off topic but please forgive me me and answer
superpollo
Tim Chase
> how much is one half times one half?
Uh, did you try it at the python prompt? If not, here's the answer:
0.1b * 0.1b = 0.01b
Now all you need is to find the recent thread that converts
binary floats to decimal floats ;-)
-tkc
Patrick Maupin
I thought it was 0b0.1 * 0b0.1 == 0b0.01
Otherwise, you might get it confused with hexadecimal floats :D
David Robinow
$ python -c "print 1/2 * 1/2"
0
But that's not what I learned in grade school.
(Maybe I should upgrade to 3.1?)
Tim Chase
> $ python -c "print 1/2 * 1/2"
> 0
>
> But that's not what I learned in grade school.
> (Maybe I should upgrade to 3.1?)
That's because you need to promote one of them to a float so you
get a floating-point result:
>>> 1/2 * 1/2
0
>>> 1/2 * 1/2.0
0.0
Oh...wait ;-)
-tkc
Patrick Maupin
Hmmm, I think I'm starting to see why we need math.fsum() to take care
of those rounding errors...
Steven D'Aprano
>>> superpollo wrote:
>>> > how much is one half times one half?
[...]
> Well, my python says:
>
> $ python -c "print 1/2 * 1/2"
> 0
>
> But that's not what I learned in grade school.
> (Maybe I should upgrade to 3.1?)
Python 2.x defaults to integer division, a design error which has been
rectified in 3.x.
One can do any of these:
[steve@sylar ~]$ python3.1 -c "print(1/2 * 1/2)"
0.25
[steve@sylar ~]$ python2.6 -c "from __future__ import division; print 1/2
* 1/2"
0.25
[steve@sylar ~]$ python2.6 -Q new -c "print 1/2 * 1/2"
0.25
[steve@sylar ~]$ python2.6 -c "print 0.5 * 0.5"
0.25
and probably many others as well.
--
Steven
Steven D'Aprano
Tim, I'm sure you know the answer to this, but for the benefit of the
Original Poster, the problem is that you need to promote *both* divisions
to floating point. Otherwise one of them will give int 0, which gives 0.0
when multiplied by 0.5.
>>> 1.0/2 * 1/2.0
0.25
If you want an exact result when multiplying arbitrary fractions, you
need to avoid floats and decimals and use Fractions:
>>> Fraction(1, 2)**2
Fraction(1, 4)
--
Steven
Lie Ryan
hmm?
>>> import math
>>> math.fsum([1/2, 1/2])
0.0
it doesn't appear to take care of those rounding errors, not in this
case at least.
Patrick Maupin
you're right! I mis-read the problem. What we REALLY need is a good
math.fmul() ;-)
David Robinow
I should have known he wouldn't get it.
Tim Chase
>> That's because you need to promote one of them to a float so you get a
>> floating-point result:
>>
>> >>> 1/2 * 1/2
>> 0
>> >>> 1/2 * 1/2.0
>> 0.0
>>
>> Oh...wait ;-)
>
> Tim, I'm sure you know the answer to this, but for the benefit of the
> Original Poster, the problem is that you need to promote *both* divisions
> to floating point. Otherwise one of them will give int 0, which gives 0.0
> when multiplied by 0.5.
>
>>>> 1.0/2 * 1/2.0
> 0.25
You can get away with just promoting one of them...you just have
to promote the _correct_ one (one involved in the first division)
so that its promotion-of-subresult-to-float carries into all
subsequent operations/operators:
>>> 1/2 * 1/2 # (((1/2)*1)/2)==(((0)*1)/2) in 2.x
0
>>> 1/2 * 1/2.0 # (((1/2)*1)/2.0)==(((0)*1)/2.0) in 2.x
0.0
>>> 1/2 * 1.0/2 # (((1/2)*1.0)/2)==(((0)*1.0)/2) in 2.x
0.0
>>> 1/2.0 * 1/2 # (((1/2.0)*1)/2)
0.25
>>> 1.0/2 * 1/2 # (((1.0/2)*1)/2)
0.25
I'd rather be explicit in *real* code that I'd write and
explicitly float'ify constants or float() integer variables. The
OP's question was both OT and pretty basic middle-school math
that google would have nicely answered[1] so IMHO warranted a bit
of fun. :)
-tkc
Patrick Maupin
> On Thu, 01 Apr 2010 22:44:51 +0200, superpollo <ute...@esempio.net>
> declaimed the following in gmane.comp.python.general:
>
> > how much is one half times one half?
>
> print math.exp((math.log(1) - math.log(2))
> + (math.log(1) - math.log(2)))
That's all well and good, but base 'e' is kind of complicated. Some
of us were using base 10, and others took Tim's lead and were using
base 2:
>>> print math.exp(((math.log(1)/math.log(2) - math.log(2)/math.log(2)) + (math.log(1)/math.log(2) - math.log(2)/math.log(2)))*math.log(2))
0.25
Steven D'Aprano
>> Tim, I'm sure you know the answer to this, but for the benefit of the
>> Original Poster, the problem is that you need to promote *both*
>> divisions to floating point. Otherwise one of them will give int 0,
>> which gives 0.0 when multiplied by 0.5.
>>
>>>>> 1.0/2 * 1/2.0
>> 0.25
>
> You can get away with just promoting one of them...you just have to
> promote the _correct_ one
Doh!
Of course you do. I knew that!
--
Steven
Wanderer
> On Apr 1, 4:42 pm, Tim Chase <python.l...@tim.thechases.com> wrote:
> > Uh, did you try it at the python prompt?
When I try it at the IPython prompt, I get
Object 'how much is one half times one half' not found.
Stefan Behnel
> On Apr 1, 11:52 pm, Dennis Lee Bieber wrote:
>> On Thu, 01 Apr 2010 22:44:51 +0200, superpollo
>>
>>> how much is one half times one half?
>>
>> import math
>> print math.exp((math.log(1) - math.log(2))
>> + (math.log(1) - math.log(2)))
>
> That's all well and good, but base 'e' is kind of complicated. Some
> of us were using base 10, and others took Tim's lead and were using
> base 2:
>
> >>> print math.exp(((math.log(1)/math.log(2) - math.log(2)/math.log(2)) + (math.log(1)/math.log(2) - math.log(2)/math.log(2)))*math.log(2))
> 0.25
The above can be rewritten as
print('0.25')
which is much faster and also a lot more readable.
Stefan
Andreas Waldenburger
wrote:
> how much is one half times one half?
While everyone else is mocking you: Can you please elaborate on why you
want to know and what kind of problem you're trying to solve with this?
Also, don't you think you should have picked a maths forum for this
kind of question?
Meanwhile:
http://en.wikipedia.org/wiki/Fractions#Multiplying_by_a_fraction
And in Italian:
http://it.wikipedia.org/wiki/Frazione_(matematica)#Moltiplicazione_e_division
/W
(Yes, I have nothing to do right now.)
--
INVALID? DE!
Patrick Maupin
wrote:
> While everyone else is mocking you: Can you please elaborate on why you
> want to know and what kind of problem you're trying to solve with this?
> Also, don't you think you should have picked a maths forum for this
> kind of question?
Methinks the OP is fluent in the way of choosing newsgroups.
According to google, he has posted 6855 messages in 213 groups.
And I can't speak for anybody else, but I just assumed it was an April
Fool's question. I meant to be laughing with the OP, not at him, so
sorry if I misunderstood.
Regards,
Pat
Mensanator
Where do you get that from?
>
> --
> Steven- Hide quoted text -
>
> - Show quoted text -
Dave Angel
Mensanator wrote:
> On Apr 1, 9:44 pm, Steven D'Aprano <st...@REMOVE-THIS-
> cybersource.com.au> wrote:
>
>> <snip>
>>>>> 1/2.0
>>>>>
>> 0.25
>>
>> If you want an exact result when multiplying arbitrary fractions, you
>> need to avoid floats and decimals and use Fractions:
>>
>>
>>>>> Fraction(1, 2)**2
>>>>>
>> Fraction(1, 4)
>>
>
> Where do you get that from?
>
>
In Python2.6,
from fractions import Fraction
And Fraction is now a class which supports fractional arithmetic.
Steven D'Aprano
>> If you want an exact result when multiplying arbitrary fractions, you
>> need to avoid floats and decimals and use Fractions:
>>
>> >>> Fraction(1, 2)**2
>>
>> Fraction(1, 4)
>
> Where do you get that from?
Where do I get what from? Fraction? Oops, sorry about that.
In Python2.6:
>>> from fractions import Fraction
In older Pythons, there was a demo module Demo/classes/Rat.py but it may
not be installed on your system. See http://bugs.python.org/issue1682
If you meant, where did I get the statement about exact results from,
both float and Decimal are fixed precision numbers. float precision is
fixed by the operating system and/or hardware; Decimal precision can be
arbitrarily chosen by the caller, but having made that choice,
calculations are rounded to that precision. Only Fraction gives exact
results for any arbitrary rational number.
--
Steven
Mensanator
cybersource.com.au> wrote:
> On Fri, 02 Apr 2010 12:35:55 -0700, Mensanator wrote:
> >> If you want an exact result when multiplying arbitrary fractions, you
> >> need to avoid floats and decimals and use Fractions:
>
> >> >>> Fraction(1, 2)**2
>
> >> Fraction(1, 4)
>
> > Where do you get that from?
>
> Where do I get what from? Fraction? Oops, sorry about that.
>
> In Python2.6:
>
> >>> from fractions import Fraction
Ok, thanks. I've been using gmpy to do rational arithmetic:
>>> import gmpy
>>> gmpy.mpq(1,2)**2
mpq(1,4)
But I don't have a lot of call for it.
>
> In older Pythons, there was a demo module Demo/classes/Rat.py but it may
> not be installed on your system. Seehttp://bugs.python.org/issue1682
>
> If you meant, where did I get the statement about exact results from,
> both float and Decimal are fixed precision numbers. float precision is
> fixed by the operating system and/or hardware; Decimal precision can be
> arbitrarily chosen by the caller, but having made that choice,
> calculations are rounded to that precision. Only Fraction gives exact
> results for any arbitrary rational number.
Yes, rationals are handy sometimes.
>
> --
> Steven
Mensanator
> On Apr 2, 2:41 pm, Andreas Waldenburger <use...@geekmail.INVALID>
> wrote:
>
> > While everyone else is mocking you: Can you please elaborate on why you
> > want to know and what kind of problem you're trying to solve with this?
> > Also, don't you think you should have picked a maths forum for this
> > kind of question?
>
> Methinks the OP is fluent in the way of choosing newsgroups.
> According to google, he has posted 6855 messages in 213 groups.
Does that really mean anything? Hell, I have 12765 messages
posted to 332 groups, but I only use 10 regularly.
>
> http://groups.google.com/groups/profile?enc_user=ul3SQhIAAAAYmLD0Oj5Y...
Patrick Maupin
> On Apr 2, 2:34 pm, Patrick Maupin <pmau...@gmail.com> wrote:
>
> > Methinks the OP is fluent in the way of choosing newsgroups.
> > According to google, he has posted 6855 messages in 213 groups.
>
> Does that really mean anything? Hell, I have 12765 messages
> posted to 332 groups, but I only use 10 regularly.
Well, I have been very wrong in my assumptions before, but yes, I do
assume it means something:
- I assume that the OP knows of the existence of more than one
newsgroup.
- I assume the OP knows how to locate different newsgroups, either via
search or some directory like yahoo, and is able to think about which
one he wants to post to and why.
- I assume that he is comfortable with the process of posting. In
fact, looking at the stats, about half as comfortable as mensanator,
and over 18 times as comfortable as me ;-)
Of course, I could be all wet in my assumptions, and it may just be
that the OP has a cat constantly walking back and forth across his
keyboard...
Regards,
Pat
Mensanator
> On Apr 2, 6:50 pm, Mensanator <mensana...@aol.com> wrote:
>
> > On Apr 2, 2:34 pm, Patrick Maupin <pmau...@gmail.com> wrote:
>
> > > Methinks the OP is fluent in the way of choosing newsgroups.
> > > According to google, he has posted 6855 messages in 213 groups.
>
> > Does that really mean anything? Hell, I have 12765 messages
> > posted to 332 groups, but I only use 10 regularly.
>
> Well, I have been very wrong in my assumptions before, but yes, I do
> assume it means something:
Yes, you are, in fact, all wet.
>
> - I assume that the OP knows of the existence of more than one
> newsgroup.
"More than one", that's fair. 213, unlikely.
>
> - I assume the OP knows how to locate different newsgroups, either via
> search or some directory like yahoo, and is able to think about which
> one he wants to post to and why.
And most of those probably involved no thought at all, probably
due to cross-posting from a relatively small number of sources
(certainly in my case). So, no, this stat proves nothing about
the OP's ability to find newsgroups or think about their
appropriateness.
>
> - I assume that he is comfortable with the process of posting. In
> fact, looking at the stats, about half as comfortable as mensanator,
> and over 18 times as comfortable as me ;-)
Well, _I've_ been here on Usenet for 10 years. But despite the stats,
I know little about most to the groups I've "posted to".
>
> Of course, I could be all wet in my assumptions, and it may just be
> that the OP has a cat constantly walking back and forth across his
> keyboard...
Don't you know how Usenet works?
>
> Regards,
> Pat
Patrick Maupin
> Don't you know how Usenet works?
No, but my cat does.
superpollo
no no you understood prfectly *but* the thing is i am a regular in an
italian language math ng which is haunted by a crackpot who insists that
1/2 * 1/2 cannot be 1/4, "because multiplication means getting bigger",
so i took a semi-serious stance and made a few posts as a statistical
tentative to "convince" said crackpot that the world is not going crazy
(but maybe he is)
thanks
ps: note that my nickname is not unique, and there are a few people
whith the same one... and i didn't ever post using googlegroups
Mensanator
> Patrick Maupin ha scritto:
>
>
>
>
>
> > On Apr 2, 2:41 pm, Andreas Waldenburger <use...@geekmail.INVALID>
> > wrote:
>
> >> While everyone else is mocking you: Can you please elaborate on why you
> >> want to know and what kind of problem you're trying to solve with this?
> >> Also, don't you think you should have picked a maths forum for this
> >> kind of question?
>
> > Methinks the OP is fluent in the way of choosing newsgroups.
> > According to google, he has posted 6855 messages in 213 groups.
>
>
> > And I can't speak for anybody else, but I just assumed it was an April
> > Fool's question. I meant to be laughing with the OP, not at him, so
> > sorry if I misunderstood.
>
> no no you understood prfectly *but* the thing is i am a regular in an
> italian language math ng which is haunted by a crackpot who insists that
> 1/2 * 1/2 cannot be 1/4, "because multiplication means getting bigger",
> so i took a semi-serious stance and made a few posts as a statistical
> tentative to "convince" said crackpot that the world is not going crazy
> (but maybe he is)
I seriously doubt your crackpot friend actually believes that.
Probably more troll than crackpot. Showing him articles and
programs that prove your premise will accomplish nothing.
However, if you personally wanted information on programming
with rational numbers, you came to the right place.
>
> thanks
>
> ps: note that my nickname is not unique, and there are a few people
> whith the same one... and i didn't ever post using googlegroups
What does it mean, "super chicken?
Steve Holden
If you think you will persuade a crackpot to drop his lunacy by logical
argument you are clearly an optimist of the first water. But since I
like a challenge (and bearing in mind this is OT so I don't claim to be
an expert) you might try first of all persuading him to agree to the
commutativity of multiplication (i.e. x * y == y * x for any x and y).
If he agrees to that, then get him to agree that x * 1 == x for any x.
If he agrees to that, then set x = 1/2 and see if he'll agree that 1/2 *
1 == 1/2.
If he does, then surely he must also agree that 1 * 1/2 == 1/2, i.e.
multiplication can indeed "make things smaller".
Good luck, though. Crackpots aren't generally responsive to appeals to
rational thinking.
regards
Steve
--
Steve Holden +1 571 484 6266 +1 800 494 3119
See PyCon Talks from Atlanta 2010 http://pycon.blip.tv/
Holden Web LLC http://www.holdenweb.com/
UPCOMING EVENTS: http://holdenweb.eventbrite.com/
superpollo
he does not, since "you cannot multiply something, and not getting some
more of it" ... he is stuck with the latin etimology of "multiply"
("multiplicare" means "increase quantity", like in the fish and bread
miracle)
superpollo
> On Apr 3, 8:00 am, superpollo <ute...@esempio.net> wrote:
>> Patrick Maupin ha scritto:
>>
>>
>>
>>
>>
>>> On Apr 2, 2:41 pm, Andreas Waldenburger <use...@geekmail.INVALID>
>>> wrote:
>>>> While everyone else is mocking you: Can you please elaborate on why you
>>>> want to know and what kind of problem you're trying to solve with this?
>>>> Also, don't you think you should have picked a maths forum for this
>>>> kind of question?
>>> Methinks the OP is fluent in the way of choosing newsgroups.
>>> According to google, he has posted 6855 messages in 213 groups.
>>> http://groups.google.com/groups/profile?enc_user=ul3SQhIAAAAYmLD0Oj5Y...
>>> And I can't speak for anybody else, but I just assumed it was an April
>>> Fool's question. I meant to be laughing with the OP, not at him, so
>>> sorry if I misunderstood.
>> no no you understood prfectly *but* the thing is i am a regular in an
>> italian language math ng which is haunted by a crackpot who insists that
>> 1/2 * 1/2 cannot be 1/4, "because multiplication means getting bigger",
>> so i took a semi-serious stance and made a few posts as a statistical
>> tentative to "convince" said crackpot that the world is not going crazy
>> (but maybe he is)
>
> I seriously doubt your crackpot friend actually believes that.
> Probably more troll than crackpot. Showing him articles and
> programs that prove your premise will accomplish nothing.
probably so, but you cannot imagine the traffic he generates...
> However, if you personally wanted information on programming
> with rational numbers, you came to the right place.
>
>> thanks
>>
>> ps: note that my nickname is not unique, and there are a few people
>> whith the same one... and i didn't ever post using googlegroups
>
> What does it mean, "super chicken?
yea!
http://www.renegadechickens.com/chickens/Toons/superchicken.gif
Steve Holden
> Steve Holden ha scritto:
[...]
>> If he agrees to that, then get him to agree that x * 1 == x for any x.
>>
>> If he agrees to that
>
> he does not, since "you cannot multiply something, and not getting some
> more of it" ... he is stuck with the latin etimology of "multiply"
> ("multiplicare" means "increase quantity", like in the fish and bread
> miracle)
>
expecting agreement on a common sense basis, then. Particularly when he
takes such a narrow-minded view.
In short, he has his head up his ass.
Would he agree that two halves make a whole? If so, he appears to deny
the commutativity of multiplication. Such people are amusing for the
first ten minutes, but I am sure he has managed to bore everyone to
death by now.
Martin P. Hellwig
<cut>
>
> If you think you will persuade a crackpot to drop his lunacy by logical
> argument you are clearly an optimist of the first water. But since I
> like a challenge (and bearing in mind this is OT so I don't claim to be
> an expert) you might try first of all persuading him to agree to the
> commutativity of multiplication (i.e. x * y == y * x for any x and y).
>
> If he agrees to that, then get him to agree that x * 1 == x for any x.
>
> If he agrees to that, then set x = 1/2 and see if he'll agree that 1/2 *
> 1 == 1/2.
>
> If he does, then surely he must also agree that 1 * 1/2 == 1/2, i.e.
> multiplication can indeed "make things smaller".
>
> Good luck, though. Crackpots aren't generally responsive to appeals to
> rational thinking.
>
I am replying to this post not because I disagree but because it
postalogically fits the best (I am by no means an expert either).
IMHO, the crackpot in this regard is actually partially right,
multiplication does mean that the number must get bigger, however for
fractions you multiply four numbers, two numerators and two
denominators. The resulting numerator and denominator by this
multiplication get indeed bigger.
--
mph
Matthew Barnett
division by a half?
Steven D'Aprano
> I am replying to this post not because I disagree but because it
> postalogically fits the best (I am by no means an expert either).
>
> IMHO, the crackpot in this regard is actually partially right,
> multiplication does mean that the number must get bigger, however for
> fractions you multiply four numbers, two numerators and two
> denominators. The resulting numerator and denominator by this
> multiplication get indeed bigger.
But you're not multiplying four numbers, you're multiplying two numbers.
One-half is not "two numbers", that would be a tuple or a list or
possibly a coordinate pair. One-half is a single number, the number which
if you double it gives one.
Fortunately multiplication is consistent. Multiplying the two numbers 0.5
and 0.5 is exactly the same as multiplying 1*1 and 2*2 then dividing to
get a single number. It's not the same as multiplying 1*1 and 2*2 to get
two numbers, 1 and 4.
You say that multiplication means that the number "must get bigger".
5*1 = 5
5*0 = 0
5*-2 = -10
I hope you won't try to argue that 5, 0 and -10 are all bigger than 5.
There really is no point trying to dignify superpollo's friend's
assertion on the basis of some technicality. His argument is no different
from the argument that says that pythons are snakes, and therefore python
can't be a programming language and this newsgroup can't possibly exist.
Words can have multiple meanings, and meanings can shift. Multiply may be
derived from a word which, once upon a time, meant to get bigger, but
that's not what multiply means. I don't like to dismiss somebody I've
never met, but on the basis of what superpollo says, yes, he's a crackpot.
Either that or about age four. When I was four I strongly believed that
"one hundred" and "a hundred" were different numbers. I argued (not very
convincingly, but with great vehemence) to my teacher and my parents that
you counted up to ninety-nine, then a hundred, a hundred and one, a
hundred and two, ... a hundred and ninety-nine, *one* hundred.
--
Steven
Patrick Maupin
regard is actually partially right,
> multiplication does mean that the number must get bigger, however for
> fractions you multiply four numbers, two numerators and two
> denominators. The resulting numerator and denominator by this
> multiplication get indeed bigger.
That argument is great! Just make sure that you've managed to leave
before the class has to learn about irrational numbers that don't
*have* numerators and denominators ;-)
Patrick Maupin
>
> no no you understood prfectly *but* the thing is i am a regular in an
> italian language math ng which is haunted by a crackpot who insists that
> 1/2 * 1/2 cannot be 1/4, "because multiplication means getting bigger",
> so i took a semi-serious stance and made a few posts as a statistical
> tentative to "convince" said crackpot that the world is not going crazy
> (but maybe he is)
If I read correctly (using my non-existent Italian, and heavily
relying on my tiny bit of Spanish and a lot of google translate), it
appears that you are what I would call a high-school math/science
teacher, who takes students to competitions?
Regards,
Pat
superpollo
right -- almost! i don't take them to competitions (i am not an official
trainer) but sometimes give some general advice to students who would be
inclined to compete, if they ask me.
bye
Martin P. Hellwig
> On Sat, 03 Apr 2010 15:43:41 +0100, Martin P. Hellwig wrote:
>
>> I am replying to this post not because I disagree but because it
>> postalogically fits the best (I am by no means an expert either).
>>
>> IMHO, the crackpot in this regard is actually partially right,
>> multiplication does mean that the number must get bigger, however for
>> fractions you multiply four numbers, two numerators and two
>> denominators. The resulting numerator and denominator by this
>> multiplication get indeed bigger.
>
> But you're not multiplying four numbers, you're multiplying two numbers.
> One-half is not "two numbers", that would be a tuple or a list or
> possibly a coordinate pair. One-half is a single number, the number which
> if you double it gives one.
>
I disagree with you there, but I only disagree with you on the
definition of the syntax, not with the logic nor the explanation.
I am not going to argue about syntax, since I don't think I would make a
great argument (being the devil's advocate) and also because I believe
when argued correctly, agreeing on disagreement of syntax allows even
the greatest untruth be true and false at the same time.
Excuse me please I need to feed Schroedinger's cat :-)
--
mph
Mensanator
cybersource.com.au> wrote:
> On Sat, 03 Apr 2010 15:43:41 +0100, Martin P. Hellwig wrote:
> > I am replying to this post not because I disagree but because it
> > postalogically fits the best (I am by no means an expert either).
>
> > IMHO, the crackpot in this regard is actually partially right,
> > multiplication does mean that the number must get bigger, however for
> > fractions you multiply four numbers, two numerators and two
> > denominators. The resulting numerator and denominator by this
> > multiplication get indeed bigger.
>
> But you're not multiplying four numbers,
You are if you're using Rationals.
> you're multiplying two numbers.
Because they're expressed as Decimals.
> One-half is not "two numbers",
Sometimes it is.
> that would be a tuple
Like this?
>>> gmpy.mpq('0.5')
mpq(1,2)
> or a list or
> possibly a coordinate pair. One-half is a single number,
When dealing with crackpots, it does not help to use the
wrong arguments. When multiplying gmpy.mpq(2,3) by gmpy.mpq(2,3),
the numerator and denominator have both indeed gotten bigger.
The trick is that when combined, the overall result is smaller.
> the number which
> if you double it gives one.
>
> Fortunately multiplication is consistent. Multiplying the two numbers 0.5
> and 0.5 is exactly the same as multiplying 1*1 and 2*2 then dividing to
> get a single number. It's not the same as multiplying 1*1 and 2*2 to get
> two numbers, 1 and 4.
>
> You say that multiplication means that the number "must get bigger".
Yes, not in every case, but in many cases it does. You need to point
out that it is wrong EVEN IN THE CASES WHERE IT'S TRUE. It is a
Non Sequitur - it does not follow that a number must be bigger if
the numerator and denominator have each gotten larger.
>
> 5*1 = 5
> 5*0 = 0
> 5*-2 = -10
>
> I hope you won't try to argue that 5, 0 and -10 are all bigger than 5.
Yes, but these special cases don't help. It needs to be pointed out
that the argument is wrong even in cases like 2/3 * 2/3.
Emile van Sebille
Ahh, but no ones arguing that irrational numbers don't get bigger --
even before you multiply them!
Emile
Steve Holden
[...]
> When dealing with crackpots, it does not help to use the
Correct. Unfortunately, it doesn't help to use the right ones either.
In fact, that could almost be a definition of "crackpot" (and alas now
we approach territory where we risk offending the religious, so I will
cease and desist).
Patrick Maupin
True, but being an optimist, just as (-1 * -1 == +1) (which
admittedly, I had a hard time trying to explain to my father years
ago), and just as (not not True == True) and just as multiplying two
imaginary numbers can have a real result, I was hoping that it would
also be the case that having a discussion with an irrational person
about irrational numbers could have a rational result. Of course,
that hope was incredibly naive of me, since most operations with
irrational numbers which do not involve either closely related
irrational numbers or zero will also result in irrational numbers. I
think induction will show that this property (that an irrational
number can make any result that it is involved in irrational) can also
be applied to irrational people and discussions. ;-)
Regards,
Pat
MRAB
then the result isn't irrational, so not all operations involving
irrational numbers will result in an irrational result (unless that's
what you mean by "closely related irrational numbers").
Patrick Maupin
Yes, I think I am closely related to myself. But in addition to that
particular disclaimer, I qualified the statement with "most" and I
also mentioned that zero is special. I stand by the assertion that if
you take a random assortment of non-zero numbers, some irrational,
some rational, and a random assortment of numeric operators, that most
operations involving an irrational number will have an irrational
result.
Regards,
Pat
Andreas Waldenburger
wrote:
> Correct. Unfortunately, it doesn't help to use the right ones either.
> In fact, that could almost be a definition of "crackpot" (and alas now
> we approach territory where we risk offending the religious, so I will
> cease and desist).
Except that you didn't. ;)
/W
--
INVALID? DE!
Martin P. Hellwig
Yeah but those numbers have their own problems anyway, one of them being
that you are never sure how big/small they actually are, so by that
logic you could argue that if you can not give an exact measure for a
given number, bickering over it size after an operation is pretty
pointless (pun intended) :-)
Beside the only number that really matters is 42 ;-)
--
mph
Steven D'Aprano
> On Apr 3, 10:17 am, Steven D'Aprano <st...@REMOVE-THIS-
> cybersource.com.au> wrote:
>> On Sat, 03 Apr 2010 15:43:41 +0100, Martin P. Hellwig wrote:
>> > I am replying to this post not because I disagree but because it
>> > postalogically fits the best (I am by no means an expert either).
>>
>> > IMHO, the crackpot in this regard is actually partially right,
>> > multiplication does mean that the number must get bigger, however for
>> > fractions you multiply four numbers, two numerators and two
>> > denominators. The resulting numerator and denominator by this
>> > multiplication get indeed bigger.
>>
>> But you're not multiplying four numbers,
>
> You are if you're using Rationals.
That is sheer unadulterated nonsense.
A rational number (element of Q) is not a pair of numbers, it is a unique
single point on the real number line R which does not depend on either
the way you calculate it, or the representation you use to write it.
The single number 1/2 can be written as any of 1/2, 2/4, 5/10, 1234/2468
or any of an infinite number of ratios representations. It can be written
as a decimal expansion 0.5, or a binary expansion 0.1, or the negative-
binary expansion 1.5, or as the base-eleven infinite expansion that
starts as 0.55555...
Numbers can also be written as continued fractions. The continued
fraction representation for 1/2 is unexciting and happens to include two
digits: [0; 2]. But the continued fraction representation of (say) 5/7 is
[0; 1, 2, 2]. 5/7 isn't four numbers, or three, or two. It is one number.
You might as well argue that 43/92 is "four numbers" -- you have a 4, and
3, and 9, and a 2, hence four numbers. The argument that 1/2 is two
numbers is exactly as foolish as that.
>> you're multiplying two numbers.
>
> Because they're expressed as Decimals.
No, the number of operands is independent of the types of the operands.
Multiplication is a binary operator: it takes exactly two arguments. Not
four, or six, or one. Regardless of whether I write:
Fraction(1,2)*Fraction(7,14)
Decimal('0.5')*Decimal('0.5')
0.5*0.5
MyFraction.from_roman('I', 'II')*MyContinedFraction([0, 2, 0, 0, 0])
I still have two numbers being multiplied.
>> One-half is not "two numbers",
>
> Sometimes it is.
Only on Bizarro world.
>> that would be a tuple
>
> Like this?
>
>>>> gmpy.mpq('0.5')
> mpq(1,2)
No, that's not a pair of numbers. It is a single number, equal to:
∑(i=1,∞,9/10**i)
----------------------
(ln(e)+sin(5π/2))
which is also a single number.
>> or a list or
>> possibly a coordinate pair. One-half is a single number,
>
> When dealing with crackpots, it does not help to use the wrong
> arguments.
And you think that telling the crackpot that he is right, multiplication
always leads to bigger numbers, is somehow going to convince him that he
is wrong about multiplication always leading to bigger numbers?
> When multiplying gmpy.mpq(2,3) by gmpy.mpq(2,3), the
> numerator and denominator have both indeed gotten bigger.
So what? "One quarter" is bigger (longer) than "one half". Your point is?
And in any case:
>>> Fraction(3, 4)*Fraction(2, 3)
Fraction(1, 2)
Would you still like to argue that the numerator and denominator always
get bigger when you multiply two fractions?
> The trick is that when combined, the overall result is smaller.
>> the number which
>> if you double it gives one.
>>
>> Fortunately multiplication is consistent. Multiplying the two numbers
>> 0.5 and 0.5 is exactly the same as multiplying 1*1 and 2*2 then
>> dividing to get a single number. It's not the same as multiplying 1*1
>> and 2*2 to get two numbers, 1 and 4.
>>
>> You say that multiplication means that the number "must get bigger".
>
> Yes, not in every case, but in many cases it does.
That makes no sense. It "must" get bigger, except for the cases where it
doesn't? Or to put it another way: No, multiplication doesn't necessarily
make numbers bigger.
>> 5*1 = 5
>> 5*0 = 0
>> 5*-2 = -10
>>
>> I hope you won't try to argue that 5, 0 and -10 are all bigger than 5.
>
> Yes, but these special cases don't help. It needs to be pointed out that
> the argument is wrong even in cases like 2/3 * 2/3.
The argument is that multiplication ALWAYS makes numbers bigger. Martin,
out of some misguided and confused sense that the representation of a
number was somehow relevant, argued that this is correct. It's not
correct, not even for integers, let alone rationals.
This is why I said that Martin should stop trying to justify the
crackpot's belief that multiplication always makes numbers bigger, even a
little bit. It's not even true for integers. It's not even true for
positive (non-zero) integers. Arguments about numerators and denominators
are just red-herrings.
If the crackpot claimed that dolphins were fish, does it help to say he's
partly right because dolphins live in water and have fins and a tail and
a head just like fish? No. He wouldn't be partly right, he would be
utterly, completely, 100% wrong, and he is utterly, completely, 100%
wrong when he says multiplication always leads to bigger numbers.
For many disagreements, neither party has it completely right and the
truth lies somewhere in between. This is not one of them. Given two
positions, that 1+1=2 and 1+1=7, the correct answer isn't halfway between
them. Given two positions, that 1/2 multiplied by 1/2 is 1/4, or that 1/2
multiplied by 1/2 is NOT 1/4, the truth is not "both positions are partly
correct". One position is just *wrong*.
--
Steven
Steven D'Aprano
>> The square root of 2 is irrational, but if you multiply it by itself
>> then the result isn't irrational, so not all operations involving
>> irrational numbers will result in an irrational result (unless that's
>> what you mean by "closely related irrational numbers").
>
> Yes, I think I am closely related to myself. But in addition to that
> particular disclaimer, I qualified the statement with "most" and I also
> mentioned that zero is special. I stand by the assertion that if you
> take a random assortment of non-zero numbers, some irrational, some
> rational, and a random assortment of numeric operators, that most
> operations involving an irrational number will have an irrational
> result.
There are an infinite number of rational numbers. There are an infinite
number of irrational numbers. But the infinity of the rationals is
countable (1, 2, 3, 4, ... or aleph-0) while the infinity of the
irrationals is uncountable (c or aleph-1), so there are infinitely more
irrationals than rationals.
To put it another way, even though there are an infinite number of
rationals, they are vanishingly rare compared to the irrationals. If you
could choose a random number from the real number line, it almost
certainly would be irrational.
(This is not to be confused with floats, which of course are all rational
numbers.)
--
Steven
Patrick Maupin
cybersource.com.au> wrote:
> To put it another way, even though there are an infinite number of
> rationals, they are vanishingly rare compared to the irrationals. If you
> could choose a random number from the real number line, it almost
> certainly would be irrational.
Yet another correspondence between the set of numbers and the set of
people ;-)
Mensanator
cybersource.com.au> wrote:
> On Sat, 03 Apr 2010 09:35:34 -0700, Mensanator wrote:
> > On Apr 3, 10:17 am, Steven D'Aprano <st...@REMOVE-THIS-
> > cybersource.com.au> wrote:
> >> On Sat, 03 Apr 2010 15:43:41 +0100, Martin P. Hellwig wrote:
> >> > I am replying to this post not because I disagree but because it
> >> > postalogically fits the best (I am by no means an expert either).
>
> >> > IMHO, the crackpot in this regard is actually partially right,
> >> > multiplication does mean that the number must get bigger, however for
> >> > fractions you multiply four numbers, two numerators and two
> >> > denominators. The resulting numerator and denominator by this
> >> > multiplication get indeed bigger.
>
> >> But you're not multiplying four numbers,
>
> > You are if you're using Rationals.
>
> That is sheer unadulterated nonsense.
You obviously don't understand the workings of computers.
>
> A rational number (element of Q) is not a pair of numbers,
Duh. Everybody knows that. But sometimes it is represented
by a pair of numbers such as 1/2 or mpq(1,2).
> it is a unique
> single point on the real number line R which does not depend on either
> the way you calculate it,
There are no "real number lines" inside my computer.
> or the representation you use to write it.
And if you want the computer to do a calculation, then you are
dependent on its representation.
>
> The single number 1/2 can be written as any of 1/2, 2/4, 5/10, 1234/2468
> or any of an infinite number of ratios representations. It can be written
> as a decimal expansion 0.5, or a binary expansion 0.1, or the negative-
> binary expansion 1.5, or as the base-eleven infinite expansion that
> starts as 0.55555...
But we are only discussing those representations that are
a pair of numbers: numerator & denominator. Now look who's
talking nonsense, bringing up things like 0.55555...
>
> Numbers can also be written as continued fractions. The continued
> fraction representation for 1/2 is unexciting and happens to include two
> digits: [0; 2]. But the continued fraction representation of (say) 5/7 is
> [0; 1, 2, 2]. 5/7 isn't four numbers, or three, or two. It is one number.
You're on a roll, aren't you?
>
> You might as well argue that 43/92 is "four numbers" -- you have a 4, and
> 3, and 9, and a 2, hence four numbers. The argument that 1/2 is two
> numbers is exactly as foolish as that.
Are you really that stupid?
>
> >> you're multiplying two numbers.
>
> > Because they're expressed as Decimals.
>
> No, the number of operands is independent of the types of the operands.
> Multiplication is a binary operator: it takes exactly two arguments. Not
> four, or six, or one. Regardless of whether I write:
>
> Fraction(1,2)*Fraction(7,14)
> Decimal('0.5')*Decimal('0.5')
> 0.5*0.5
> MyFraction.from_roman('I', 'II')*MyContinedFraction([0, 2, 0, 0, 0])
>
> I still have two numbers being multiplied.
And you claim that the internal workings of all the above are
the same?
>
> >> One-half is not "two numbers",
>
> > Sometimes it is.
>
> Only on Bizarro world.
I thought you were supposed to be a Python expert?
That you're supposed to understand the difference
between an object and its contents?
Is [1,2,3,4] one number? Of course not, it's four numbers
that are part of one object. A Rational is two numbers,
one object. Yes, squaring a Rational does mean multiplying
two objects, but you know damn well that it involves four
numbers.
>
> >> that would be a tuple
>
> > Like this?
>
> >>>> gmpy.mpq('0.5')
> > mpq(1,2)
>
> No, that's not a pair of numbers.
Yes, it is. Two numbers, one object. Perhaps you need to
read the Tutorial?
> It is a single number, equal to:
The word you want here is "object". This is exactly the reason
these words were invented. They're probably spinning in their grave.
>
> ∑(i=1,∞,9/10**i)
> ----------------------
> (ln(e)+sin(5π/2))
>
> which is also a single number.
"Object".
>
> >> or a list or
> >> possibly a coordinate pair. One-half is a single number,
>
> > When dealing with crackpots, it does not help to use the wrong
> > arguments.
>
> And you think that telling the crackpot that he is right, multiplication
> always leads to bigger numbers, is somehow going to convince him that he
> is wrong about multiplication always leading to bigger numbers?
Of course not. But it may help the OP understand that's one of the
main fallacies that crackpots often engage in. Focusing on something
that's true but is a Non Sequitur.
>
> > When multiplying gmpy.mpq(2,3) by gmpy.mpq(2,3), the
> > numerator and denominator have both indeed gotten bigger.
>
> So what? "One quarter" is bigger (longer) than "one half". Your point is?
That in this case, multiplication did, in fact, make things larger.
It didn't make the object larger, but the numbers it contains are.
The crackpot focuses on the numbers while ignoring the object.
For you to say only the object matters and it's smaller makes you
just as wrong as the crackpot.
>
> And in any case:
>
> >>> Fraction(3, 4)*Fraction(2, 3)
>
> Fraction(1, 2)
Now you're cheating. Again, you know damn well that
Fraction(3, 4)*Fraction(2, 3) = Fraction(6,12)
and what you're seeing is reduction to lowest terms.
I take that back, maybe you really are that ignorant
since you don't seem to grasp the concept of objects.
>
> Would you still like to argue that the numerator and denominator always
> get bigger when you multiply two fractions?
Yep.
But then, you never understand where the crackpot is coming
from. If the crackpot is, in fact, a troll, his goal is not
to get you to believe his bogus math (which he knows is bogus),
but to get you so confused you don't know what's right or how to
defend it.
> It's not even true for integers. It's not even true for
> positive (non-zero) integers. Arguments about numerators and denominators
> are just red-herrings.
Right, as I said, a Non Sequitur.
>
> If the crackpot claimed that dolphins were fish, does it help to say he's
> partly right because dolphins live in water and have fins and a tail and
> a head just like fish? No. He wouldn't be partly right, he would be
> utterly, completely, 100% wrong, and he is utterly, completely, 100%
> wrong when he says multiplication always leads to bigger numbers.
Sounds like you'll never understand math. Better stick
to regular expressions.
>
> For many disagreements, neither party has it completely right and the
> truth lies somewhere in between. This is not one of them. Given two
> positions, that 1+1=2 and 1+1=7, the correct answer isn't halfway between
> them. Given two positions, that 1/2 multiplied by 1/2 is 1/4, or that 1/2
> multiplied by 1/2 is NOT 1/4, the truth is not "both positions are partly
> correct". One position is just *wrong*.
And it seems you can't grasp the concept of a smaller forest
having larger trees.
>
> --
> Steven
Andreas Waldenburger
wrote:
> On Apr 3, 9:03 pm, Steven D'Aprano <st...@REMOVE-THIS-
> cybersource.com.au> wrote:
> > On Sat, 03 Apr 2010 09:35:34 -0700, Mensanator wrote:
> > > On Apr 3, 10:17 am, Steven D'Aprano <st...@REMOVE-THIS-
> > > cybersource.com.au> wrote:
> > >> But you're not multiplying four numbers,
> >
> > > You are if you're using Rationals.
> >
> > That is sheer unadulterated nonsense.
>
> You obviously don't understand the workings of computers.
>
Now this is what's wrong about internet discussions. Nobody actually
defines what they are talking about *until* it becomes a problem. And
then the retconning starts.
This discussion up to this point had not explicitly been about the
workings of computers. It had not really explicitly been about
mathematical numbers either (although to my understanding this had
been implicit, but that's personal).
Let this be a reminder that defining your terms is one of the best
ideas ever. Its the reason for the success of mathematics. I'd like it
to be a reason for the success of discussions as well.
/W
PS: Accusing someone publicly of "obviously" not understanding [some
topic] is pretty low by any standards. And especially so when the
argument for doing so is bogus: Computers by themselves have as much a
notion of Rationals as they have of Irrationals, or, for that matter,
the cuteness puppies. Software does.
--
INVALID? DE!
Andreas Waldenburger
<use...@geekmail.INVALID> wrote:
> Computers by themselves have as much a notion of Rationals as they
> have of Irrationals, or, for that matter, the cuteness puppies.
Strike that. Floats in computers are Rationals. So computers do know
them. However, they are still not "two numbers".
/W
--
INVALID? DE!
superpollo
> On Apr 1, 3:44 pm, superpollo <ute...@esempio.net> wrote:
>> how much is one half times one half?
>
> This is amazing, how can such an off topic post based completely on
> lunacy exist so long here? 54 posts and counting. I think i had this
> very argument in grade school. We have SD'A, Tim Chase, MSRB, and yes
> even Steve Holden again participating in the troll fest (even though
> some of their arguments are true). Of course i would expect mensenator
> to jump into this, but...
>
> A while back i had wondered why Guido never posts to c.l.py anymore.
> Was it because he thinks himself better than us, no, it's because of
> the "low-brow-infantile-Jerry-Springer-ish-nature" that this list has
> imploded into. *puke*
relax mate.
Patrick Maupin
> This is amazing, how can such an off topic post based completely on
> lunacy exist so long here? 54 posts and counting. I think i had this
> very argument in grade school. We have SD'A, Tim Chase, MSRB, and yes
> even Steve Holden again participating in the troll fest (even though
> some of their arguments are true). Of course i would expect mensenator
> to jump into this, but...
Excellent technique. Pick a topic that is guaranteed in any universe
to generate a lot of posts (a short provocative question asked on
April Fool's Day), then stay above the fray, not posting until the
traffic dies down, and only then make a post expressly engineered to
try to start the traffic up again. Rinse and repeat as necessary.
I bow at the feet of the master.
Lie Ryan
Not really. The set of all irrational numbers is not enumerable
(aleph-1) and thus uncountable, but the set of all irrational people is
a countable finite set (even though it may be very difficult to
enumerate them).
Steven D'Aprano
> A while back i had wondered why Guido never posts to c.l.py anymore. Was
> it because he thinks himself better than us, no, it's because of the
> "low-brow-infantile-Jerry-Springer-ish-nature" that this list has
> imploded into. *puke*
Complaining about the infantile nature of the list immediately before
throwing up. Methinks "rantingrick" is projecting just a little.
--
Steven