> [Close quote]
If you're going to use those as your sole
and ultimate rules for parsing algebraic
expressions, then you've first got to
realize that that no one of those rules
tells you how to interpret "3x^2". The
only way to determine what to do is to
recognize that "3x^2" is the same as
"3*x*x" and then apply the particular
rule that your annotation singles out.
But, doing that, you end up with the
interpretation "3x^2" = "3 times x times x"
(or, equivalently, "3 times x^2").
I mean, check it out ...
"3x^2" has neither parentheses or brackets,
so the first rule doesn't apply. It _has_
an exponent, so the second rule _does_
apply -- but '2' is about as simple as it
can get, so the second rule doesn't change
anything. In order to apply the remaining
rules, there's an unspoken assumption that
you've manaeged to express everything in
terms of the 4 basic arithmetic operations:
addition, subtraction, multiplication and
division. Doing that gets you from "3x^2"
to "3*x*x", as I claimed. So your rules
really _do_ force you to what everyone else
has been telling you is the standard
evaluation of "3x^2" ...
|> What he calls the "standard interpretation" is NOT the standard
|> algebraic interpretation. However, I did not question his
Yeah ... it _is_.
|> different interpretation, as I did not question the
|> interpretation of the others. I was MERELY showing what
|> resulted from my OWN, SIMPLE algebraic interpretation of the
|> equation... while NEVER assuming my interpretation was the
|> correct one... in fact, my assumption was just the opposite,
|> that my interpretation was NOT correct... which I stated and
|> restated with every post of mine.
|> You don't approve my dislike of him? I'm sorry, but that's just
|> the way it is. I didn't set the rules with him, he did. I
|> don't care if he ever replies to me on ANYthing.
|> Regards - Pax
<* snip *>
I removed the copy you posted of Matthew
Wiener's e-mail to you. It's generally
regarded as a Really Bad Thing to *post*
someone's e-mail -- if they wanted to share
it with a worldwide audience, they would
have posted it themselves ...
--
Ed Hook | Copula eam, se non posit
Computer Sciences Corporation | acceptera jocularum.
NAS, NASA Ames Research Center | All opinions herein expressed are
Internet: ho...@nas.nasa.gov | mine alone
Richard Carr
:Date: Tue, 18 Jul 2000 15:56:33 -0600
:From: Virgil <vm...@frii.com>
:Newsgroups: sci.math
:Subject: Re: Which rational x makes 3x^2-7x an integer?
:
:3*(x^2) - 7*x is an integer provided that x is an integer or x = 7/3.
:
:Is there any rational but non-integer value besides x = 7/3 for which
:
:3*(x^2) - 7*x is an integer? If there is, could someone give a specific
:example of such a rational number?
:
There are loads of them. e.g x=1/3, 4/3, 10/3, 13/3, 16/3, ..., -2/3,
-5/3, -8/3, -11/3, -14/3, ... .
:--
:Virgil
:vm...@frii.com
:
Pax
[Matthew P Wiener]
The above is in flat out contradiction to what the webpage you
cite says. ***^2 is an exponent, and therefore takes priority
over the 3.***
> [Pax]
> What he calls the "standard interpretation" is NOT the
> standard algebraic interpretation.
[Matthew P Wiener]
Yes, it is. 3x^2 is 3*x*x. There is no other interpretation.
[Pax]
You are correct and I stand very corrected. My apologies.
http://www.algebrahelp.com/simpoopspg3.htm
[Open quote]
Order of Operations
1. Parenthesis and Brackets from the inside out.
2. Exponents of numbers or parenthesis.
3. Multiplication and Division in the order they appear.
4. Addition and Subtraction in the order they appear.
[Close quote]
Regards - Pax
Jan Kristian Haugland
1/3, 4/3, 10/3, 13/3, 16/3, 19/3, ... :-)
On Tue, 18 Jul 2000, Virgil wrote:
> 3*(x^2) - 7*x is an integer provided that x is an integer or x = 7/3.
>
> Is there any rational but non-integer value besides x = 7/3 for which
>
> 3*(x^2) - 7*x is an integer? If there is, could someone give a specific
> example of such a rational number?
>
> --
> Virgil
> vm...@frii.com
>
>
Lynn Killingbeck
Be aware that the expression "a/b*c" is frequently to be
interpreted as "a/(b*c)", because multiplication (per some authors, but
not all of them!) has precedence over division. Your "in the order they
appear" is not universal (but, it is common). It's usually up to the
reader to figure out which convention applies(!), based on several books
I've bought over the past few years. Math-oriented tends to be
multiplication before division; programming-oriented tends to be from
left to right. It's nice to see you explicitly give your precedence.
Lynn Killingbeck
Virgil
<Pine.LNX.4.21.00071...@cpw.math.columbia.edu>,
Richard Carr <ca...@cpw.math.columbia.edu> wrote:
>:3*(x^2) - 7*x is an integer? If there is, could someone give a specific
>:example of such a rational number?
>:
>
>There are loads of them. e.g x=1/3, 4/3, 10/3, 13/3, 16/3, ..., -2/3,
>-5/3, -8/3, -11/3, -14/3, ... .
It then appears that the non-integral rationals for which 3*(x^2) - 7*x
is integral include all x = n + 1/3, for n an integer.
Is the following true?
For rational x, 3*(x^2) - 7*x is an integer if and only if either x is
an integer or x - 1/3 is an integer.
--
Virgil
vm...@frii.com
Jan Kristian Haugland
On Tue, 18 Jul 2000, Virgil wrote:
Yes. Note that if 3x^2 - 7x is an integer, then
(6x - 7)^2 = 12(3x^2 - 7x) + 49 is an integer.
If x is rational and (6x - 7)^2 is an integer
then 6x - 7 is an integer. So x has the form
n/6 where n is an integer, giving 3x^2 - 7x
= n(n - 14)/12, which is an integer if and
only if n is even and == 0 or 2 (mod 3), i.e.,
if x or x - 1/3 is an integer.
Pax
>
>Be aware that the expression "a/b*c" is frequently to be
>interpreted as "a/(b*c)", because multiplication (per some
authors, but
>not all of them!) has precedence over division. Your "in the
order they
>appear" is not universal (but, it is common). It's usually up
to the
>reader to figure out which convention applies(!), based on
several books
>I've bought over the past few years. Math-oriented tends to be
>multiplication before division; programming-oriented tends to
be from
>left to right. It's nice to see you explicitly give your
precedence.
>
>Lynn Killingbeck
>
>
That's very kind of you, thank you. :) My programming must
stick out. Always used brackets, too. Belt-'n'-suspenders.
Haven't programmed in over ten years, though, so VERY rusty on
everything but "balance your bank account"-type math. My
regular NG got into a discussion re 0.999...=1 EXACTLY. It
really piqued my interest concerning the advanced math they were
throwing around (I've never had anything but Algebra, and only
truly applied that in programming), so, thought I'd come to the
sci.math forum and see if it was being discussed here. It was,
and Dave Seaman clarified everything for me.
Never intended to try to speak with authority on a subject in
which I'm not qualified... planned to lurk (after I found out
what I initially came here to discover), until I actually knew
something. Then the header of this thread hooked me DUE to the
lack of bracketing in the equation. I worked it with brackets
all over it in different positions, after I "straight-lined"
it. :)
Was just having fun, juggling numbers... (unfortunate family
trait)... as I learned something. From what I've read re some
of the Greats of math, they had fun and enjoyed the numbers,
too. Life is very short. Guess one way to make it SEEM longer
is to be serious about every inch of it. "Oh, frabjous day!
What a long, tedious life I see before me!" (shudder!)
In a profession where 1+1 CAN equal 5 (ala the informative Mr.
Seaman and his "mod"s), where do you draw the line as far
as "correct" goes, anyway? :) But before the stones start
flying, I hastily add concerning math methods, it must be as the
very green martians replied in the movie 'Martians Go Home' when
asked if they liked green, "Yes... but not THAT green!" :) From
here on, I will watch every tiny little nuance of green I plan
to smear about so as not to inadvertently mar someone's
frabjously tedious day. :)
Warm regards - Pax
PS - Mathematician: "Life is real, life is earnest."
Mathematics Heretic: "I'll miss Ernest, he was a funny guy." :)
Iain Davidson
Virgil <vm...@frii.com> wrote in message
news:vmhjr-0E55FF....@news.frii.com...
> 3*(x^2) - 7*x is an integer provided that x is an integer or x = 7/3.
>
>
> 3*(x^2) - 7*x is an integer? If there is, could someone give a specific
> example of such a rational number?
10/3 or more generally (3m+1)/3
Pax
>In article <06501ba0...@usw-ex0104-032.remarq.com>,
> Pax <pax1NO...@whitesweb.com.invalid> writes:
>
>
>
>|> His reply was in the form of an insult, as has been usual
from
>|> the first time he ever replied to me on anything.
>
> There's just the slightest possibility that
> you're a bit too sensitive. I'd read what
> Prof. Ullrich posted as simply some good advice.
> After all, if you _are_ traversing unfamiliar
> territory and you happen upon someone who
> seems to know something more about it than you
> do, why would you _not_ try to understand
> what he was telling you ??
Hello, Mr. Hook, :)
It's very hard for me to explain myself, since I consider
it "making excuses". This is approximately a week since my
first enjoyment of D. Ullrich's brand of "Welcome newcomer." He
is, I assume, a regular here, and I am the interloper. It's his
turf, not mine. AS it is his turf, I guess that gives him the
right to be as high-handed and insulting as he wishes, since he
has been that way from his very first interaction with me. I
accept that fact. I do not have to respect him for it. If I
seem overly sensitized as regards my interactions with him, it's
only because I am.
>|> The notation was NOT clear TO ME. The
>|> standard way of reading it Algebraically is all I had to go
>
> See, that (in fact) is _not_ the "standard
> way of reading it". The *standard* way interprets
> "3x^2" as "3 times the square of x". This actually
> follows from the stuff that you quoted next ..
I have explained my definition of "standard" elsewhere, AND
corrected my mistatement with another quote from the same
website as the one below stating the correct procedure... WITH
an apology.
"3*x*x" is unclear to your meaning, since you're actually
stating the need for "x*x*3". "3*x*x" is exactly what I did, if
you're going strictly left to right. :) (Precisely: (3*x)^2) I
know now, that the exponent should be worked first... but,
without brackets, I probably would've still tried to square 3x,
resulting in (3^2)*(x^2)... then multiplication/division, then
addition/subtraction. (Been a lot of years since I took high
school Algebra.) In programming I always bracketed to make sure
the computer interpreted the equation properly. Would never
have entered such an equation as 3x^2-7x.
>|> What he calls the "standard interpretation" is NOT the
standard
>|> algebraic interpretation. However, I did not question his
>
> Yeah ... it _is_.
Agreed... although... come to think of it... where is the rule
that states that you're supposed to separate the 3 from the x
and work the exponent on the x alone? What is 3 if not a
multiplier of x? There's 7x standing there, with its 7 an
obvious multiplier of x, tied to x, in other words... so why is
the 3 of 3x^2 a loose cannon? Further, why is it not assumed
that it should be 3(x^2-7)x, if the multipliers are singletons
and may be divided from the x without harm? But then what?
Should it be done as (x^(2-7)) or ((x^2)-7)?
Both 3 and 7 are counters of x. They are not real numbers,
unless you were to juggle the x out of the equation... and by
doing so, slice that 3 and 7 to 2 and 6... but would you have
anything remotely resembling the orginal intent of the
equation? Doesn't seem so. So the x needs its counters and the
counters need their x. If they are so tied, why should x be
considered separately for any operation? What justification is
there in separating a counter that has no actual numerical value
on its own from the real number whose periodicity it is there to
indicate?
This is the same argument that was given in my regular NG to
justify 0.999... being exactly equal to 1. They set x to
0.999..., then juggled x out of the equation and worked with the
multipliers. It scrambled my brains. So I am truly asking...
DO you know the rule that justifies a separation of x and its
multiplier?
> I removed the copy you posted of Matthew
> Wiener's e-mail to you. It's generally
> regarded as a Really Bad Thing to *post*
> someone's e-mail -- if they wanted to share
> it with a worldwide audience, they would
> have posted it themselves ...
Hmmm... perhaps someone will think twice before sending me
another such unsolicited email then? If I make a public
mistake, exactly WHO of knowledge within the public that reads
it will not be aware of my mistake? The place to discuss such
things is on the forum in which it was presented. The mistake
SHOULD be corrected publicly.
Math is a hard subject, I'm sure there are many who come here to
learn the proper methods. Why would I want a mistake of mine
hanging around to perhaps influence someone in the wrong
direction? Although, I must say in my defense that I stated
plainly in every post that I was almost certain the method I was
using was not the proper one. But it seems many here have two
healthy feet just itching to jump in the middle of someone else
who even makes an innocent observation using an unorthodox
method. One must wonder how unfulfilled such lives must be,
overall.
Kind regards - Pax
>--
> Ed Hook | Copula eam, se
non posit
> Computer Sciences Corporation | acceptera
jocularum.
> NAS, NASA Ames Research Center | All opinions herein
expressed are
> Internet: ho...@nas.nasa.gov | mine alone
>
>
david_...@my-deja.com
Pax <pax1NO...@whitesweb.com.invalid> wrote:
>
>
> I DID say thank you. Don't you see it at the first of my reply
> below?
>
> the first time he ever replied to me on anything.
>
> If you actually do want to learn some mathematics then when
> someone who sounds like he might know what he's talking about
> makes a correction like this you should try to figure out
> whether he's right and if so why.
>
> You seem to realize that the notation 3x^2 could be read in two
> different ways. One of those readings is the standard
> interpretation - all you have to do is find a book somewhere and
> look it up: 3x^2 means 3*(x^2). If a person wants to write (3x)
> ^2 the parentheses are required.
> [Close quote]
You seem to be the only person who finds anything insulting
about this.
> My reply was not immediately after either Hans' or Doug's reply
> to me. I did research. The notation was NOT clear TO ME. The
> standard way of reading it Algebraically is all I had to go
> by... which is (3x)^2,
No, that is not the standard interpretation. You say in another
post that it's been a while since you took Algebra. This is clear.
Seems like it's been a while since you looked at polynomials
at all - notation like 3x^2 comes up all the time, and if you think
your interpretation is the standard one you've been getting
the wrong answers to _everything_.
This is sci.math. There are other newsgroups devoted to
elementary algebra and arithmetic.
> since x is usually the term being worked
> upon/with, the 3 being a multiplier of x, the ^2 being another.
> I proceeded to work the equation from left to right, as I was
> taught.
>
> http://www.algebrahelp.com/simpoops.htm
> [Open quote]
> Parenthesis and Brackets -- Simplify the inside of parenthesis
> and brackets before you deal with the exponent (if any) of the
> parenthesis or remove the parenthesis.
> Exponents -- Simplify the exponent of a number or of a
> parenthesis before you multiply, divide, add, or subtract it.
> [**PLEASE NOTE**]
> **Multiplication and Division** -- Simplify multiplication and
> division in the order they appear from left to right.
> Addition and Subtraction -- Simplify addition and subtraction in
> the order they appear from left to right.
> [Close quote]
And you complain about me not reading the ENTIRETY
of your post. The above quote _says_ that 3x^2 is 3*(x^2).
Note the line immediately preceding the line you marked
"PLEASE NOTE". You do the exponentiation first - it _says_
so right there.
> What he calls the "standard interpretation" is NOT the standard
> algebraic interpretation. However, I did not question his
> different interpretation, as I did not question the
> interpretation of the others. I was MERELY showing what
> resulted from my OWN, SIMPLE algebraic interpretation of the
> equation... while NEVER assuming my interpretation was the
> correct one... in fact, my assumption was just the opposite,
> that my interpretation was NOT correct... which I stated and
> restated with every post of mine.
>
> You don't approve my dislike of him? I'm sorry, but that's just
> the way it is. I didn't set the rules with him, he did. I
> don't care if he ever replies to me on ANYthing.
You should learn a teensy bit about things before making
statmenets about them in public. I mean you were supposed
to learn that 3x^2 = 3*(x^2) in seventh grade or something.
[If you find that last paragraph a little insulting you may
have a point. But you should note that (i) it's also a simple
_fact_ = everyone else here _did_ learn what 3x^2 meant
when they were much much younger (ii) it's something I
_refrained_ from saying yesterday, because I was trying
hard _not_ to insulting. When you say things that indicate
you have not mastered elementary algebra it can be
hard to keep a straight face when someone corrects
you - I thought I did a remarkably good job.
That's when you say something indicating you have
not mastered elementary algebra in a context where
adults talk about actual mathematics; saying something
like this in an elementary-algebra group would be
differemt. You'd get a straight answer there. Just like
you did here, dammit.]
Like I said the other day: If you're going to insist on being
insulted when people correct your errors you need to find
a different field. Here not all answers are equally valid.
> Regards - Pax
>
> ----- Original Message -----
> From: "Wiener, Matthew" <MWi...@m-s-g.com>
> To: <pa...@whitesweb.com>
> Sent: Tuesday, July 18, 2000 2:33 PM
> Subject: Re: Which rational x makes 3x^2-7x an integer?
>
> >Thank you. Guess you didn't bother to read the ENTIRETY of my
> >post which asked that exact question.
>
> Uh, what are you talking about????
>
> You asked a question, David *answered* that exact question, and
> then you insult him, saying he hadn't noticed that you asked
> that exact question??? How else could he answer it? Why don't
> you say thank you, or whatnot?
>
> Sheesh, that doesn't even make any sense.
> --
> -Matthew P Wiener (mwi...@m-s-g.com)
>
> ---
>
> The purpose of Light is to fill the darkness and travel on;
> the purpose of Life is to find the Light and travel with it. - Pax
>
> -----------------------------------------------------------
>
> Got questions? Get answers over the phone at Keen.com.
> Up to 100 minutes free!
> http://www.keen.com
>
>
Ed Hook
Pax <pax1NO...@whitesweb.com.invalid> writes:
|> ho...@nas.nasa.gov (Ed Hook) wrote:
|> >In article <06501ba0...@usw-ex0104-032.remarq.com>,
|> > Pax <pax1NO...@whitesweb.com.invalid> writes:
|> >|> His reply was in the form of an insult, as has been usual
|> from
|> >|> the first time he ever replied to me on anything.
|> > There's just the slightest possibility that
|> > you're a bit too sensitive. I'd read what
|> > Prof. Ullrich posted as simply some good advice.
|> > After all, if you _are_ traversing unfamiliar
|> > territory and you happen upon someone who
|> > seems to know something more about it than you
|> > do, why would you _not_ try to understand
|> > what he was telling you ??
|> Hello, Mr. Hook, :)
|> It's very hard for me to explain myself, since I consider
|> it "making excuses". This is approximately a week since my
|> first enjoyment of D. Ullrich's brand of "Welcome newcomer."
I admit that I must have missed your
entrance, then. Because I haven't noticed
David Ullrich being particularly unkind to
you. Did you first arrive here in a "EL Hemetis"
thread ? Or Pertti ?? Or Rajarshi Ray ? I don't
bother with any of those, so that might explain
my ignorance ... And it might also explain how
you were welcomed -- those sorts of threads tend
to generate more heat than light, and there's
usually a good deal of collateral damage :-)
|> He
|> is, I assume, a regular here, and I am the interloper. It's his
|> turf, not mine. AS it is his turf, I guess that gives him the
|> right to be as high-handed and insulting as he wishes, since he
|> has been that way from his very first interaction with me. I
|> accept that fact. I do not have to respect him for it. If I
|> seem overly sensitized as regards my interactions with him, it's
|> only because I am.
Part of the problem might be the well-known
fact that these sorts of interactions have
no ability to be "subtly nuanced". So it's
very easy for one party to an exchange to
misinterpret what the other party intends.
(And it's fairly common that the first party
screwed up the attempt to impart whatever
meaning he intended -- that is, it's difficult
on both ends to get this right.) That being
the case, it's probably best to be as
thick-skinned as you can manage here -- that
way, you might learn stuff even from those
whom you find offensive ...
What's "unclear" about "3*x*x" (which _is_,
I grant you, the same as "x*x*3" -- so I don't
understand *that* part of your comment, either) ??
"Going left to right", and inserting parentheses
to nail down *exactly* what's intended,
3*x*x = ((3*x)*x)
while
(3*x)^2 = (3*x)*(3*x)
and those are not at all the same. Indeed,
they agree precisely when x = 0.
I
|> know now, that the exponent should be worked first... but,
|> without brackets, I probably would've still tried to square 3x,
|> resulting in (3^2)*(x^2)... then multiplication/division, then
|> addition/subtraction. (Been a lot of years since I took high
|> school Algebra.) In programming I always bracketed to make sure
|> the computer interpreted the equation properly. Would never
|> have entered such an equation as 3x^2-7x.
In a program, that's probably as reasonable
an approach as any (even though programming
languages have rigid rules that define precisely
how any arithmetic expression is interpreted,
so the _need_ to parenthesize should be much
less in that situation). But, beyond a certain
level of complexity, fully-parenthesized
expressions quickly beome (in effect)
incomprehensible -- life's too short to want
to spend much of it trying to pair up parentheses
in order to figure out what someone is trying to
say/compute/... That's _why_ there are standard
rules that dictate how otherwise-ambiguous
expressions should be parsed -- it's for _our_
benefit, the machines couldn't care less. If it helps
any, most programming languages have adopted these
same rules, so you're probably already familiar
with them. For instance, in Fortran, the precedence
of the arithmetic operators (in descending order)
is
exponentiation
multiplication, division
addition, subtraction
where exponentiation associates from right to left
and all of the others associate from left to right.
And parentheses are only needed if you want your
expression to be evaluated in some other order.
Applying those rules to our old friend "3x^2", the
exponentiation symbolized by "^2" has to happen
_before_ the multiplication by 3 -- that is, the
expression is parsed as "3*(x*x)".
|> >|> What he calls the "standard interpretation" is NOT the
|> standard
|> >|> algebraic interpretation. However, I did not question his
|> > Yeah ... it _is_.
|> Agreed... although... come to think of it... where is the rule
|> that states that you're supposed to separate the 3 from the x
|> and work the exponent on the x alone?
It's implicit in the discussion up above.
As I noted, the "usual rules" provide a
_unique_ interpretation for "3x^2" ... and
it's the one that you're still resisting with
that question :-)
|> What is 3 if not a
|> multiplier of x? There's 7x standing there, with its 7 an
|> obvious multiplier of x, tied to x, in other words... so why is
|> the 3 of 3x^2 a loose cannon? Further, why is it not assumed
|> that it should be 3(x^2-7)x, if the multipliers are singletons
|> and may be divided from the x without harm? But then what?
|> Should it be done as (x^(2-7)) or ((x^2)-7)?
Nope. (That's the response to _each_ of those
questions :-) Applying the rules up above (the
Fortran flavor, just to be explicit), the
expression "3x^2 - 7x" is equivalent to the
fully-parenthesized expression
((3*(x^2)) - (7*x))
with no 'if's, 'and's or 'but's ...
|> Both 3 and 7 are counters of x. They are not real numbers,
Sure they are ...
|> unless you were to juggle the x out of the equation... and by
|> doing so, slice that 3 and 7 to 2 and 6... but would you have
|> anything remotely resembling the orginal intent of the
|> equation? Doesn't seem so. So the x needs its counters and the
|> counters need their x. If they are so tied, why should x be
|> considered separately for any operation? What justification is
|> there in separating a counter that has no actual numerical value
|> on its own from the real number whose periodicity it is there to
|> indicate?
OK, I understood almost _none_ of that
paragraph. '3' and '7' are certainly
real numbers (of the integer sort) and
they appear as coefficients in the
expression -- but they're on an _equal_
footing with 'x^2' and 'x' in there.
|>
|> This is the same argument that was given in my regular NG to
|> justify 0.999... being exactly equal to 1. They set x to
|> 0.999..., then juggled x out of the equation and worked with the
|> multipliers. It scrambled my brains. So I am truly asking...
|> DO you know the rule that justifies a separation of x and its
|> multiplier?
Yes -- the rule(s) for interpreting
arithmetic expressions.
I assume that the discussion that first
brought you here was a proof that looked
something like:
Let x = 0.9999... . Then
10x = 9.9999... = 9 + x
so 9x = 9, which implies that x = 1.
Right ? Well, as a proof, that's open to
various objections, but the algebraic
manipulations are just fine. (The nature
of the valid objections would be that the
proof assumes that you understand - in
great detail - just how to operate with
nonterminating decimal representations.
But anyone who _has_ that understanding
already *knows* why 0.9999... = 1, so
the above proof sort of misses the point.)
|> > I removed the copy you posted of Matthew
|> > Wiener's e-mail to you. It's generally
|> > regarded as a Really Bad Thing to *post*
|> > someone's e-mail -- if they wanted to share
|> > it with a worldwide audience, they would
|> > have posted it themselves ...
|> Hmmm... perhaps someone will think twice before sending me
|> another such unsolicited email then? If I make a public
|> mistake, exactly WHO of knowledge within the public that reads
|> it will not be aware of my mistake? The place to discuss such
|> things is on the forum in which it was presented. The mistake
|> SHOULD be corrected publicly.
That's your opinion and you are, of
course, entitled to it. But what I
said up above is true -- it _is_
generally regarded as a breach of
netiquette to post someone's e-mail.
And doing so will not generally win
you any friends -- certainly not among
those who think that observing a few
basic rules might stave off the Imminent
Death of Usenet ("film at 11!") just a
little bit longer ...
Oh ... and, as you might have noticed,
no perceived/imagined/actual mistake made
on sci.math goes uncorrected for very
long (its "time to first correction" is
typically on the order of "a New York minute"),
so your concern above is unfounded.
|> Math is a hard subject, I'm sure there are many who come here to
|> learn the proper methods. Why would I want a mistake of mine
|> hanging around to perhaps influence someone in the wrong
|> direction? Although, I must say in my defense that I stated
|> plainly in every post that I was almost certain the method I was
|> using was not the proper one. But it seems many here have two
|> healthy feet just itching to jump in the middle of someone else
|> who even makes an innocent observation using an unorthodox
|> method. One must wonder how unfulfilled such lives must be,
|> overall.
"Are you talkin' to _me_ ?!? I'm
the only one here, so ..." :-)
I think it's more that there are a
number of people here who are interested
in mathematics and want to help -- if your
"unorthodox method" makes any kind of sense,
then it might generate a discussion about
the circumstances where it might apply and
the sorts of uses it might have. If, on the
other hand, it's simply wrong, then you'll
get numerous replies pointing that out --
you might even get the feeling that we're
"piling on", but a lot of that is due to the
propagation delays that are endemic to
Usenet -- I might see your post, check that
no one else has replied yet and go ahead
(even though _your_ news system already has
a gazillion replies waiting for you) -- if
enough of us do that, you'll end up feeling
shell-shocked, even though none of us is
trying for that effect.
Pax
>
> Like I said the other day: If you're going to insist on
being
>insulted when people correct your errors you need to find
>a different field. Here not all answers are equally valid.
>
You are exhausting. I don't care if others correct my errors, I
care if YOU correct my errors. I wish no further interaction
with you, Ullrich. Is that too difficult for you to parse?
- Pax
David C. Ullrich
<pax1NO...@whitesweb.com.invalid> wrote:
>david_...@my-deja.com wrote:
>>
>> Like I said the other day: If you're going to insist on
>being
>>insulted when people correct your errors you need to find
>>a different field. Here not all answers are equally valid.
>>
>
>You are exhausting. I don't care if others correct my errors, I
>care if YOU correct my errors. I wish no further interaction
>with you, Ullrich. Is that too difficult for you to parse?
And you complain about _me_ insulting _you_.
(In contexts where various people have been explicit about
the fact that they don't see anything insulting about what
I wrote, btw.)
Sorry to be the one to tell you this, but when you
make a post in a public newsgroup you don't get to say
who replies and who doesn't.
When you make comments about your disbelief
in the validity of arguments that we all learned as first-year
grad students and then it turns out you don't have
seventh-grade math straight that's the sort of thing
we expect around here, no big deal. But when you
_argue_ with people over the meaning of "3x^2"
you should expect that at some point you will
annoy people. Really - we all deal with that sort
of thing every day, if we all had it wrong we'd all
be getting everything wrong, and by now we
would have noticed. This seems kind of obvious.
(Please don't bother reminding us that you've
said over and over that you're probably wrong. It's
actually "I'm probably wrong, but I'm right" that
you've been repeating.)
> - Pax
Pax
>
Could you tell me if you have a natural proclivity for
astounding anal retention or if you have acquired your current
level through years and years of diligent practice?
- Pax
Pax
ho...@nas.nasa.gov (Ed Hook) wrote:
>Pax <pax1NO...@whitesweb.com.invalid> writes:
>|> It's very hard for me to explain myself, since I consider
>|> it "making excuses". This is approximately a week since my
>|> first enjoyment of D. Ullrich's brand of "Welcome newcomer."
>I admit that I must have missed your
>entrance, then. Because I haven't noticed
>David Ullrich being particularly unkind to
>you. Did you first arrive here in a "EL Hemetis"
>thread ? Or Pertti ?? Or Rajarshi Ray ? I don't
>bother with any of those, so that might explain
>my ignorance ... And it might also explain how
>you were welcomed -- those sorts of threads tend
>to generate more heat than light, and there's
>usually a good deal of collateral damage :-)
Hello once more, Mr. Hook, :)
It was in the thread "Zeno gets naked", his first post to me was
rather short and rude... and it went downhill from there.
>Part of the problem might be the well-known
>fact that these sorts of interactions have
>no ability to be "subtly nuanced". So it's
>very easy for one party to an exchange to
>misinterpret what the other party intends.
>(And it's fairly common that the first party
>screwed up the attempt to impart whatever
>meaning he intended -- that is, it's difficult
>on both ends to get this right.) That being
>the case, it's probably best to be as
>thick-skinned as you can manage here -- that
>way, you might learn stuff even from those
>whom you find offensive ...
That's good advice. :) But as far as Ullrich goes, I'd rather
pretend he never happened.
>What's "unclear" about "3*x*x" (which _is_,
>I grant you, the same as "x*x*3" -- so I don't
>understand *that* part of your comment, either) ??
>"Going left to right", and inserting parentheses
>to nail down *exactly* what's intended,
>
>3*x*x = ((3*x)*x)
>
>while
>
>(3*x)^2 = (3*x)*(3*x)
This last example is what I did wrong. :) If x=1 doing it this
way, then the product is 9 ... (3*1)*(3*1)=9.
>and those are not at all the same. Indeed,
>they agree precisely when x = 0.
Agreed, and agreed... anything times 0 tends to do that. :)
>In a program, that's probably as reasonable
>an approach as any (even though programming
>languages have rigid rules that define precisely
>how any arithmetic expression is interpreted,
>so the _need_ to parenthesize should be much
>less in that situation). But, beyond a certain
>level of complexity, fully-parenthesized
>expressions quickly become (in effect)
>incomprehensible -- life's too short to want
>to spend much of it trying to pair up parentheses
>in order to figure out what someone is trying to
>say/compute/... That's _why_ there are standard
>rules that dictate how otherwise-ambiguous
>expressions should be parsed -- it's for _our_
>benefit, the machines couldn't care less. If it helps
>any, most programming languages have adopted these
>same rules, so you're probably already familiar
>with them. For instance, in Fortran, the precedence
>of the arithmetic operators (in descending order)
>is
>
>exponentiation
>
>multiplication, division
>
>addition, subtraction
>
>where exponentiation associates from right to left
>and all of the others associate from left to right.
>And parentheses are only needed if you want your
>expression to be evaluated in some other order.
>Applying those rules to our old friend "3x^2", the
>exponentiation symbolized by "^2" has to happen
>_before_ the multiplication by 3 -- that is, the
>expression is parsed as "3*(x*x)".
Right. :)
By the way, as to all those nested brackets you were talking
about, I did them. :) When you're working with large sums of
other people's money, they want EXACT. I didn't trust the
natural "order of operation", I designated specifically.
Almost all the programs I wrote were accounting and/or
inventory, on top of that. White-paper ledgers set up according
to the method used by the companies in their hand-kept books, to
facilitate change-over to computer use with minimum shock. In
every instance my programs were checked for accuracy against
both a continued set of hand-kept books and verified by the IRS.
So, you see? It was all a matter of basic math, actually...
hence my memory lapse as to the finer points of method re
unbracketed equations. Haven't programmed in over ten years.
Haven't actually done unbracketed equations for almost 35
years. VERY rusty. Don't trust my memory, either... and never
said at any time that I did.
What caused all this was my doing it in my head, without
brackets, left-to-right, multiplication then subtraction,
counting 3x as a number on its own and not to be divided, which
I then squared (rather than squaring just x), and subtracted 7x
from. I stated at the time that I didn't think it was the
proper way to do the equation. That SHOULD have been good
enough... (especially since I was only pointing out the unusual
row of 18s I discovered through subtraction)... but it wasn't.
>|> Agreed... although... come to think of it... where is the
rule
>|> that states that you're supposed to separate the 3 from the
x
>|> and work the exponent on the x alone?
>It's implicit in the discussion up above.
>As I noted, the "usual rules" provide a
>_unique_ interpretation for "3x^2" ... and
>it's the one that you're still resisting with
>that question :-)
Not "resisting", actually, just trying to justify why it's as
you say it is. :)
[ALERT!! ALERT!! BELOW CONTAINS WRONGNESS!! TAKE ALL NECESSARY
PRECAUTIONS!! SHIELD SENSITIVE NETHER REGIONS IMMEDIATELY!!
ULLRICH, THIS MEANS YOU!!]
WRONGNESS: My problem is I'm too used to thinking of the
variable as the end-all-and-be-all of the equation, with the
other numbers that interact with x being nothing more than
operators for the variable, important as counters, but ONLY as
counters, when they're nailed into the equation and not
variables themselves. So, to me, 3x was actually the product of
the operation 3*x. (Believe it or not, the majority of people
I've asked who did plenty okay in high school Algebra but
haven't used it since, look at it that same way... so it's a
common misconception.)
Let me try to explain the simple way I was looking at it that
got me to the wrong... oh, really, really wrong... OH!! WRONG!!
OH, BOY, OH, BOY!!! OH, REALLY!!! NO KIDDING!!! Was it
REALLY, REALLY WRONG!!! (The execution is Tuesday)... answer
that started all of this:
WRONGNESS: If x=1 ball, 3x=a bag of 3 balls... that's what I
meant by "tied"... you would have to tear open the bag to do
something to one ball by itself, so you'd be left with a bag of
2 balls and a single ball doing whatever. 3x means the same as
x+x+x. Looking at it that way, if you square one x, you'd have
to do the same operation to each x to come out with the correct
answer.
SAFE ZONE: But what you're saying is that the correct way is to
separate the x from its 3 operator and don't consider the 3
again until you square the x, then you bring the 3 into
consideration and multiply the product of x^2 by it. So, before
the balls are ever bagged, you blow them up, paint them red,
whatever (the ^2), THEN you bag them 3 to a bag. That's
logical, since the exponent operation (^2) is an earlier
operation performed on x than the later multiplication by 3.
What the 3 is saying is that we have 3 of this particular brand
of x, and that brand was determined by x^2. :)
>|> What is 3 if not a
>|> multiplier of x? There's 7x standing there, with its 7 an
>|> obvious multiplier of x, tied to x, in other words... so why
is
>|> the 3 of 3x^2 a loose cannon? Further, why is it not assumed
>|> that it should be 3(x^2-7)x, if the multipliers are
singletons
>|> and may be divided from the x without harm? But then what?
>|> Should it be done as (x^(2-7)) or ((x^2)-7)?
>Nope. (That's the response to _each_ of those
>questions :-) Applying the rules up above (the
>Fortran flavor, just to be explicit), the
>expression "3x^2 - 7x" is equivalent to the
>fully-parenthesized expression
>((3*(x^2)) - (7*x))
>with no 'if's, 'and's or 'but's ...
Thank you for those good ol' brackets! :) :)
>|> Both 3 and 7 are counters of x. They are not real numbers,
>Sure they are ...
Even in frequency times wavelength equals light speed, the
frequency is only a counter for the actual waves represented by
wavelength... (which doesn't mean frequency is unimportant).
>OK, I understood almost _none_ of that
>paragraph.
:) :) :) It doesn't matter.
> '3' and '7' are certainly
>real numbers (of the integer sort) and
>they appear as coefficients in the
>expression -- but they're on an _equal_
>footing with 'x^2' and 'x' in there.
"_equal_ footing"? I understand equal footing with the "^2",
but equal footing with the x? Even when you do 3*4 you're going
to have one of those that's an actual thing and one of those
that's only there to indicate how many of that thing, aren't
you? Of course, that doesn't mean "how many" isn't important,
but it is just an indicator of the quantity of a real thing
under consideration, isn't it?
>|> This is the same argument that was given in my regular NG to
>|> justify 0.999... being exactly equal to 1. They set x to
>|> 0.999..., then juggled x out of the equation and worked with
the
>|> multipliers. It scrambled my brains. So I am truly asking...
>|> DO you know the rule that justifies a separation of x and
its
>|> multiplier?
>Yes -- the rule(s) for interpreting
>arithmetic expressions.
I agree. :) The only time it probably comes up is if you assign
x. If you're solving for x, it's different, and none of those
operations gets done, for the most part. 3(x^2)-7x, (3(x^2)-7x)
+7x=7x, 3(x^2)=7x, (3(x^2))/x=(7x)/x, 3x=7, (3x)/3=7/3, x=7/3.
Doing it that way, which is only one very simple way, I'm sure
(and probably wrong again), you never really get rid of the tied
3x until the very end, when you throw the 3 at the 7, but you
never have to worry about "order of operation" with it either.
>I assume that the discussion that first
>brought you here was a proof that looked
>something like:
>
>Let x = 0.9999... . Then
>
>10x = 9.9999... = 9 + x
>
>so 9x = 9, which implies that x = 1.
>Right?
Right, but 9*0.999... isn't 9 exactly. :)
>Well, as a proof, that's open to
>various objections, but the algebraic
>manipulations are just fine. (The nature
>of the valid objections would be that the
>proof assumes that you understand - in
>great detail - just how to operate with
>nonterminating decimal representations.
>But anyone who _has_ that understanding
>already *knows* why 0.9999... = 1, so
>the above proof sort of misses the point.)
But IS the algebraic manipulation valid? What if x equaled 0.99
(9x=8.91), 0.44 (9x=3.96), 0.11 (9x=0.99), etc.? That's the
whole argument that brought me here in the first place. :) If
it can't work with finite decimals, why is it valid when
infinite decimals are used?
It seems no one would even try to use that method with finites,
at least not to attempt to prove exactness. The excuse that an
infinite constantly fills up the back-end with 9s, so it's okay,
seems rather lame. It's rather like the question can you have
an infinity of mass within an infinity of space and still have
mostly space? It's a head-whacker. :)
>That's your opinion and you are, of
>course, entitled to it. But what I
>said up above is true -- it _is_
>generally regarded as a breach of
>netiquette to post someone's e-mail.
"Etiquette" PLUS "net" equals "netiquette". The rules of
etiquette should apply in both directions on the net, too. It's
not very good form to kick someone under the table. It's sheer
bullyish ignorance to think the person they've kicked has no
recourse against any such further action.
>And doing so will not generally win
>you any friends -- certainly not among
>those who think that observing a few
>basic rules might stave off the Imminent
>Death of Usenet ("film at 11!") just a
>little bit longer ...
There's something else that goes along with Usenet (at least in
my particular neck of the woods), that is the right NOT to be
contacted by private email for no better reason than to bitch me
out. Just as phone harassment is a punishable offense, so is
such email harassment... at least when it applies to me.
It's very simple, if a total stranger contacts me privately and
doesn't want it posted, they shouldn't contact me for the sole
purpose of bitching at me re something I've said publicly on a
NG. If they feel strongly enough about it to comment, they
should carve it in stone publicly, otherwise, they should keep
it to themselves.
However, I must admit that the few emails I've gotten of that
sort I usually just delete without replying. Matthew got caught
in the backwash of my distaste for Ullrich... but, he didn't say
anything embarrassing to himself, in any event, he was only
defending Ullrich and (pretty much) calling me an idiot. :)
>Oh ... and, as you might have noticed,
>no perceived/imagined/actual mistake made
>on sci.math goes uncorrected for very
>long (its "time to first correction" is
>typically on the order of "a New York minute"),
>so your concern above is unfounded.
OH, yes! :) :) I've noticed that about this NG. :) :)
>|> Math is a hard subject, I'm sure there are many who come
here to
>|> learn the proper methods. Why would I want a mistake of mine
>|> hanging around to perhaps influence someone in the wrong
>|> direction? Although, I must say in my defense that I stated
>|> plainly in every post that I was almost certain the method I
was
>|> using was not the proper one. But it seems many here have
two
>|> healthy feet just itching to jump in the middle of someone
else
>|> who even makes an innocent observation using an unorthodox
>|> method. One must wonder how unfulfilled such lives must be,
>|> overall.
>"Are you talkin' to _me_ ?!? I'm
>the only one here, so ..." :-)
No, actually, I truly wasn't. :) :) You've been very kind, and
a gentleman.
>I think it's more that there are a
>number of people here who are interested
>in mathematics and want to help -- if your
>"unorthodox method" makes any kind of sense,
>then it might generate a discussion about
>the circumstances where it might apply and
>the sorts of uses it might have. If, on the
>other hand, it's simply wrong, then you'll
>get numerous replies pointing that out --
>you might even get the feeling that we're
>"piling on", but a lot of that is due to the
>propagation delays that are endemic to
>Usenet -- I might see your post, check that
>no one else has replied yet and go ahead
>(even though _your_ news system already has
>a gazillion replies waiting for you) -- if
>enough of us do that, you'll end up feeling
>shell-shocked, even though none of us is
>trying for that effect.
Actually, once again, I've had no problem with ANY of the
respondents except for Ullrich. I truly don't mind being
corrected, neither do I mind being wrong. Everyone's usually
wrong first before they get it right sometime or other. With
all the things I'm interested in, I hit Dead Wrong full blast
LOTS of times... but I hit it because I want to find out what's
right. I always have the option of forgetting about it. If I
choose not to exercise that option, I've got to be able to live
with the very real probability of being wrong yet again until I
know better. :)
Warmest regards :) - Pax
>--
>Ed Hook | Copula eam, se non posit
>Computer Sciences Corporation | acceptera jocularum.
>NAS, NASA Ames Research Center | All opinions herein expressed
are
>Internet: ho...@nas.nasa.gov | mine alone
---
David C. Ullrich
<pax1NO...@whitesweb.com.invalid> wrote:
>
[...]
>
>Right, but 9*0.999... isn't 9 exactly. :)
>
No, 9*0.999... is equal to 9. Exactly.
Whether you believe it or not. Not because
anyone says so, because we can _prove_
it. At various points in all this you've explained
you didn't follow this part of the argument
and that part was too hard for you. There's
nothing wrong with that. But given that it's
extremely curious how you can continue
to insist that the proofs are wrong.
>>Well, as a proof, that's open to
>>various objections, but the algebraic
>>manipulations are just fine. (The nature
>>of the valid objections would be that the
>>proof assumes that you understand - in
>>great detail - just how to operate with
>>nonterminating decimal representations.
>>But anyone who _has_ that understanding
>>already *knows* why 0.9999... = 1, so
>>the above proof sort of misses the point.)
>
>
>But IS the algebraic manipulation valid? What if x equaled 0.99
>(9x=8.91), 0.44 (9x=3.96), 0.11 (9x=0.99), etc.? That's the
>whole argument that brought me here in the first place. :) If
>it can't work with finite decimals, why is it valid when
>infinite decimals are used?
The same manipulations work just fine with
x = 0.99 . They do not show that 0.99 = 1, which is
good because 0.99 does not equal 1:
x = 0.99
10x = 9.9
Subtract:
9x = 9.9 - 0.99
9x = 8.91
Divide by 9:
x=8.91 / 9
And 8.91/9 = 0.99. The manipulations work just
fine, and they show that 0.99 = 0.99. (Which is
not big news.)
>It seems no one would even try to use that method with finites,
>at least not to attempt to prove exactness. The excuse that an
>infinite constantly fills up the back-end with 9s, so it's okay,
>seems rather lame.
But nobody here has said "inifinite constantly fills
up the back-end with 9's so it's ok". That _would_ be pretty
lame, but that has nothing to do with the proof.
David C. Ullrich
<pax1NO...@whitesweb.com.invalid> wrote:
>ull...@math.okstate.edu (David C. Ullrich) wrote:
>>
>>
>>
>>[Cut with a bloody axe]
>>
>
>
>Could you tell me if you have a natural proclivity for
>astounding anal retention or if you have acquired your current
>level through years and years of diligent practice?
Again: Your complaint is that I have not been
polite to you, right? I've been insulting you, right?
(The gentle reader might note that when he
started complaining about this I asked for an example
where I'd said anything about _him_, as opposed to
about his "opinions" on mathematics - he didn't come
up with any examples. Instead he explained that
corrections to his statements on mathematics were
insults to his character. Anyone curious whether
his staments on mathematics need correcting should
note that he is _still_ claiming that 0.999... does not
equal 1 exactly, _today_, in other posts in this
same thread. (What he actually said today was
that 9*0.999... does not equal 9 exactly.)
And anyone without an "up" button should
note that _several_ people have stated explicitly
that they saw nothing insulting in the last post of
mine at the top of the currect subthread.)
> - Pax
Richard Carr
On Wed, 19 Jul 2000, Pax wrote:
:Date: Wed, 19 Jul 2000 12:29:24 -0700
:From: Pax <pax1NO...@whitesweb.com.invalid>
:Newsgroups: sci.math
:Subject: Re: Which rational x makes 3x^2-7x an integer?
:
:david_...@my-deja.com wrote:
:>
:> Like I said the other day: If you're going to insist on
:being
:>insulted when people correct your errors you need to find
:>a different field. Here not all answers are equally valid.
:>
:
:You are exhausting. I don't care if others correct my errors, I
:care if YOU correct my errors. I wish no further interaction
:with you, Ullrich.
Then in the very next sentence, indicating a wish for further
interaction, Pax wrote:
:Is that too difficult for you to parse?
: - Pax
:
:
:
:---
:
:The purpose of Light is to fill the darkness and travel on;
:the purpose of Life is to find the Light and travel with it. - Pax
:
:-----------------------------------------------------------
:
:Got questions? Get answers over the phone at Keen.com.
:Up to 100 minutes free!
:http://www.keen.com
:
:
Then a very short later, Pax, who wants no interaction with David
C. Ullrich wrote:
On Wed, 19 Jul 2000, Pax wrote:
:Date: Wed, 19 Jul 2000 18:37:52 -0700
:From: Pax <pax1NO...@whitesweb.com.invalid>
:Newsgroups: sci.math
:Subject: Re: Which rational x makes 3x^2-7x an integer?
:
:ull...@math.okstate.edu (David C. Ullrich) wrote:
:>
:>
:>
:>[Cut with a bloody axe]
:>
:
:
:Could you tell me if you have a natural proclivity for
:astounding anal retention or if you have acquired your current
:level through years and years of diligent practice?
: - Pax
:
It seems to me that you do want to interact with David C. Ullrich after
all. I'm not sure whence comes your proctological diagnosis but I think
most people would admit that your initial insistence that people here were
unable to interpret 3x^2 correctly is taking a far bigger liberty and
is much more insulting than anything that David might have said- not that
it seems that he said anything insulting at all. To assume this is really
extraordinary- you might as well go and tell Tiger Woods he doesn't know
the difference between a sand wedge and a driver.
david_...@my-deja.com
<Pine.LNX.4.21.00072...@cpw.math.columbia.edu>,
Strange but true. Your confusion shows you simply haven't
been paying attention: the amount of interaction he wants with
me is "none. But not EXACTLY".
> I'm not sure whence comes your proctological diagnosis but I
think
> most people would admit that your initial insistence that people here
were
> unable to interpret 3x^2 correctly is taking a far bigger liberty and
> is much more insulting than anything that David might have said- not
that
> it seems that he said anything insulting at all. To assume this is
really
> extraordinary- you might as well go and tell Tiger Woods he doesn't
know
> the difference between a sand wedge and a driver.
Pax
>
>It seems to me that you do want to interact with David C.
Ullrich after
I think
>most people would admit that your initial insistence that
people here were
>unable to interpret 3x^2 correctly is taking a far bigger
liberty and
>is much more insulting than anything that David might have said-
not that
>it seems that he said anything insulting at all. To assume this
is really
>extraordinary- you might as well go and tell Tiger Woods he
doesn't know
>the difference between a sand wedge and a driver.
You guys are really unbelieveable. :) You build your own case,
construct all the evidence yourselves, then judge me and hang me
without further adieu. I'm fine with it, but I'm beginning to
feel rather sorry for all of you of like mind. Do you feel so
badly about yourselves that you must come on UseNet and attack
someone else in order to say, "Well, at least I'm better than
THAT guy!"
Exactly when did I say those here with greater math knowledge
than me (which includes almost everybody) didn't know what they
were talking about re 3x^2? My whole entrance into this thread
was with the stated assumption that I was doing it wrong, but
had accidentally, while doing it the wrong way, discovered
something I thought was interesting. Is it too hard for you to
believe that someone would sully your ivied NG with nothing more
than a pleasant comment meant to have no weight?
As TO my method, the only reason I showed it was to show the
results at the bottom of it, since everyone who knew the correct
way couldn't even visualize how I might have come to it
(understandable, since I forgot the exponent order of operation
after 35 years of non-use). It never crossed my mind it was the
proper way to do the equation... (except as fleeting hope I
wasn't as clueless as I seemed to myself to have become re
Algebra over the years). I've stated that time and time
again... but it makes no difference to you or anyone else, does
it? When I'm totally wrong, how much more wrong can I get?
So when is Ullrich's Mathematician of the Year party? Are you
having him bronzed?
Regards - Pax
Pax
>> It seems to me that you do want to interact with David C.
Ullrich
>after
>> all.
>
>been paying attention: the amount of interaction he wants with
>me is "none. But not EXACTLY".
You know, David dear, you and your friend are absolutely right!
The truth is out, so I might as well come clean and admit it! I
dream of you at night, and secretly long to have your children.
Ahhhh...(sigh)... a plethora of pedantic little pompous asses
pontificating at my feet! The JOY!!
So, let's become great friends. :) :) I'll tell you all my
deepest, darkest math stupidities, and you can preen and prance
about as you tell me just how amazingly brainless I truly am.
Why, this relationship could last FOREVER, given the infinite
depth of my stupidity and your infinite capacity for
supercilious solipsism.
Pax
><pax1NO...@whitesweb.com.invalid> wrote:
>
>>
>[...]
>>
>>
>
>Whether you believe it or not. Not because
>anyone says so, because we can _prove_
>it. At various points in all this you've explained
>you didn't follow this part of the argument
>and that part was too hard for you. There's
>nothing wrong with that. But given that it's
>extremely curious how you can continue
>to insist that the proofs are wrong.
>
>>>various objections, but the algebraic
>>>manipulations are just fine. (The nature
>>>of the valid objections would be that the
>>>proof assumes that you understand - in
>>>great detail - just how to operate with
>>>nonterminating decimal representations.
>>>But anyone who _has_ that understanding
>>>already *knows* why 0.9999... = 1, so
>>>the above proof sort of misses the point.)
>>
>>
>>But IS the algebraic manipulation valid? What if x equaled
0.99
>>(9x=8.91), 0.44 (9x=3.96), 0.11 (9x=0.99), etc.? That's the
>>whole argument that brought me here in the first place. :) If
>>it can't work with finite decimals, why is it valid when
>>infinite decimals are used?
>
>x = 0.99 . They do not show that 0.99 = 1, which is
>good because 0.99 does not equal 1:
>
>x = 0.99
>10x = 9.9
>Subtract:
>9x = 9.9 - 0.99
>9x = 8.91
>Divide by 9:
>x=8.91 / 9
>
>And 8.91/9 = 0.99. The manipulations work just
>fine, and they show that 0.99 = 0.99. (Which is
>not big news.)
>
>>at least not to attempt to prove exactness. The excuse that an
>>infinite constantly fills up the back-end with 9s, so it's
okay,
>>seems rather lame.
>
>up the back-end with 9's so it's ok". That _would_ be pretty
>lame, but that has nothing to do with the proof.
>
>
in it.
- Pax
Pax
><pax1NO...@whitesweb.com.invalid> wrote:
>
>>ull...@math.okstate.edu (David C. Ullrich) wrote:
>>>
>>>
>>>
>>>
>>
>>
>>Could you tell me if you have a natural proclivity for
>>astounding anal retention or if you have acquired your current
>>level through years and years of diligent practice?
>
>polite to you, right? I've been insulting you, right?
That's just the way I am, David dear... completely thankless...
and you so admirably forthcoming all the while.
> (The gentle reader might note that when he
>started complaining about this I asked for an example
>where I'd said anything about _him_, as opposed to
>about his "opinions" on mathematics - he didn't come
>up with any examples. Instead he explained that
>corrections to his statements on mathematics were
>insults to his character. Anyone curious whether
>his staments on mathematics need correcting should
>note that he is _still_ claiming that 0.999... does not
>equal 1 exactly, _today_, in other posts in this
>same thread. (What he actually said today was
>that 9*0.999... does not equal 9 exactly.)
Yes, "he" did.
> And anyone without an "up" button should
>note that _several_ people have stated explicitly
>that they saw nothing insulting in the last post of
>mine at the top of the currect subthread.)
>
Well, of COURSE they didn't, you are always such a pleasant
person! It's obvious I'm totally at fault!
- Pax
Richard Carr
:Date: Thu, 20 Jul 2000 13:45:13 -0700
:From: Pax <pax1NO...@whitesweb.com.invalid>
:Newsgroups: sci.math
:Subject: Re: Which rational x makes 3x^2-7x an integer?
:
:david_...@my-deja.com wrote:
:>> It seems to me that you do want to interact with David C.
:Ullrich
:>after
:>> all.
:>
:> Strange but true. Your confusion shows you simply haven't
:>been paying attention: the amount of interaction he wants with
:>me is "none. But not EXACTLY".
:
:
:You know, David dear, you and your friend are absolutely right!
:The truth is out, so I might as well come clean and admit it! I
:dream of you at night, and secretly long to have your children.
:Ahhhh...(sigh)... a plethora of pedantic little pompous asses
:pontificating at my feet! The JOY!!
It seems to me that that could be a little difficult. If you haven't done
mathematics for 35 years (as indicated in another post) then the chances
are that you are probably at the stage (50+) where meeting with someone on
a newsgroup, having a dislike of them but nonetheless seeking them
out and having a plethora of children with them would take more
time than you have left for that, biologically speaking.
(Also, why on earth would anyone want to bronze someone? It's not like
we're some kind of Auric Goldfinger wannabes. Neither is it insulting to
try to correct someone who insisted (but no longer does, admittedly) that
everyone else didn't know the standard notation/terminology etc. relating
to things they do everyday when you havenot even done the same things for
35 years.)
:
:So, let's become great friends. :) :) I'll tell you all my
:deepest, darkest math stupidities, and you can preen and prance
:about as you tell me just how amazingly brainless I truly am.
:Why, this relationship could last FOREVER, given the infinite
:depth of my stupidity and your infinite capacity for
:supercilious solipsism.
: - Pax
:
:
Pax
>It seems to me that that could be a little difficult. If you
haven't done
>mathematics for 35 years (as indicated in another post) then
the chances
>are that you are probably at the stage (50+) where meeting with
someone on
>a newsgroup, having a dislike of them but nonetheless seeking
them
>out and having a plethora of children with them would take more
>time than you have left for that, biologically speaking.
WOW!! Can't put anything over on YOU, you mathematician you!!
Did you have help, or did you calculate that all by your little
ol' lonesome? I'm 51, actually. Tell me, deary, do you
actually think I meant the above?
>(Also, why on earth would anyone want to bronze someone? It's
not like
>we're some kind of Auric Goldfinger wannabes. Neither is it
insulting to
>try to correct someone who insisted (but no longer does,
admittedly) that
>everyone else didn't know the standard notation/terminology
etc. relating
>to things they do everyday when you havenot even done the same
things for
>35 years.)
>
I forgot ONE order of operation, and I never said... Oh, what's
the use? GET A LIFE!!!
Pax
>(Also, why on earth would anyone want to bronze someone?
One can always hope, can't one?
David C. Ullrich
<pax1NO...@whitesweb.com.invalid> wrote:
[...]
>
>I forgot ONE order of operation,
That's a little incomplete. You forgot ONE order
of operation, and then you spent days insisting that
all the professional mathematicians were wrong.
(And not even wrong about matters of fact - you
spent days insisiting that all the professional
mathematicians were wrong about what the
notation "3x^2" means. For heaven's sake.)
>and I never said... Oh, what's
>the use? GET A LIFE!!!
David C. Ullrich
<pax1NO...@whitesweb.com.invalid> wrote:
>Richard Carr <ca...@cpw.math.columbia.edu> wrote:
>>
>>It seems to me that you do want to interact with David C.
>Ullrich after
>>all. I'm not sure whence comes your proctological diagnosis but
>I think
>>most people would admit that your initial insistence that
>people here were
>>unable to interpret 3x^2 correctly is taking a far bigger
>liberty and
>>is much more insulting than anything that David might have said-
> not that
>>it seems that he said anything insulting at all. To assume this
>is really
>>extraordinary- you might as well go and tell Tiger Woods he
>doesn't know
>>the difference between a sand wedge and a driver.
>
>
>You guys are really unbelieveable. :) You build your own case,
>construct all the evidence yourselves, then judge me and hang me
>without further adieu. I'm fine with it, but I'm beginning to
>feel rather sorry for all of you of like mind. Do you feel so
>badly about yourselves that you must come on UseNet and attack
>someone else in order to say, "Well, at least I'm better than
>THAT guy!"
>
>Exactly when did I say those here with greater math knowledge
>than me (which includes almost everybody) didn't know what they
>were talking about re 3x^2? My whole entrance into this thread
>was with the stated assumption that I was doing it wrong,
Nope. Over and over you simulataneously said you
probably had it wrong yet insisted you had it right. Over and
over several people tell you that 3x^2 means 3*(x^2) and
over and over you say ok, but you were assuming the
standard interpretation, (3*x)^2.
There's actually a clue here why you're
unable to understand why 0.999... = 1, EXACTLY:
You simply do not know what the notation means.
Your replies have consistently indicated you do
not know what the notation means, you've
consistently "rejected" people's explanations
of what it _does_ mean, but when people suggest
that you don't know what "0.999..." means you
don't seem to believe it.
You finally do seem to believe that you
did not have the meaning of "3x^2" straight. And
you also seem to believe that you _do_ need to
know what "3x^2" means before you can say
intelligent things about 3x^2. The same applies
to "0.999...": If you ever _do_ want to understand
why 0.999... _does_ equal 1, EXACTLY, the
first step will be to admit that you really don't
know what "0.999..." means. You need to do
that first - _then_ you can try to get someone
to tell you what it does mean (or you can go
back and try to follow Seaman's repeated
explanations that you "rejected" when you
rejected the notion of equivalence class, or
whatever the heck it was you rejected that
day.
> but
>had accidentally, while doing it the wrong way, discovered
>something I thought was interesting. Is it too hard for you to
>believe that someone would sully your ivied NG with nothing more
>than a pleasant comment meant to have no weight?
>
>As TO my method, the only reason I showed it was to show the
>results at the bottom of it, since everyone who knew the correct
>way couldn't even visualize how I might have come to it
>(understandable, since I forgot the exponent order of operation
>after 35 years of non-use). It never crossed my mind it was the
>proper way to do the equation... (except as fleeting hope I
>wasn't as clueless as I seemed to myself to have become re
>Algebra over the years). I've stated that time and time
>again... but it makes no difference to you or anyone else, does
>it? When I'm totally wrong, how much more wrong can I get?
>
>So when is Ullrich's Mathematician of the Year party? Are you
>having him bronzed?
>
>Regards - Pax
David C. Ullrich
<pax1NO...@whitesweb.com.invalid> wrote:
>ull...@math.okstate.edu (David C. Ullrich) wrote:
>>On Thu, 20 Jul 2000 00:20:35 -0700, Pax
>><pax1NO...@whitesweb.com.invalid> wrote:
>>
>>>
>>[...]
>>>
>>>Right, but 9*0.999... isn't 9 exactly. :)
>>>
>>
>> No, 9*0.999... is equal to 9. Exactly.
>>Whether you believe it or not. Not because
>>anyone says so, because we can _prove_
>>it. At various points in all this you've explained
>>you didn't follow this part of the argument
>>and that part was too hard for you. There's
>>nothing wrong with that. But given that it's
>>extremely curious how you can continue
>>to insist that the proofs are wrong.
>>
>>>>Well, as a proof, that's open to
>>>>various objections, but the algebraic
>>>>manipulations are just fine. (The nature
>>>>of the valid objections would be that the
>>>>proof assumes that you understand - in
>>>>great detail - just how to operate with
>>>>nonterminating decimal representations.
>>>>But anyone who _has_ that understanding
>>>>already *knows* why 0.9999... = 1, so
>>>>the above proof sort of misses the point.)
>>>
>>>
>>>But IS the algebraic manipulation valid? What if x equaled
>0.99
>>>(9x=8.91), 0.44 (9x=3.96), 0.11 (9x=0.99), etc.? That's the
>>>whole argument that brought me here in the first place. :) If
>>>it can't work with finite decimals, why is it valid when
>>>infinite decimals are used?
>>
>> The same manipulations work just fine with
>>x = 0.99 . They do not show that 0.99 = 1, which is
>>good because 0.99 does not equal 1:
>>
>>x = 0.99
>>10x = 9.9
>>Subtract:
>>9x = 9.9 - 0.99
>>9x = 8.91
>>Divide by 9:
>>x=8.91 / 9
>>
>>And 8.91/9 = 0.99. The manipulations work just
>>fine, and they show that 0.99 = 0.99. (Which is
>>not big news.)
>>
>>>It seems no one would even try to use that method with finites,
>>>at least not to attempt to prove exactness. The excuse that an
>>>infinite constantly fills up the back-end with 9s, so it's
>okay,
>>>seems rather lame.
>>
>> But nobody here has said "inifinite constantly fills
>>up the back-end with 9's so it's ok". That _would_ be pretty
>>lame, but that has nothing to do with the proof.
>>
>>
>Thank you, THANK YOU!!! My life is now complete since you are
>in it.
> - Pax
I don't know where you got the idea that other people
enjoyed this any more than you did. This is sci.math. That
means when you say something untrue people are going to
say that what you said was untrue. That's an important
aspect of sci.math - if the nonsense goes unchallenged
then clueless readers will get wrong ideas. (People
sometimes say that we shouldn't worry about this
since nobody could possibly be misled. That may be
so in totally wacko cases - it's not that important to
point out that the universe is not a plutonium atom.
But there are plenty of people out there who _do_
have lots of wrong ideas about things like whether
0.999... = 1.)
If you want people to stop saying your wrong
you should stop posting nonsense. If you want
people to stop being so nasty you need a reality
check - nobody's been anything like as nasty to you
as you've been to them. If you want people to
_become_ extremely nasty, well never mind, you
obviously don't need any advice on how to
accomplish that.
Lee Rudolph
>You finally do seem to believe that you
>did not have the meaning of "3x^2" straight. And
>you also seem to believe that you _do_ need to
>know what "3x^2" means before you can say
>intelligent things about 3x^2. The same applies
>to "0.999...": If you ever _do_ want to understand
>why 0.999... _does_ equal 1, EXACTLY, the
>first step will be to admit that you really don't
>know what "0.999..." means. You need to do
>that first - _then_ you can try to get someone
>to tell you what it does mean
I dunno, Dave, this language sounds to me like you're suggesting
he get into one of those 11.999...-step programs. But if he can't
even handle 3x^2, how in the *world* will he deal with a Higher
Power?
Lee Rudolph (just a friend of Bourbaki)
david_...@my-deja.com
lrud...@panix.com (Lee Rudolph) wrote:
> ull...@math.okstate.edu (David C. Ullrich) writes:
>
> >You finally do seem to believe that you
> >did not have the meaning of "3x^2" straight. And
> >you also seem to believe that you _do_ need to
> >know what "3x^2" means before you can say
> >intelligent things about 3x^2. The same applies
> >to "0.999...": If you ever _do_ want to understand
> >why 0.999... _does_ equal 1, EXACTLY, the
> >first step will be to admit that you really don't
> >know what "0.999..." means. You need to do
> >that first - _then_ you can try to get someone
> >to tell you what it does mean
>
> I dunno, Dave, this language sounds to me like you're suggesting
> he get into one of those 11.999...-step programs.
Exactly.
> But if he can't
> even handle 3x^2, how in the *world* will he deal with a Higher
> Power?
>
> Lee Rudolph (just a friend of Bourbaki)
>
Richard Carr
:Date: Thu, 20 Jul 2000 20:08:33 -0700
:From: Pax <pax1NO...@whitesweb.com.invalid>
:Newsgroups: sci.math
:Subject: Re: Which rational x makes 3x^2-7x an integer?
:
:Richard Carr <ca...@cpw.math.columbia.edu> wrote:
:>It seems to me that that could be a little difficult. If you
:haven't done
:>mathematics for 35 years (as indicated in another post) then
:the chances
:>are that you are probably at the stage (50+) where meeting with
:someone on
:>a newsgroup, having a dislike of them but nonetheless seeking
:them
:>out and having a plethora of children with them would take more
:>time than you have left for that, biologically speaking.
:
:
:WOW!! Can't put anything over on YOU, you mathematician you!!
Actually, I'm not a mathematician.
:Did you have help, or did you calculate that all by your little
:ol' lonesome?
I did calculate it all by myself. It wasn't so hard. All I needed was some
addition. I made two hypotheses: a) you probably left school at 15+ and
b) I could add 15 to 35 correctly. Since hypothesis a) was not completely
certain I added the word probably.
:I'm 51, actually. Tell me, deary, do you
:actually think I meant the above?
It sounded like you wanted a plethora of children with David C. Ullrich.
:
:
:>(Also, why on earth would anyone want to bronze someone? It's
:not like
:>we're some kind of Auric Goldfinger wannabes. Neither is it
:insulting to
:>try to correct someone who insisted (but no longer does,
:admittedly) that
:>everyone else didn't know the standard notation/terminology
:etc. relating
:>to things they do everyday when you havenot even done the same
:things for
:>35 years.)
:>
:
:I forgot ONE order of operation, and I never said... Oh, what's
You also insisted a number of times that many other people didn't know the
standard interpretation of that notation- people who use it daily. That is
the big problem here- not that you forgot what it meant but that you
insisted that everybody else didn't know what it meant even
(initially) after they had told you what it did (in fact) mean.
There's no shame in making mistakes, but to insist that everybody else is
making the mistake in that situation was a bit too much (and yes, I know
you have since retracted). Also, if nobody had pointed it out, PL might
have had a page on you now, cataloguing you mathematical error.
:the use? GET A LIFE!!!
If I didn't have one, I couldn't be typing this, now could I?
: - Pax
:
:
:
:---
:
:The purpose of Light is to fill the darkness and travel on;
:
:
Ed Hook
Pax <pax1NO...@whitesweb.com.invalid> writes:
|>
|> ho...@nas.nasa.gov (Ed Hook) wrote:
|> >Pax <pax1NO...@whitesweb.com.invalid> writes:
<* major snippage *>
|> [ALERT!! ALERT!! BELOW CONTAINS WRONGNESS!! TAKE ALL NECESSARY
|> PRECAUTIONS!! SHIELD SENSITIVE NETHER REGIONS IMMEDIATELY!!
|> ULLRICH, THIS MEANS YOU!!]
|> WRONGNESS: My problem is I'm too used to thinking of the
|> variable as the end-all-and-be-all of the equation, with the
|> other numbers that interact with x being nothing more than
|> operators for the variable, important as counters, but ONLY as
|> counters, when they're nailed into the equation and not
|> variables themselves. So, to me, 3x was actually the product of
|> the operation 3*x. (Believe it or not, the majority of people
|> I've asked who did plenty okay in high school Algebra but
|> haven't used it since, look at it that same way... so it's a
|> common misconception.)
... which could lead us into a discussion of
innumeracy in everyday life. But that's a
different thread ...
|> Let me try to explain the simple way I was looking at it that
|> got me to the wrong... oh, really, really wrong... OH!! WRONG!!
|> OH, BOY, OH, BOY!!! OH, REALLY!!! NO KIDDING!!! Was it
|> REALLY, REALLY WRONG!!! (The execution is Tuesday)... answer
|> that started all of this:
|>
|> WRONGNESS: If x=1 ball, 3x=a bag of 3 balls... that's what I
|> meant by "tied"... you would have to tear open the bag to do
|> something to one ball by itself, so you'd be left with a bag of
|> 2 balls and a single ball doing whatever. 3x means the same as
|> x+x+x. Looking at it that way, if you square one x, you'd have
|> to do the same operation to each x to come out with the correct
|> answer.
OK. But (as you say) that's wrong. It
turns out to be _much_ more useful to
think of these things in the way that
I've been indicating. (That increased
usefulness is _why_ the approach that
everyone has been recommending to you
has _become_ the "standard" way of
thinking about this stuff.)
Your description ("colorful" though
it is) is too vague to serve us in the
real world. For instance, our old
nemesis "3x^2" has _two_ operations
adorning that 'x' -- just exactly how
do you determine that you should put
3 'x's in your bag and only then apply
the squaring operation ? Why not put
3 'x^2's in the bag ?? And just exactly
how is one to interpret a bag (whether
filled with 'x's or 'x^2's) as a real
number ??? Do I add together all of the
things that I find in the bag ? Why
wouldn't I _multiply_ them instead ??
I guess my point is that _our_ way of
handling these things is a _whole_ lot
simpler (and more useful) than yours.
So (if you care about doing these things
correctly) you might want to look into
learning the few simple rules that
determine how things are done. (Of
course, in other posts, you've indicated
that you're *almost* as old as I am ...
so you might not want to bother -- but,
if you've got some time on your hands, it
would be a worthwhile thing to do :-)
|> SAFE ZONE: But what you're saying is that the correct way is to
|> separate the x from its 3 operator and don't consider the 3
|> again until you square the x, then you bring the 3 into
|> consideration and multiply the product of x^2 by it. So, before
|> the balls are ever bagged, you blow them up, paint them red,
|> whatever (the ^2), THEN you bag them 3 to a bag. That's
|> logical, since the exponent operation (^2) is an earlier
|> operation performed on x than the later multiplication by 3.
|> What the 3 is saying is that we have 3 of this particular brand
|> of x, and that brand was determined by x^2. :)
I was hopeful there for a moment. :-)
OK - yeah - that's kinda the idea. The
precedence rules that I stated before
tell you something like that (if you really
_need_ this bag concept to make progress),
so they serve to disambiguate what is
otherwise your very mushily-defined process.
|> >|> Both 3 and 7 are counters of x. They are not real numbers,
|> >Sure they are ...
|> Even in frequency times wavelength equals light speed, the
|> frequency is only a counter for the actual waves represented by
|> wavelength... (which doesn't mean frequency is unimportant).
Well, we're doing _mathematics_ here ...
which is a very different thing than doing
_physics_. So, in the expression "3x^2", it's
just as reasonable to think of "x^2" as the
coefficient of "3" as it is to think of "3"
as the coefficient of "x^2".
|> > '3' and '7' are certainly
|> >real numbers (of the integer sort) and
|> >they appear as coefficients in the
|> >expression -- but they're on an _equal_
|> >footing with 'x^2' and 'x' in there.
|> "_equal_ footing"? I understand equal footing with the "^2",
|> but equal footing with the x? Even when you do 3*4 you're going
|> to have one of those that's an actual thing and one of those
|> that's only there to indicate how many of that thing, aren't
|> you? Of course, that doesn't mean "how many" isn't important,
|> but it is just an indicator of the quantity of a real thing
|> under consideration, isn't it?
No. If _I_ write "3*4", both 3 and 4
are numbers of the same sort -- there's
really no distinction between them.
And even if (in my mind) I'm secretly
thinking that one of them is a "counter"
and the other is "a real thing", there's
no way for you to know which is which --
so it's useless to try to interpret
things in terms of that sort of distinction.
After all, 3*4 = 4*3 -- so which is "counter"
and which is "real" ??
|> >|> This is the same argument that was given in my regular NG to
|> >|> justify 0.999... being exactly equal to 1. They set x to
|> >|> 0.999..., then juggled x out of the equation and worked with
|> the
|> >|> multipliers. It scrambled my brains. So I am truly asking...
|> >|> DO you know the rule that justifies a separation of x and
|> its
|> >|> multiplier?
|> >Yes -- the rule(s) for interpreting
|> >arithmetic expressions.
|> I agree. :) The only time it probably comes up is if you assign
|> x. If you're solving for x, it's different, and none of those
|> operations gets done, for the most part. 3(x^2)-7x, (3(x^2)-7x)
|> +7x=7x, 3(x^2)=7x, (3(x^2))/x=(7x)/x, 3x=7, (3x)/3=7/3, x=7/3.
|> Doing it that way, which is only one very simple way, I'm sure
|> (and probably wrong again), you never really get rid of the tied
|> 3x until the very end, when you throw the 3 at the 7, but you
|> never have to worry about "order of operation" with it either.
I'll probably regret this, but ... :-)
You _always_ have to worry about "order
of operations". To take your example (and
assuming, as seems to be commonplace, that
"solving for x" requires that you set the
given expression equal to 0) suppose
3x^2 - 7x = 0.
If we use the _standard_ interpretation,
the steps are
x(3x - 7) = 0
x = 0 or 3x - 7 = 0
------
3x = 7
x = 7/3
-------
so there are two solutions. If we use your
(previous, acknowledged-to-be-wrong) parsing
of the lefthand side, we get instead
(3x)^2 - 7x = 0
9x^2 - 7x = 0
x(9x - 7) = 0
x = 0 or 9x - 7 = 0
-----
9x = 7
x = 7/9
------- ;
again, two solutions ... but not the _same_
two solutions.
|> >I assume that the discussion that first
|> >brought you here was a proof that looked
|> >something like:
|> >Let x = 0.9999... . Then
|> >10x = 9.9999... = 9 + x
|> >so 9x = 9, which implies that x = 1.
|> >Right?
|> Right, but 9*0.999... isn't 9 exactly. :)
Well ... actually ... 9*0.999... _is_ 9 ... *exactly*.
That's because 0.999... _is_ 1 ... *exactly*.
As noted, the above is not a particularly good
proof of this fact - but it's a fact nonetheless.
And there are airtight, ironclad proofs of this
available -- I don't present one, 'cuz I don't
think that you're ready to fight your way through
it ...
|> >Well, as a proof, that's open to
|> >various objections, but the algebraic
|> >manipulations are just fine. (The nature
|> >of the valid objections would be that the
|> >proof assumes that you understand - in
|> >great detail - just how to operate with
|> >nonterminating decimal representations.
|> >But anyone who _has_ that understanding
|> >already *knows* why 0.9999... = 1, so
|> >the above proof sort of misses the point.)
|> But IS the algebraic manipulation valid? What if x equaled 0.99
|> (9x=8.91), 0.44 (9x=3.96), 0.11 (9x=0.99), etc.? That's the
|> whole argument that brought me here in the first place. :) If
|> it can't work with finite decimals, why is it valid when
|> infinite decimals are used?
"It" works just fine with finite decimals,
if by "it" you mean the algebraic manipulation.
But you can't use the above argument to prove
that x = 1 starting from x = 0.99 (or 0.44 or ...).
Is that what you're worried about ?
As I said, to make sense of the given proof,
you have to _first_ understand how to define
the arithmetic operations on real numbers when
they're represented as infinite decimal expansions.
_When_ you arrive at that understanding, the
above will make perfect sense to you. (But, as
noted, the above will *also* strike you as
totally unnecessary.)
|> It seems no one would even try to use that method with finites,
|> at least not to attempt to prove exactness.
To prove "exactness" of *what* ??
Grade-school children worldwide do this
stuff every day -- barring mistakes, they
get _exact_ answers to the problems that
they are set. Any one of them would be
able to show you that 9*0.99 = 8.91 or
that 8.91/9 = 0.99, thus verifying in any
particular case that the manipulations that
trouble you work out just as shown.
I guess that I'm mystified ...
|> The excuse that an
|> infinite constantly fills up the back-end with 9s, so it's okay,
|> seems rather lame.
Yeah ... that *would* be pretty lame.
Did someone here actually say that ??
|> It's rather like the question can you have
|> an infinity of mass within an infinity of space and still have
|> mostly space? It's a head-whacker. :)
|> >That's your opinion and you are, of
|> >course, entitled to it. But what I
|> >said up above is true -- it _is_
|> >generally regarded as a breach of
|> >netiquette to post someone's e-mail.
|> "Etiquette" PLUS "net" equals "netiquette".
Yes, that's the etymology ...
|> The rules of
|> etiquette should apply in both directions on the net, too.
They do. The consensus about posting e-mail
is perfectly symmetrical -- neither party
should do it, unless both consent.
And I didn't notice Matthew Wiener posting
any private communication from _you_ to him ...
|> It's
|> not very good form to kick someone under the table. It's sheer
|> bullyish ignorance to think the person they've kicked has no
|> recourse against any such further action.
Generally speaking, people don't kick one
another under the table on Usenet -- if I
want to beat up on you (or even simply flame
you), I'll post my attempt. If I send you
e-mail, that's generally because I think that
you may be making yourself appear foolish needlessly
... and I'm (really, truly) trying to help
you avoid that. Now, as the recipient of such
a message, you make take umbrage at the suggestion
that you're making a fool of yourself, but still ...
|> >And doing so will not generally win
|> >you any friends -- certainly not among
|> >those who think that observing a few
|> >basic rules might stave off the Imminent
|> >Death of Usenet ("film at 11!") just a
|> >little bit longer ...
|> There's something else that goes along with Usenet (at least in
|> my particular neck of the woods), that is the right NOT to be
|> contacted by private email for no better reason than to bitch me
|> out. Just as phone harassment is a punishable offense, so is
|> such email harassment... at least when it applies to me.
You _really_ might want to rethink your
decision to participate in Usenet then.
By posting, you invite responses -- you
apparently feel that all responses should
be posted, but that's simply _not_ how it
works. I'd be willing to bet that your
news software has both a "Followup" _and_
a "Reply" option for dealing with postings.
And that can save you from a public roasting
if you participate in some of the more
acrimonious threads. (I note that your
ongoing exchanges with David Ullrich are
veering off in that direction ... )
|> It's very simple, if a total stranger contacts me privately and
|> doesn't want it posted, they shouldn't contact me for the sole
|> purpose of bitching at me re something I've said publicly on a
|> NG. If they feel strongly enough about it to comment, they
|> should carve it in stone publicly, otherwise, they should keep
|> it to themselves.
|> However, I must admit that the few emails I've gotten of that
|> sort I usually just delete without replying. Matthew got caught
|> in the backwash of my distaste for Ullrich... but, he didn't say
|> anything embarrassing to himself, in any event, he was only
|> defending Ullrich and (pretty much) calling me an idiot. :)
Erm ... all the more reason _not_ to post
the message. He gave some pretty cogent
reasons for that conclusion, at least as
concerns your exchange(s) with Professor
Ullrich. In your situation, I don't think
that I'd want to *broadcast* something
like that :-)
|> Actually, once again, I've had no problem with ANY of the
|> respondents except for Ullrich. I truly don't mind being
|> corrected, neither do I mind being wrong. Everyone's usually
|> wrong first before they get it right sometime or other. With
|> all the things I'm interested in, I hit Dead Wrong full blast
|> LOTS of times... but I hit it because I want to find out what's
|> right. I always have the option of forgetting about it. If I
|> choose not to exercise that option, I've got to be able to live
|> with the very real probability of being wrong yet again until I
|> know better. :)
That seems like the right sort of attitude.
Putting it into practice can be difficult
at times, though. (Particularly if you
misapprehend the local culture upon first
arriving in a strange territory ... such as
'sci.math'. We can sometimes appear a bit
curt ... .)
In deference to your blood pressure, you
might want to investigate whatever killfile
mechanism you have available to you -- the
way things are going, you're launched upon
an unfortunate downward spiral ...
Pax
><pax1NO...@whitesweb.com.invalid> wrote:
>
>[...]
>>
>>I forgot ONE order of operation,
>
>of operation, and then you spent days insisting that
>all the professional mathematicians were wrong.
>(And not even wrong about matters of fact - you
>spent days insisiting that all the professional
>mathematicians were wrong about what the
>notation "3x^2" means. For heaven's sake.)
>
Today is the 21st...
On the 16th I made the stupid mistake of replying to this thread
with a short paragraph not meant to be anything of signifigance.
On the 17th I told Hans I thought I had a bracketing problem,
and asked him for the correct bracketing. In the same post I
asked Doug where his idea re "9x" came from since, at the time,
I couldn't figure it out (have now). Ending the post with:
"So, whatever you're talking about... guess it's over my head if
it's past my simple interpretation of the original equation
under question, which is:
((3x)^2) - (7x) = y
but I assumed that it was probably over my head when I
replied. :)"
On the 18th I told you in words to the effect that you were an
asshole... I did not question your advice, however. In another
post on the same day, I told Wiener I thought I was right,
according to a website (I had misread), to which I posted the
link. Then, in another post that same day, I told Clyde:
"I NEVER said I was doing it properly, all I had the misfortune
of doing in my credulous simplicity was showing what in-my-head
algebra came up with when I first looked at the problem, working
it simply from left to right, as standard Algebra dictates. It
never crossed my mind that what I saw was the proper way to work
the problem. ALL I was doing was showing something interesting
(to me) I happened to notice."
Again, you will see that I am still deep in my misconception,
and it is still the 18th. On the heels of the above post,
Wiener sent me another email, to which I replied on the NG:
"[Pax(quote from NG post)]
What he calls the "standard interpretation" is NOT the standard
algebraic interpretation.
[Matthew P Wiener]
Yes, it is. 3x^2 is 3*x*x. There is no other interpretation.
[Pax]
You are correct and I stand very corrected. My apologies."
I also included a link to the proper order of operation. This
is STILL the 18th. On this same day I also answered a kind post
from Lynn Killingbeck, who understood my bracketing problem.
So, what's this "spent days insisiting that all the professional
mathematicians were wrong" stuff? I had one day of actual
contentious confusion with Wiener, who is not a professional
mathematician (but that doesn't make him wrong). I HAVE "spent
days" apologizing... and calling you an asshole... at least I
enjoyed the last part.
Pax
[Cut because I don't care]
I'm starting the think you're certifiable.
Richard Carr
:Date: Fri, 21 Jul 2000 12:11:01 -0700
:From: Pax <pax1NO...@whitesweb.com.invalid>
:Newsgroups: sci.math
:Subject: Re: Which rational x makes 3x^2-7x an integer?
:
:ull...@math.okstate.edu (David C. Ullrich) wrote:
:>On Thu, 20 Jul 2000 20:08:33 -0700, Pax
You probably won't find it advantageous to call him such if you want to
have a plethora of his children.
: - Pax
:
:
Pax
>enjoyed this any more than you did. This is sci.math. That
>means when you say something untrue people are going to
>say that what you said was untrue. That's an important
>aspect of sci.math - if the nonsense goes unchallenged
>then clueless readers will get wrong ideas.
It was one SHORT post that didn't even say anything about the
way I did it past designating x as 1, then x=x+1. How is that
wrong? You guys are the ones who have stirred it up into the
rampant stupidity it has become. True I was very wrong as to my
order of operation, but my original statement said I was no
mathematician. It was a light-hearted post, meant for nothing
else.
As far as I'm concerned, I came away with a burned-in knowledge
of the proper order of operation, so I'm happy. If you're not
happy, well, that makes me even happier.
Oh, and by the way, you're an asshole.
- Pax
Pax
>I dunno, Dave, this language sounds to me like you're suggesting
can't
>even handle 3x^2, how in the *world* will he deal with a Higher
>Power?
>
>Lee Rudolph (just a friend of Bourbaki)
>
>
equation that lemma posted?
Richard Carr
:Date: Fri, 21 Jul 2000 12:30:02 -0700
:From: Pax <pax1NO...@whitesweb.com.invalid>
:Newsgroups: sci.math
:Subject: Re: Which rational x makes 3x^2-7x an integer?
:
:lrud...@panix.com (Lee Rudolph) wrote:
:>I dunno, Dave, this language sounds to me like you're suggesting
:>he get into one of those 11.999...-step programs. But if he
:can't
:>even handle 3x^2, how in the *world* will he deal with a Higher
:>Power?
:>
:>Lee Rudolph (just a friend of Bourbaki)
:>
:>
:Is almost no one interested in solving correctly the original
:equation that lemma posted?
It was solved- by several people.
: - Pax
:
:
Pax
>You probably won't find it advantageous to call him such if you
want to
>have a plethora of his children.
:) :) :) :)
Sweetheart, your literal interpretation is delightful! Unless
God wants to start a whole new people to claim as His own with
another miracle of birth, that's not going to happen... for
reasons too numerous to mention.
Kind regards - Pax
Richard Carr
:Date: Fri, 21 Jul 2000 13:02:39 -0700
:From: Pax <pax1NO...@whitesweb.com.invalid>
:Newsgroups: sci.math
:Subject: Re: Which rational x makes 3x^2-7x an integer?
:
:Richard Carr <ca...@cpw.math.columbia.edu> wrote:
:>You probably won't find it advantageous to call him such if you
:want to
:>have a plethora of his children.
:
:
::) :) :) :)
:
:Sweetheart,
That's extraordinary fickle. This is the sort of thins you should be
saying to David, not to me.
:your literal interpretation is delightful! Unless
:God wants to start a whole new people to claim as His own with
:another miracle of birth, that's not going to happen... for
:reasons too numerous to mention.
So let me get this clear- you're trying to tell me you don't want David's
children after all????
:
:Kind regards - Pax
:
:
Pax
>On Thu, 20 Jul 2000, Pax wrote:
>:WOW!! Can't put anything over on YOU, you mathematician you!!
>
>Actually, I'm not a mathematician.
:) :) :)
>:Did you have help, or did you calculate that all by your little
>:ol' lonesome?
>I did calculate it all by myself. It wasn't so hard. All I
needed was some
>addition. I made two hypotheses: a) you probably left school at
15+ and
>b) I could add 15 to 35 correctly. Since hypothesis a) was not
completely
>certain I added the word probably.
No, hypothesis a) is incorrect, actually. I graduated high
school, even went to college. :) :) Art major. Commercial
artist. Art teacher. Wasn't allowed to take anything higher
than Algebra II in high school because I was female, the small-
town school I attended wouldn't let anyone but males continue
their math education past that level.
>:I'm 51, actually. Tell me, deary, do you
>:actually think I meant the above?
>
>It sounded like you wanted a plethora of children with David C.
Ullrich.
Ooooookay. :) :) :)
>:I forgot ONE order of operation, and I never said... Oh, what's
>
>You also insisted a number of times that many other people
didn't know the
>standard interpretation of that notation- people who use it
daily. That is
>the big problem here- not that you forgot what it meant but
that you
>insisted that everybody else didn't know what it meant even
>(initially) after they had told you what it did (in fact) mean.
No, actually, I didn't. I got rankled at Wiener, that's the
only time I insisted I was doing it properly... but immediately
after that, I retracted my statement, saying that I was wrong,
with an apology.
>There's no shame in making mistakes, but to insist that
everybody else is
>making the mistake in that situation was a bit too much (and
yes, I know
>you have since retracted). Also, if nobody had pointed it out,
PL might
>have had a page on you now, cataloguing you mathematical error.
If nobody had pointed WHAT out? I didn't list any procedure in
my original post, and I asked for proper clarification in my
second and subsequent, showing my bracketed interpretation of
the equation to highlight where I thought the error was.
>:the use? GET A LIFE!!!
>
>If I didn't have one, I couldn't be typing this, now could I?
Yes, you'd just have LOTS and LOTS of time to do it in. :) :) :)
Pax
>On Fri, 21 Jul 2000, Pax wrote:
>::) :) :) :)
>:
>:Sweetheart,
>
should be
>saying to David, not to me.
HAHAHAHAHAHAH!!!! :) :) :) :)
>:your literal interpretation is delightful! Unless
>:God wants to start a whole new people to claim as His own with
>:another miracle of birth, that's not going to happen... for
>:reasons too numerous to mention.
>
>So let me get this clear- you're trying to tell me you don't
want David's
>children after all????
>
HAHAHAHAHAHAH!!!! :) :) :) :)
Yes... guess that's exactly what I'm trying to tell you. :) :) :)
Richard Carr
:Date: Fri, 21 Jul 2000 13:21:35 -0700
:From: Pax <pax1NO...@whitesweb.com.invalid>
:Newsgroups: sci.math
:Subject: Re: Which rational x makes 3x^2-7x an integer?
:
:Richard Carr <ca...@cpw.math.columbia.edu> wrote:
:>On Thu, 20 Jul 2000, Pax wrote:
:>:WOW!! Can't put anything over on YOU, you mathematician you!!
:>
:>Actually, I'm not a mathematician.
:
:
::) :) :)
:
I'm serious.
:
:>:Did you have help, or did you calculate that all by your little
:>:ol' lonesome?
:
:
:>I did calculate it all by myself. It wasn't so hard. All I
:needed was some
:>addition. I made two hypotheses: a) you probably left school at
:15+ and
:>b) I could add 15 to 35 correctly. Since hypothesis a) was not
:completely
:>certain I added the word probably.
:
:
:No, hypothesis a) is incorrect, actually. I graduated high
:school, even went to college. :) :) Art major. Commercial
You did all this before 15? (ast 15+ meaning at >=15).
David C. Ullrich
<pax1NO...@whitesweb.com.invalid> wrote:
>ull...@math.okstate.edu (David C. Ullrich) wrote:
>> I don't know where you got the idea that other people
>>enjoyed this any more than you did. This is sci.math. That
>>means when you say something untrue people are going to
>>say that what you said was untrue. That's an important
>>aspect of sci.math - if the nonsense goes unchallenged
>>then clueless readers will get wrong ideas.
>
>It was one SHORT post that didn't even say anything about the
>way I did it past designating x as 1, then x=x+1. How is that
>wrong? You guys are the ones who have stirred it up into the
>rampant stupidity it has become. True I was very wrong as to my
>order of operation, but my original statement said I was no
>mathematician.
You're assuming nobody has an Up button. It's
clear from the omitted context that the bit of nonsense I
was alluding to was the stuff about how 0.999... is not
equal to 1 EXACTLY. You were still saying that on the
20th.
Don't bother with the long list of citations where
you say you're probably wrong. They're just as incomplete
as the bit above: what you've been saying over and over
is you're probably wrong, but you're right.
>It was a light-hearted post, meant for nothing
>else.
Then why spend so much... never mind.
>As far as I'm concerned, I came away with a burned-in knowledge
>of the proper order of operation, so I'm happy. If you're not
>happy, well, that makes me even happier.
>
>Oh, and by the way, you're an asshole.
> - Pax
And elsewhere you _say_ that oh btw you enjoyed
saying that just now. But you're still complaining about me
being insulting, right?
Richard Carr
:Date: Fri, 21 Jul 2000 17:10:54 -0400
:From: Richard Carr <ca...@cpw.math.columbia.edu>
:Newsgroups: sci.math
:Subject: Re: Which rational x makes 3x^2-7x an integer?
:
That should be "at" not "ast".
:
:
:
Pax
>On Fri, 21 Jul 2000, Pax wrote:
>
>:>Actually, I'm not a mathematician.
>:
>:
>::) :) :)
>:
>
>I'm serious.
And I'm certain you are serious. :) :)
>:>I did calculate it all by myself. It wasn't so hard. All I
>:needed was some
>:>addition. I made two hypotheses: a) you probably left school
at
>:15+ and
>:>b) I could add 15 to 35 correctly. Since hypothesis a) was not
>:completely
>:>certain I added the word probably.
>:
>:
>:No, hypothesis a) is incorrect, actually. I graduated high
>:school, even went to college. :) :) Art major.
>
>You did all this before 15? (at 15+ meaning at >=15).
I stand corrected. :) :)
Kind regards - Pax
---
David C. Ullrich
on Fri, 21 Jul 2000 12:14:02 -0700, Pax
<pax1NO...@whitesweb.com.invalid> wrote:
>ull...@math.okstate.edu (David C. Ullrich) wrote:
>
>
>[Cut because I don't care]
>
>
>I'm starting the think you're certifiable.
> - Pax
Hard to decide which of the two I find
more devastating. (I'll let you know if I decide.)
I do think it's a wise choice to snip
everything I say, btw: Your objections make
much more sense than they do when you
actually try to say something about something
someone said.
Pax
><pax1NO...@whitesweb.com.invalid> wrote:
>
>>It was one SHORT post that didn't even say anything about the
>>way I did it past designating x as 1, then x=x+1. How is that
>>wrong? You guys are the ones who have stirred it up into the
>>rampant stupidity it has become. True I was very wrong as to
my
>>order of operation, but my original statement said I was no
>>mathematician.
>
> You're assuming nobody has an Up button. It's
>clear from the omitted context that the bit of nonsense I
>was alluding to was the stuff about how 0.999... is not
>equal to 1 EXACTLY. You were still saying that on the
>20th.
The "Zeno" thread is down, alphabetically, from this one. I
still hold the same opinion re 0.999..., but what difference
does
0.0000000000000000000000000000000000000000000000000000000..."To
infinity and beyond!!"...1 make?
> Don't bother with the long list of citations where
>you say you're probably wrong. They're just as incomplete
>as the bit above: what you've been saying over and over
>is you're probably wrong, but you're right.
About 0.999...? Yes. I still think I am in the context I was
speaking. Could you tell me what part of the world hangs in the
balance? I would like to divest myself of it.
>>It was a light-hearted post, meant for nothing
>>else.
>
> Then why spend so much... never mind.
Never mind, indeed!
>>As far as I'm concerned, I came away with a burned-in knowledge
>>of the proper order of operation, so I'm happy. If you're not
>>happy, well, that makes me even happier.
>>
>>Oh, and by the way, you're an asshole.
>> - Pax
>
> And elsewhere you _say_ that oh btw you enjoyed
>saying that just now. But you're still complaining about me
>being insulting, right?
>
No. Haven't complained about that for ages. The "by the way"
was to be sure you didn't miss it.
- Pax
Pax
>on Fri, 21 Jul 2000 12:14:02 -0700, Pax
><pax1NO...@whitesweb.com.invalid> wrote:
>
>>
>>
>>I'm starting the think you're certifiable.
>> - Pax
>
> Hard to decide which of the two I find
>more devastating. (I'll let you know if I decide.)
Oh, I'm positive you will!
> I do think it's a wise choice to snip
>everything I say, btw: Your objections make
>much more sense than they do when you
>actually try to say something about something
>someone said.
Well of course you don't think it's a wise choice, as in love
with yourself as you are. I, however, don't have that
particular problem where you're concerned. I snip what you say
because I don't like you. That infamous, aforementioned "UP"
button can suffice for those who care.
Pax
news:8l9qsd$hr2$1...@sun500.nas.nasa.gov...
> In article <0360ef9c...@usw-ex0103-024.remarq.com>,
> Pax <pax1NO...@whitesweb.com.invalid> writes:
> |>
> |> ho...@nas.nasa.gov (Ed Hook) wrote:
> |> >Pax <pax1NO...@whitesweb.com.invalid> writes:
>
> <* major snippage *>
>
> innumeracy in everyday life. But that's a
> different thread ...
Agreed. :)
Have just gotten a whole lot of materials to do just that. :)
> |> SAFE ZONE: But what you're saying is that the correct way is to
> |> separate the x from its 3 operator and don't consider the 3
> |> again until you square the x, then you bring the 3 into
> |> consideration and multiply the product of x^2 by it. So, before
> |> the balls are ever bagged, you blow them up, paint them red,
> |> whatever (the ^2), THEN you bag them 3 to a bag. That's
> |> logical, since the exponent operation (^2) is an earlier
> |> operation performed on x than the later multiplication by 3.
> |> What the 3 is saying is that we have 3 of this particular brand
> |> of x, and that brand was determined by x^2. :)
>
> I was hopeful there for a moment. :-)
Guess I over analogized... sorry. :)
> OK - yeah - that's kinda the idea. The
> precedence rules that I stated before
> tell you something like that (if you really
> _need_ this bag concept to make progress),
Nope. Don't need it. :)
> so they serve to disambiguate what is
> otherwise your very mushily-defined process.
1) Parenthesis/brackets, innermost first (exponents inside parenthesis/brackets
first operation within parenthesis/brackets). 2) Exponents (outside
parenthesis/brackets). 3) Multiplication/division. 4) Addition/subtraction. 5)
If you do something balancing to one side, do it to the other.
> |> Even in frequency times wavelength equals light speed, the
> |> frequency is only a counter for the actual waves represented by
> |> wavelength... (which doesn't mean frequency is unimportant).
>
> Well, we're doing _mathematics_ here ...
> which is a very different thing than doing
> _physics_. So, in the expression "3x^2", it's
> just as reasonable to think of "x^2" as the
> coefficient of "3" as it is to think of "3"
> as the coefficient of "x^2".
"Pure" numbers. Got it. :)
> |> Of course, that doesn't mean "how many" isn't important,
> |> but it is just an indicator of the quantity of a real thing
> |> under consideration, isn't it?
>
> No. If _I_ write "3*4", both 3 and 4
> are numbers of the same sort -- there's
> really no distinction between them.
> And even if (in my mind) I'm secretly
> thinking that one of them is a "counter"
> and the other is "a real thing", there's
> no way for you to know which is which --
> so it's useless to try to interpret
> things in terms of that sort of distinction.
> After all, 3*4 = 4*3 -- so which is "counter"
> and which is "real" ??
I understand. :)
> |> >Yes -- the rule(s) for interpreting
> |> >arithmetic expressions.
>
>
> |> I agree. :) The only time it probably comes up is if you assign
> |> x. If you're solving for x, it's different, and none of those
> |> operations gets done, for the most part. 3(x^2)-7x, (3(x^2)-7x)
> |> +7x=7x, 3(x^2)=7x, (3(x^2))/x=(7x)/x, 3x=7, (3x)/3=7/3, x=7/3.
> |> Doing it that way, which is only one very simple way, I'm sure
> |> (and probably wrong again), you never really get rid of the tied
> |> 3x until the very end, when you throw the 3 at the 7, but you
> |> never have to worry about "order of operation" with it either.
>
> I'll probably regret this, but ... :-)
Why is everyone so certain the only reason I'm here is to argue my position?
Does no one who doesn't know come here to learn from those who do? I came here
to find something out, Dave Seaman was kind enough to enlighten me. I
accidentally stumbled into this, and have relearned something I really needed to
remember, which is nothing but a plus. :)
> You _always_ have to worry about "order
> of operations". To take your example (and
> assuming, as seems to be commonplace, that
> "solving for x" requires that you set the
> given expression equal to 0)
See... I'd forgotten that little specific, too, simple and logical as it is.
Just worked it without an "=" until I needed to put one. "=0" gives the
equation a whole new flavor in my mind.
> suppose
>
> 3x^2 - 7x = 0.
>
> If we use the _standard_ interpretation,
> the steps are
>
> x(3x - 7) = 0
>
> x = 0 or 3x - 7 = 0
> ------
> 3x = 7
>
> x = 7/3
> -------
(7/3)*((3*(7/3))-7)=0, (7/3)*((21/3)-7)=0, (7/3)*(7-7)=0, (7/3)*0=0!! :) :) :)
But still having all kinds of trouble when I plug 7/3 in as x in 3x^2-7x. Don't
worry about it, though, I'll get it eventually. :)
> so there are two solutions. If we use your
> (previous, acknowledged-to-be-wrong) parsing
> of the lefthand side, we get instead
>
> (3x)^2 - 7x = 0
>
> 9x^2 - 7x = 0
>
> x(9x - 7) = 0
>
> x = 0 or 9x - 7 = 0
> -----
> 9x = 7
>
> x = 7/9
> ------- ;
>
> again, two solutions ... but not the _same_
> two solutions.
Obviously. :)
> |> >I assume that the discussion that first
> |> >brought you here was a proof that looked
> |> >something like:
>
> |> >Let x = 0.9999... . Then
>
> |> >10x = 9.9999... = 9 + x
>
> |> >so 9x = 9, which implies that x = 1.
> |> >Right?
>
>
> |> Right, but 9*0.999... isn't 9 exactly. :)
>
> Well ... actually ... 9*0.999... _is_ 9 ... *exactly*.
> That's because 0.999... _is_ 1 ... *exactly*.
> As noted, the above is not a particularly good
> proof of this fact - but it's a fact nonetheless.
> And there are airtight, ironclad proofs of this
> available -- I don't present one, 'cuz I don't
> think that you're ready to fight your way through
> it ...
Truth is, I don't think it matters a hill of beans what I think and, right now,
it's not important. Probably would get lost anyway. :) I REALLY don't care to
get that started up again, either... Dave Seaman explained it to my
satisfaction.
> |> But IS the algebraic manipulation valid? What if x equaled 0.99
> |> (9x=8.91), 0.44 (9x=3.96), 0.11 (9x=0.99), etc.? That's the
> |> whole argument that brought me here in the first place. :) If
> |> it can't work with finite decimals, why is it valid when
> |> infinite decimals are used?
>
> "It" works just fine with finite decimals,
> if by "it" you mean the algebraic manipulation.
> But you can't use the above argument to prove
> that x = 1 starting from x = 0.99 (or 0.44 or ...).
> Is that what you're worried about ?
Yes.
> As I said, to make sense of the given proof,
> you have to _first_ understand how to define
> the arithmetic operations on real numbers when
> they're represented as infinite decimal expansions.
> _When_ you arrive at that understanding, the
> above will make perfect sense to you. (But, as
> noted, the above will *also* strike you as
> totally unnecessary.)
Modulo 1?
> |> It seems no one would even try to use that method with finites,
> |> at least not to attempt to prove exactness.
>
> To prove "exactness" of *what* ??
>
> Grade-school children worldwide do this
> stuff every day -- barring mistakes, they
> get _exact_ answers to the problems that
> they are set. Any one of them would be
> able to show you that 9*0.99 = 8.91 or
> that 8.91/9 = 0.99, thus verifying in any
> particular case that the manipulations that
> trouble you work out just as shown.
>
> I guess that I'm mystified ...
I really don't want to get into this again, it's like pouring water down a rat
hole, it has no end!
> |> The excuse that an
> |> infinite constantly fills up the back-end with 9s, so it's okay,
> |> seems rather lame.
>
> Yeah ... that *would* be pretty lame.
> Did someone here actually say that ??
Yes, but not here... at least not to my knowledge. :)
> |> The rules of
> |> etiquette should apply in both directions on the net, too.
>
> They do. The consensus about posting e-mail
> is perfectly symmetrical -- neither party
> should do it, unless both consent.
>
> And I didn't notice Matthew Wiener posting
> any private communication from _you_ to him ...
That's not what I meant. What does the phrase "kick someone under the table"
imply to you? Is it a public action, or is it done out-of-sight so that no one
else besides the kicker and the one kicked knows about it?
> |> It's
> |> not very good form to kick someone under the table. It's sheer
> |> bullyish ignorance to think the person they've kicked has no
> |> recourse against any such further action.
>
> Generally speaking, people don't kick one
> another under the table on Usenet -- if I
> want to beat up on you (or even simply flame
> you), I'll post my attempt.
That's what someone OF HONOR would do, yes. :)
> If I send you
> e-mail, that's generally because I think that
> you may be making yourself appear foolish needlessly
> ... and I'm (really, truly) trying to help
> you avoid that. Now, as the recipient of such
> a message, you make take umbrage at the suggestion
> that you're making a fool of yourself, but still ...
I'm certain that's what you would do. :) I was not talking about that.
> |> There's something else that goes along with Usenet (at least in
> |> my particular neck of the woods), that is the right NOT to be
> |> contacted by private email for no better reason than to bitch me
> |> out. Just as phone harassment is a punishable offense, so is
> |> such email harassment... at least when it applies to me.
>
> You _really_ might want to rethink your
> decision to participate in Usenet then.
Do you know there are certain rules that apply to continued usage of ISPs? I
should not have to, in effect, "lock myself in my house and never go out again,"
because someone might not like what I have to say on a NG, and so decides to
launch a brutish private email assault on me.
That's what I meant about netiquette applying in both directions. Or do you
think it's alright if someone sends multiple private hateful emails to a UseNet
poster for no better reason than that they made an uninformed comment on a NG?
UseNet is public, private email is quite another thing.
Friendly private email discussion, begun as a result of such a blunder by a NG
poster, is not initiated for the purpose of continuing harassment no matter how
times the NG poster asks/tells the accoster to desist, and I was not talking
about that.
I'm very interested in your reply.
> By posting, you invite responses -- you
> apparently feel that all responses should
> be posted, but that's simply _not_ how it
> works. I'd be willing to bet that your
> news software has both a "Followup" _and_
> a "Reply" option for dealing with postings.
> And that can save you from a public roasting
> if you participate in some of the more
> acrimonious threads. (I note that your
> ongoing exchanges with David Ullrich are
> veering off in that direction ... )
I don't mind the public debate. I mind being privately harassed.
> |> It's very simple, if a total stranger contacts me privately and
> |> doesn't want it posted, they shouldn't contact me for the sole
> |> purpose of bitching at me re something I've said publicly on a
> |> NG. If they feel strongly enough about it to comment, they
> |> should carve it in stone publicly, otherwise, they should keep
> |> it to themselves.
>
> |> However, I must admit that the few emails I've gotten of that
> |> sort I usually just delete without replying. Matthew got caught
> |> in the backwash of my distaste for Ullrich... but, he didn't say
> |> anything embarrassing to himself, in any event, he was only
> |> defending Ullrich and (pretty much) calling me an idiot. :)
>
> Erm ... all the more reason _not_ to post
> the message. He gave some pretty cogent
> reasons for that conclusion, at least as
> concerns your exchange(s) with Professor
> Ullrich. In your situation, I don't think
> that I'd want to *broadcast* something
> like that :-)
Guess you've got more of an ego than I do, then. I can keep my mouth shut,
never take chances, and be the Dummy In the Corner, or I can stick my neck out
on the chance that it will further whatever goal I have by helping me learn
something. One of the worst fears in the world to live with is the fear you
might be proven wrong at some point, because NONE of us is right all the time.
There's a difference between ignorance and stupidity because, as they say,
ignorance can be cured, stupidity is terminal.
Think about Einstein. Should he have forgotten all about it and become a
mailman because his teachers kept telling him he was not very bright, awful in
math, and a "lazy dog"? He came up with Lambda because he thought the universe
was Steady State, called it his biggest blunder, died thinking it was, but did
it lessen his credibility? Besides that, Lambda is still a real possibility if
what we take as universal expansion turns out to be the wrong interpretation of
the data.
Should Faraday have left electricity alone because he never went to college?
Should Tesla have stopped because no one could really understand much of what he
was doing? Did any of these men do what they were doing because they wanted the
praise of the masses, or did they achieve new heights because they HAD TO KNOW?
When you HAVE TO know, all the people in the world telling you you're stupid
doesn't make much difference, because you're not doing it for them, you're doing
it for yourself.
> |> Actually, once again, I've had no problem with ANY of the
> |> respondents except for Ullrich. I truly don't mind being
> |> corrected, neither do I mind being wrong. Everyone's usually
> |> wrong first before they get it right sometime or other. With
> |> all the things I'm interested in, I hit Dead Wrong full blast
> |> LOTS of times... but I hit it because I want to find out what's
> |> right. I always have the option of forgetting about it. If I
> |> choose not to exercise that option, I've got to be able to live
> |> with the very real probability of being wrong yet again until I
> |> know better. :)
>
> That seems like the right sort of attitude.
> Putting it into practice can be difficult
> at times, though. (Particularly if you
> misapprehend the local culture upon first
> arriving in a strange territory ... such as
> 'sci.math'. We can sometimes appear a bit
> curt ... .)
Just like everywhere else, people are just people... sci.math people included...
some are like Ullrich, some are like you and Dave Seaman. With my Pollyanna
attitude, I tend to believe there are more like you and Dave, even in sci.math,
than there are like Ullrich. :) :)
> In deference to your blood pressure, you
> might want to investigate whatever killfile
> mechanism you have available to you -- the
> way things are going, you're launched upon
> an unfortunate downward spiral ...
Thanks for the kind advice. Know what you mean. :) :) Wish my news service
didn't update slower than Christmas... but I don't have much use for a killfile.
Just as everyone else, I always have the option of not reading posts if I get
truly annoyed. I'm not... yet... really do have fairly thick skin. :) :)
Kind regards - Pax
> --
> Ed Hook | Copula eam, se non posit
> Computer Sciences Corporation | acceptera jocularum.
> NAS, NASA Ames Research Center | All opinions herein expressed are
> Internet: ho...@nas.nasa.gov | mine alone
--
o~O~oo~O~oo~O~oo~O~oo~O~oo~O~oo~O~oo~O~oo~O~oo~O~oo~O~oo~O~o
As Pogo said: "We has met thu enuhmy 'n' he is US!"
Pax
news:Pine.LNX.4.21.000721...@cpw.math.columbia.edu...
> On Fri, 21 Jul 2000, Pax wrote:
>
> :From: Pax <pax1NO...@whitesweb.com.invalid>
> :Newsgroups: sci.math
> :Subject: Re: Which rational x makes 3x^2-7x an integer?
> :
> :>I dunno, Dave, this language sounds to me like you're suggesting
> :>he get into one of those 11.999...-step programs. But if he
> :can't
> :>even handle 3x^2, how in the *world* will he deal with a Higher
> :>Power?
> :>
> :>Lee Rudolph (just a friend of Bourbaki)
> :>
> :>
> :Is almost no one interested in solving correctly the original
> :equation that lemma posted?
>
> It was solved- by several people.
If you'll check this thread, most of the posts have been to "correct" my
mistake. In the NG I call mine, riddles and such are answered by numerous
people, for the sheer fun of it. :)
Kind regards - Pax
o~O~oo~O~oo~O~oo~O~oo~O~oo~O~oo~O~oo~O~oo~O~oo~O~oo~O~oo~O~o
David C. Ullrich
<pax1NO...@whitesweb.com.invalid> wrote:
>ull...@math.okstate.edu (David C. Ullrich) wrote:
>>On Fri, 21 Jul 2000 12:27:08 -0700, Pax
>><pax1NO...@whitesweb.com.invalid> wrote:
>>
>>>It was one SHORT post that didn't even say anything about the
>>>way I did it past designating x as 1, then x=x+1. How is that
>>>wrong? You guys are the ones who have stirred it up into the
>>>rampant stupidity it has become. True I was very wrong as to
>my
>>>order of operation, but my original statement said I was no
>>>mathematician.
>>
>> You're assuming nobody has an Up button. It's
>>clear from the omitted context that the bit of nonsense I
>>was alluding to was the stuff about how 0.999... is not
>>equal to 1 EXACTLY. You were still saying that on the
>>20th.
>
>The "Zeno" thread is down, alphabetically, from this one.
Yes it is. And the post of mine that you conveniently
misquoted said this:
" I don't know where you got the idea that other people
enjoyed this any more than you did. This is sci.math. That
means when you say something untrue people are going to
say that what you said was untrue. That's an important
aspect of sci.math - if the nonsense goes unchallenged
then clueless readers will get wrong ideas. (People
sometimes say that we shouldn't worry about this
since nobody could possibly be misled. That may be
so in totally wacko cases - it's not that important to
point out that the universe is not a plutonium atom.
But there are plenty of people out there who _do_
have lots of wrong ideas about things like whether
0.999... = 1.)"
That's two or three posts up, in this thread.
When you replied to the above you quoted the first
few sentences
" I don't know where you got the idea that other people
enjoyed this any more than you did. This is sci.math. That
means when you say something untrue people are going to
say that what you said was untrue. That's an important
aspect of sci.math - if the nonsense goes unchallenged
then clueless readers will get wrong ideas."
and then replied as though I was referring to the 3x^2
thing. It's extremely clear from what I said that that's
not what I was referring to.
You're either neing intentionally misleading
or showing once again that you don't have a clue
what's even been _said_.
>still hold the same opinion re 0.999..., but what difference
>does
>0.0000000000000000000000000000000000000000000000000000000..."To
>infinity and beyond!!"...1 make?
Nobody has any idea what you mean by that. None of
the people who've tried to explain why 0.999...=1 have said
that '.0..... "To infinifty and beyond!" makes a difference.
Whatever the hell that means.
>> Don't bother with the long list of citations where
>>you say you're probably wrong. They're just as incomplete
>>as the bit above: what you've been saying over and over
>>is you're probably wrong, but you're right.
>
>About 0.999...? Yes. I still think I am in the context I was
>speaking.
You're entitled to think what you want. You
can think the Earth is flat if you wish. You can even
_say_ the Earth is flat. When you do that you should
expect people to say it's round. When people say
that no the Earth is round and explain how they know
you're free to ignore what they say and call them names.
Not going to convince many people you're right acting
that way, but you can act that way if you want.
>Could you tell me what part of the world hangs in the
>balance?
I don't recall anyone saying that any part
of the world hung in the balance.
>I would like to divest myself of it.
>
>>>It was a light-hearted post, meant for nothing
>>>else.
>>
>> Then why spend so much... never mind.
>
>Never mind, indeed!
>
>>>As far as I'm concerned, I came away with a burned-in knowledge
>>>of the proper order of operation, so I'm happy. If you're not
>>>happy, well, that makes me even happier.
>>>
>>>Oh, and by the way, you're an asshole.
>>> - Pax
>>
>> And elsewhere you _say_ that oh btw you enjoyed
>>saying that just now. But you're still complaining about me
>>being insulting, right?
>>
>
>No. Haven't complained about that for ages. The "by the way"
>was to be sure you didn't miss it.
David C. Ullrich
>"Ed Hook" <ho...@nas.nasa.gov> wrote in message
[...]
>
>Why is everyone so certain the only reason I'm here is to argue my position?
>Does no one who doesn't know come here to learn from those who do?
The people who are interested in learning things don't usually
insist they're right and all of sci.math is wrong about grade-school
algebra.
>I came here
>to find something out, Dave Seaman was kind enough to enlighten me.
What in the world does this mean? He tried to enlighten
you about the fact that yes, 0.999... does equal 1, exactly. _Today_
you're still insisting elsewhere in this thread that no 0.999...
does not equal 1. How do you feel he's "enlightened" you?
Do you even _try_ to make sense? A few posts up you're
insisting that 0.999... does not equal 1 (yes, you said you still
think you're right about that). How can you say that and
simultaneously say that Seaman explained "to your
satisfaction" that it _does_ equal 1?
>> |> But IS the algebraic manipulation valid? What if x equaled 0.99
>> |> (9x=8.91), 0.44 (9x=3.96), 0.11 (9x=0.99), etc.? That's the
>> |> whole argument that brought me here in the first place. :) If
>> |> it can't work with finite decimals, why is it valid when
>> |> infinite decimals are used?
You're deaf, right? "It" works just fine with
0.99. Instead of showing 0.99 = 1 exactly the same
manipulations show that 0.99 = 0.99. People have
already explained this, in detail.
>> "It" works just fine with finite decimals,
>> if by "it" you mean the algebraic manipulation.
>> But you can't use the above argument to prove
>> that x = 1 starting from x = 0.99 (or 0.44 or ...).
>> Is that what you're worried about ?
>
>Yes.
>
>> As I said, to make sense of the given proof,
>> you have to _first_ understand how to define
>> the arithmetic operations on real numbers when
>> they're represented as infinite decimal expansions.
>> _When_ you arrive at that understanding, the
>> above will make perfect sense to you. (But, as
>> noted, the above will *also* strike you as
>> totally unnecessary.)
>
>Modulo 1?
???????????????????
>> |> It seems no one would even try to use that method with finites,
>> |> at least not to attempt to prove exactness.
>>
>> To prove "exactness" of *what* ??
>>
>> Grade-school children worldwide do this
>> stuff every day -- barring mistakes, they
>> get _exact_ answers to the problems that
>> they are set. Any one of them would be
>> able to show you that 9*0.99 = 8.91 or
>> that 8.91/9 = 0.99, thus verifying in any
>> particular case that the manipulations that
>> trouble you work out just as shown.
>>
>> I guess that I'm mystified ...
>
>I really don't want to get into this again, it's like pouring water down a rat
>hole, it has no end!
>
>> |> The excuse that an
>> |> infinite constantly fills up the back-end with 9s, so it's okay,
>> |> seems rather lame.
>>
>> Yeah ... that *would* be pretty lame.
>> Did someone here actually say that ??
>
>Yes, but not here... at least not to my knowledge. :)
Try to make sense. When he asks whether
someone here said that and you reply "yes, but not
here" _presumably_ what you mean is "no".
If nobody here has given such a lame
explanation then what's your point in pointing
out how lame it is? If you want to explain why
we're all wrong about this 0.999... thing you
should explain what's wrong about what _we_
have said.
You've put your finger on the problem right here. Most of us
do not feel that this is one of the worst fears we can live with - we
understand that none of us is right all the time, SO when someone
says we're wrong about something we're able to consider what is
said and decide whether we _are_ wrong, instead of taking a
refutation as an insult to our character (as you've said you do).
>There's a difference between ignorance and stupidity because, as they say,
>ignorance can be cured,
Not when you continue to insist you're right about matters
that you know nothing about. (Or about matters that you even
_say_ you know nothing about, incredibly.)
You've called me an asshole. You've said you think
I'm certifiable. A second ago you _claimed_ that you were
no longer complaining about _me_ being insulting. But
it appears you still are. You should _really_ give a quote
where I say anything _anywhere_ near as offensive to
you as what you've been saying to me. You really should.
See, believe it or not you can't say whatever
you want about anyone - the fact that you have enough
HONOR to say it to the entire planet doesn't make it
ok.
>> In deference to your blood pressure, you
>> might want to investigate whatever killfile
>> mechanism you have available to you -- the
>> way things are going, you're launched upon
>> an unfortunate downward spiral ...
>
>Thanks for the kind advice. Know what you mean. :) :) Wish my news service
>didn't update slower than Christmas... but I don't have much use for a killfile.
>Just as everyone else, I always have the option of not reading posts if I get
>truly annoyed. I'm not... yet... really do have fairly thick skin. :) :)
I hope we never get to see what happens when you _are_
annoyed then.
David C. Ullrich
[...]
>
>o~O~oo~O~oo~O~oo~O~oo~O~oo~O~oo~O~oo~O~oo~O~oo~O~oo~O~oo~O~o
>
>As Pogo said: "We has met thu enuhmy 'n' he is US!"
So you finally figured out how incongrous it is to say
>[snipped with a bloody knife]
>The purpose of Light is to fill the darkness and travel on;
>the purpose of Life is to find the Light and travel with it. - Pax
>btw, you're an asshole.
>The purpose of Light is to fill the darkness and travel on;
>the purpose of Life is to find the Light and travel with it. - Pax
>Im beginning to think you're certifiable.
>The purpose of Light is to fill the darkness and travel on;
>the purpose of Life is to find the Light and travel with it. - Pax
Good for you - at least you've figured out _something_ here.
Richard Carr
:Date: Fri, 21 Jul 2000 20:53:27 -0500
:From: Pax <pa...@whitesweb.com>
:Newsgroups: sci.math
:Subject: Re: Which rational x makes 3x^2-7x an integer?
:
:"Richard Carr" <ca...@cpw.math.columbia.edu> wrote in message
:news:Pine.LNX.4.21.000721...@cpw.math.columbia.edu...
:> On Fri, 21 Jul 2000, Pax wrote:
:>
:> :Date: Fri, 21 Jul 2000 12:30:02 -0700
:> :From: Pax <pax1NO...@whitesweb.com.invalid>
:> :Newsgroups: sci.math
:> :Subject: Re: Which rational x makes 3x^2-7x an integer?
:> :
:> :lrud...@panix.com (Lee Rudolph) wrote:
:> :>I dunno, Dave, this language sounds to me like you're suggesting
:> :>he get into one of those 11.999...-step programs. But if he
:> :can't
:> :>even handle 3x^2, how in the *world* will he deal with a Higher
:> :>Power?
:> :>
:> :>Lee Rudolph (just a friend of Bourbaki)
:> :>
:> :>
:> :Is almost no one interested in solving correctly the original
:> :equation that lemma posted?
:>
:> It was solved- by several people.
:
:If you'll check this thread, most of the posts have been to "correct" my
:mistake. In the NG I call mine, riddles and such are answered by numerous
:people, for the sheer fun of it. :)
Before that, though, the problem was solved- by several people.
:
:Kind regards - Pax
:
:
:
:o~O~oo~O~oo~O~oo~O~oo~O~oo~O~oo~O~oo~O~oo~O~oo~O~oo~O~oo~O~o
:
:
:
:
:
:
Kent
> stuff every day -- barring mistakes, they
> get _exact_ answers to the problems that
> they are set. Any one of them would be
> able to show you that 9*0.99 = 8.91 or
> that 8.91/9 = 0.99, thus verifying in any
> particular case that the manipulations that
> trouble you work out just as shown.
Grade-school children worldwide perhaps, but only if you exclude the USA. If
any one of them could do these in grade-school, then something must happen
after grade-school to remove this ability. A lot of 8th-graders would be
able to do the first computation without a calculator, but a lot of them
wouldn't. Virtually none would be able to do the second computation, even
with a calculator! The fact that the fraction bar corresponds to the
operation of division is not a widely known fact among middle-schoolers.
Also, sometime in this thread someone said that learning the order of
operations was supposed to happen in 7th grade algebra. Of course they were
just guessing, but there really isn't any 7th grade algebra in US public
schools. Algebra is usually first taught in 9th grade, sometimes in 8th
grade for the better performing students.
I only point these things out because I think they should be different.
Kent.
Pax
>>
>>As Pogo said: "We has met thu enuhmy 'n' he is US!"
>
>
>>[snipped with a bloody knife]
>
>>The purpose of Light is to fill the darkness and travel on;
>>the purpose of Life is to find the Light and travel with it. -
Pax
>
>>btw, you're an asshole.
>
>>The purpose of Light is to fill the darkness and travel on;
>>the purpose of Life is to find the Light and travel with it. -
Pax
>
>>Im beginning to think you're certifiable.
>
>
>>The purpose of Light is to fill the darkness and travel on;
>>the purpose of Life is to find the Light and travel with it. -
Pax
>
>Good for you - at least you've figured out _something_ here.
>
>
win. Our son just had another mild heart attack, so I really
don't have time to bandy words with you anymore. It's been fun
though. Goodbye.
- Pax
---
The purpose of Light is to fill the darkness and travel on;
the purpose of Life is to find the Light and travel with it. - Pax
-----------------------------------------------------------
Bill Dubuque
> Which rational x makes 3x^2-7x an integer? [...]
Hint: RATIONAL ROOT TEST => if 3 X^2 - 7 X - n = 0 and
X is a reduced rational then the denominator of X divides 3.
-Bill Dubuque
John R Ramsden
>
> For which rational numbers x is 3x^2 - 7x an integer? Find necessary and
> sufficient conditions.
This reply is a bit late, as I have a backlog of over 2K sci.math posts to
skim through. So apologies if I'm reiterating someone else's solution.
If x is a rational fraction then it can be written as p/q where p, q are both
rational integers, with q > 0 and GCD(p, q) = 1.
If we then write r = 3.x^2 - 7.x then your problem becomes in effect to find
every integer solution of 3.p^2 - 7.p.q = q^2.r, with p, q satisfying the
conditions above.
But as the latter equation can be rearranged as p / q = q.r / (3.p - 7.q),
and we know the LHS [left hand side] is already in reduced form, that means
there must be another integer s such that: q.r, 3.p - 7.q = p.s, q.s.
The second of the latter equations implies that q divides 3.p, and this
means that since GCD(p, q) = 1, q must divide 3 and hence, since q > 0,
q must equal either 1 or 3. (I chose q > 0 to half the number of cases.)
With q = 1 we obviously get all the integer solutions, x = p, which are
one special class of rational solutions.
With q = 3 the first of the latter pair of equations implies q divides p.s,
and again since GCD(p, q) = 1 this requires q divides s, i.e. s = 3.t, and
in this case the rational solutions are given by is x = t + 7/3, for which
r = t.(3.t + 7).
Cheers
---------------------------------------------------------------------------
John R Ramsden (j...@redmink.demon.co.uk)
---------------------------------------------------------------------------
The new is in the old concealed, the old is in the new revealed.
St Augustine.
---------------------------------------------------------------------------