point 9 bar... .99999999999999999999 (ok that's enough... hehe)
Josh Boyd
For those of you who do not believe that .9 bar isn't equal to 1. ;)
Here's the mathematical proof... (There will be a real world proof for
you to think about, also, that I thought of all by myself (at least, I
think I did) if you don't believe the math. ;) )
-------
If x is = to some fraction... (converting an infinate repeating decimal
to a fraction)
x = .9999999999...
Multiplying x by 10 gives...
10x = 9.99999999...
x = .99999999...
Subtracting these two equasions gives...
9x = 9
Solving for x ---
x = 9/9 or x = 1
----------
Ok... Now for the physical proof (for those who are so eager to see
another side to this.) ;)
I'm sure you all will agree that if you have two points that you CAN'T
find another point in between, then they MUST be the same point? Right?
A point in between (3,4) and (3,5) would be (3,4.5) ...
A point in between (2,2) and (2,2) would be... Umm... They're the same
point! There's no point in between them...
Ok then. ;) Find a point for me in-between (1,.999...) and (1,1).
Can't be done...
I hope this helps some of you who have a hard time believing that .9 bar
is not equal to 1... (Trival stuff) ;)
Have a good day in math class.
Josh
Raymond E. Griffith
_____________________________________________________________________
| |
Josh Boyd wrote:
For those of you who do not believe that .9 bar isn't equal to 1. ;)
Here's the mathematical proof... (There will be a real world proof for
you to think about, also, that I thought of all by myself (at least, I
think I did) if you don't believe the math. ;) )
If x is = to some fraction...(converting an infinate repeating decimal
to a fraction)
x = .9999999999...
Multiplying x by 10 gives...
10x = 9.99999999...
x = .99999999...
Subtracting these two equasions gives...
9x = 9
Solving for x ---
x = 9/9 or x = 1
----------
Ok... Now for the physical proof (for those who are so eager to see
another side to this.) ;)
I'm sure you all will agree that if you have two points that you CAN'T
find another point in between, then they MUST be the same point? Right?
A point in between (3,4) and (3,5) would be (3,4.5) ...
A point in between (2,2) and (2,2) would be...Umm...They're the same
point! There's no point in between them...
Ok then. ;) Find a point for me in-between (1,.999...) and (1,1).
Can't be done...
I hope this helps some of you who have a hard time believing that .9
bar is not equal to 1... (Trival stuff) ;)
Have a good day in math class.
Josh
|_____________________________________________________________________|
Nice "informal" proof based on the density of the real numbers--Thanks!!
(By the way, I think that some of the argument on this topic is not out
of ignorance, but out of orneriness. Only my guess, of course, but some
people will take an unreasonable position simply because they like to
argue...)
BLStansbury
On Sat, 25 Jan 1997 00:52:13 -0800, Josh Boyd <jb...@mail.coos.or.us>
wrote:
>Ok then. ;) Find a point for me in-between (1,.999...) and (1,1).
>
>Can't be done...
Just because I can't find one, does not mean one does not exist. For
those of us who can comprehend infinity, .9 bar certainly does not
equal 1. Sure is close though.
BLS
Haran Pilpel
the infinite series:
0.9 + 0.09 + 0.009 + 0.0009 + ....
Using the formula for the sum of a geometric series:
S = [ 1 / (1-q) ] * 0.9 = [1/(1-0.1)] * 0.9 = [1/(0.9)] * 0.9 = 1.
Haran
--
e^(Pi*i) + 1 = 0 (Euler)
--
e^(Pi*i) + 1 = 0 (Euler)
Lee Jaap
|>For those of you who do not believe that .9 bar isn't equal to 1. ;)
|>
|>Here's the mathematical proof... (There will be a real world proof for
|>you to think about, also, that I thought of all by myself (at least, I
|>think I did) if you don't believe the math. ;) )
|>
|>If x is = to some fraction...(converting an infinate repeating decimal
|>to a fraction)
|>
|> x = .9999999999...
|>
|> Multiplying x by 10 gives...
|>
|> 10x = 9.99999999...
|> x = .99999999...
|>
|> Subtracting these two equasions gives...
|>
|> 9x = 9
|>
|> Solving for x ---
|>
|> x = 9/9 or x = 1
I wish this weren't called a "mathematical" proof. Sure you're
performing arithmetic manipulations, but it isn't mathematical.
It *is* an appeal to intuition about "reasonable" operations on
"numbers".
To be mathematical, .9999999... needs to be defined. Any
mathematically precise definition will make it obvious that it
is just another way of writing the quantity 1. (Just like 2+3
is another "name" for the quantity commonly written as 5.)
Cheers.
--
J Lee Jaap <Jaa...@ASMSun.LaRC.NASA.Gov> +1 757/865-7093
employed by, not necessarily speaking for,
AS&M Inc, Hampton VA 23666-1340
Dave Weisbeck
In article <32ec24a2...@news.datasync.com>, bs...@datasync.com (BLStansbury) wrote:
>On Sat, 25 Jan 1997 00:52:13 -0800, Josh Boyd <jb...@mail.coos.or.us>
>wrote:
>
>>Ok then. ;) Find a point for me in-between (1,.999...) and (1,1).
>>
>>Can't be done...
>
>Just because I can't find one, does not mean one does not exist. For
>those of us who can comprehend infinity, .9 bar certainly does not
>equal 1. Sure is close though.
>
>BLS
>
No, .9 bar is 1, for those who truly understand infinity.
9 bar can be written as the following geometric series.
infinity
0.9 * Sigma (1/10)^n = 0.9 * 1 / (1 - 0.1) = 1
n=0
The ancient Greeks had the same problem with infinity. They didn't believe
infinite series could converge the way they do.
Dave Weisbeck
z2...@ugrad.cs.ubc.ca
SANDMAN
Raymond E. Griffith wrote:
>
> _____________________________________________________________________
> | |
> Josh Boyd wrote:
> For those of you who do not believe that .9 bar isn't equal to 1. ;)
>
> Here's the mathematical proof... (There will be a real world proof for
> you to think about, also, that I thought of all by myself (at least, I
> think I did) if you don't believe the math. ;) )
>
> If x is = to some fraction...(converting an infinate repeating decimal
> to a fraction)
>
> x = .9999999999...
>
> Multiplying x by 10 gives...
>
> 10x = 9.99999999...
> x = .99999999...
>
> Subtracting these two equasions gives...
>
> 9x = 9
>
> Solving for x ---
>
> x = 9/9 or x = 1
>
>
> Ok... Now for the physical proof (for those who are so eager to see
> another side to this.) ;)
>
> I'm sure you all will agree that if you have two points that you CAN'T
> find another point in between, then they MUST be the same point? Right?
>
> A point in between (3,4) and (3,5) would be (3,4.5) ...
>
> A point in between (2,2) and (2,2) would be...Umm...They're the same
> point! There's no point in between them...
>
>
> Can't be done...
>
> bar is not equal to 1... (Trival stuff) ;)
>
> Have a good day in math class.
>
> Josh
> |_____________________________________________________________________|
> Nice "informal" proof based on the density of the real numbers--Thanks!!
>
> (By the way, I think that some of the argument on this topic is not out
> of ignorance, but out of orneriness. Only my guess, of course, but some
> people will take an unreasonable position simply because they like to
> argue...)
I know I'm in on this a little late but where did you learn your'e math
If you start off with x = .999999999999 and then say
10x = 9.999999999999 you have multiplied both sides by 10
To reverse the equation back to x you can't subtract x from one side
and .99999999 from the other. so you'r equation is total fantasy.
You must divide both sides by the same quantity that x is being
multiplied by. In this case 10.
Also you could keep adding 9 to your bar and you will never reach 1.
The 9's will get smaller and smaller and you will get closer and closer
to 1 but you will never get there.
Dave Weisbeck
In article <32F2D4...@IX.NETCOM.COM>, WDE...@IX.NETCOM.COM wrote:
>
>I know I'm in on this a little late but where did you learn your'e math
>
>If you start off with x = .999999999999 and then say
>
> 10x = 9.999999999999 you have multiplied both sides by 10
>
>
> To reverse the equation back to x you can't subtract x from one side
>
>and .99999999 from the other. so you'r equation is total fantasy.
But x = .9 bar so you can do that. There is no fantasy.
> You must divide both sides by the same quantity that x is being
>
>multiplied by. In this case 10.
>
> Also you could keep adding 9 to your bar and you will never reach 1.
>
>The 9's will get smaller and smaller and you will get closer and closer
>to 1 but you will never get there.
NO (sorry for yelling :-). .9 bar is 1. There has been 2 proofs and one
intuition showing just that in this thread. I suggest you take a book on
analysis out from your library and look up geometric series.
Don't feel bad if you don't see this though. Of the three greatest
mathematicians of all time (Gauss, Newton and Archimedes) only two
knew this to be true. Of course now I am going to hear all about who else
belongs on that greatest mathematician list. :-)
Dave Weisbeck
z2...@ugrad.cs.ubc.ca
Josh Boyd
> To reverse the equation back to x you can't subtract x from one side
Why can't I subtract first? See the other example that someone did?
x = 2
10x = 20
-x = -2
9x = 18
x = 2
Josh
Albert Y.C. Lai
In article <32F2D4...@IX.NETCOM.COM>,
SANDMAN <WDE...@IX.NETCOM.COM> wrote:
>If you start off with x = .999999999999 and then say
>
> 10x = 9.999999999999 you have multiplied both sides by 10
>
>
Yes we can. (Once 0.999... is defined.)
> Also you could keep adding 9 to your bar and you will never reach 1.
>The 9's will get smaller and smaller and you will get closer and closer
>to 1 but you will never get there.
This is Zeno's Flaw. I refuse to call it a paradox; it is flawed
reasoning not paradox. (To be fair, it is ok reasoning for a
philosophy class.) It happens when one confuses the bar notation with
the terminating decimal fractions. The point is that the terminating
decimal fractions do terminate, but the bar notation does not. You
said we are keep adding 9's to it; well that is a concept for
terminating fractions. No one is adding 9's to 0.9bar, the 9's are all
there at the very beginning, no one is adding more, no one is taking
away any.
--
Albert Y.C. Lai tre...@vex.net http://www.vex.net/~trebla/
J. Pimentel
>For those of you who do not believe that .9 bar isn't equal to 1. ;)
>If x is = to some fraction... (converting an infinate repeating decimal
>to a fraction)
>x = .9999999999...
>Multiplying x by 10 gives...
>10x = 9.99999999...
> x = .99999999...
>Subtracting these two equasions gives...
> 9x = 9
>Solving for x ---
> x = 9/9 or x = 1
Very good. Now can you say that .99999999999....... is approximately equal to
one? Why, because that is what you have proven. Nothing more, nothing less.
Regardless of how many nines you append to this number it is still less than
one, however, it's best approximation is one, however, an approximation is
never the exact.
>Have a good day in math class.
Always.
>Josh
---
John Pimentel
BrianScott
John Pimentel points out that no matter how many 9s you write
down in the expression 0.999999...9 you have only a number
close to 1, not 1 itself. This is true, provided that he is talking
about a *finite* number of 9s; however, the non-terminating
decimal 0.99999... is *by definition* the limit of the infinite sequence
0.9, 0.99, 0.999, 0.9999, etc. (This is not subject to argument:
this *is* the definition of the value of this non-terminating decimal.)
And as John himself seems willing to agree, this sequence does
indeed converge to 1.0. There fore it is perfectly true that
0.9999... = 1.0
This topic comes up rather often in math-related newsgroups,
and inevitably it turns out that those who maintain that 0.9999...
isn't 1 don't understand the formal concept of limit, without which
non-terminating decimals are simply meaningless strings of
symbols. The usual result is the expenditure of a great deal of
hot air; the remedy is a good calculus course or, better yet, a
course in which the real numbers are constructed formally.
Brian M. Scott
Do Not Use: brian...@aol.com
Always Use: sc...@math.csuohio.edu
prot...@gmail.com
> In article <32ec24a2...@news.datasync.com>, bs...@datasync.com (BLStansbury) wrote:
> >On Sat, 25 Jan 1997 00:52:13 -0800, Josh Boyd <jb...@mail.coos.or.us>
> >wrote:
> >
> >>
> >>Can't be done...
> >
> >those of us who can comprehend infinity, .9 bar certainly does not
> >equal 1. Sure is close though.
> >
> >BLS
> >
>
> No, .9 bar is 1, for those who truly understand infinity.
>
> 9 bar can be written as the following geometric series.
>
> infinity
> 0.9 * Sigma (1/10)^n = 0.9 * 1 / (1 - 0.1) = 1
> n=0
>
> The ancient Greeks had the same problem with infinity. They didn't believe
> infinite series could converge the way they do.
>
> Dave Weisbeck
> z2...@ugrad.cs.ubc.ca
then it is definite that you do not
because if it could be understood ...... it would not be infinity.
it is just our idea of what it is that you know
just a few formulas which equate true
Barb Knox
On 29/05/18 06:06, prot...@gmail.com wrote:
> On Thursday, January 30, 1997 at 1:30:00 PM UTC+5:30, Dave Weisbeck wrote:
>> In article <32ec24a2...@news.datasync.com>, bs...@datasync.com (BLStansbury) wrote:
>>> On Sat, 25 Jan 1997 00:52:13 -0800, Josh Boyd <jb...@mail.coos.or.us>
>>> wrote:
>>>
>>>> Ok then. ;) Find a point for me in-between (1,.999...) and (1,1).
>>>>
>>>> Can't be done...
>>>
>>> Just because I can't find one, does not mean one does not exist. For
>>> those of us who can comprehend infinity,
done so.)
The issue is not that *you* can't find some X such that .9 bar < X < 1,
but it is *provable* that no such X exists:
For any X < 1, then for some N number of digits,
X < .999...9 (N digits). N might be very large, but it is still finite.
.999...9 (N digits) < .9 bar (which certainly has more than N digits).
So, .9 bar < X < .999...9 (N digits) < .9 bar
So, .9 bar < .9 bar. Oops. The only possible source of this
contradiction is the initial assumption that .9 bar < X < 1. So there
is no such X.
Note that this proof does not mention "infinity" at all. This is the
way "limit" proofs are done (since at least the time of Archimedes).
>>> .9 bar certainly does not
>>> equal 1. Sure is close though.
>>>
>>> BLS
>>>
>>
>> No, .9 bar is 1, for those who truly understand infinity.
>>
>> 9 bar can be written as the following geometric series.
>>
>> infinity
>> 0.9 * Sigma (1/10)^n = 0.9 * 1 / (1 - 0.1) = 1
>> n=0
>>
>> The ancient Greeks had the same problem with infinity. They didn't believe
>> infinite series could converge the way they do.
>>
>> Dave Weisbeck
>> z2...@ugrad.cs.ubc.ca
>
> if you say ---- " ... those who truely understand infinity"
> then it is definite that you do not
>
> because if it could be understood ...... it would not be infinity.
> it is just our idea of what it is that you know
> just a few formulas which equate true
>
---------------------------
| BBB b \ Barbara at LivingHistory stop co stop uk
| B B aa rrr b |
| BBB a a r bbb | ,008015L080180,022036,029037
| B B a a r b b | ,047045,L014114L4.
| BBB aa a r bbb |
-----------------------------
Mathedman
> On Thursday, January 30, 1997 at 1:30:00 PM UTC+5:30, Dave Weisbeck wrote:
>> In article <32ec24a2...@news.datasync.com>, bs...@datasync.com (BLStansbury) wrote:
>>> On Sat, 25 Jan 1997 00:52:13 -0800, Josh Boyd <jb...@mail.coos.or.us>
>>> wrote:
>>>
>>>> Ok then. ;) Find a point for me in-between (1,.999...) and (1,1).
>>>>
>>>> Can't be done...
>>>
>>> Just because I can't find one, does not mean one does not exist. For
>>> those of us who can comprehend infinity, .9 bar certainly does not
>>> equal 1. Sure is close though.
>>>
>>> BLS
>>>
>>
>> No, .9 bar is 1, for those who truly understand infinity.
>>
smart as you.
Barb Knox
didn't bother to quote) which I believe you are referring to is:
having done so.)
<https://en.wikipedia.org/wiki/Infinity>. The nice thing about
ignorance is that unlike stupidity it can often be remedied with some
effort. But note that continuing willful ignorance does seem pretty
stupid. Your choice.