Path: csiph.com!fu-berlin.de!uni-berlin.de!not-for-mail
From: Ian Kelly <ian.g.kelly@gmail.com>
Newsgroups: comp.lang.python
Subject: Re: for / while else doesn't make sense
Date: Mon, 23 May 2016 09:53:12 -0600
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Message-ID: <mailman.36.1464043241.20402.python-list@python.org>
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On Mon, May 23, 2016 at 9:30 AM, Rustom Mody <rustompmody@gmail.com> wrote:
> Yes the point is being missed but in a different direction:
> The SET (as a completed whole) of real numbers (=E2=84=9D) is no more tha=
n a 100 years
> old.
> People may have used fractions earlier
>
> And even here the first line of Steven's http://nrich.maths.org/2515 says
> "Did you know that fractions as we use them today didn't exist in Europe =
until the 17th century?"
>
> Egypt and Babylon (and India for that matter) are really only of archaeol=
ogical
> interest in the sense that there is almost complete loss of continuity
> from then to now

So 13th century European merchants would have been entirely incapable
of cutting a cheese wheel in half in order to accommodate a customer
who didn't the whole thing?

> That the set =E2=84=9D legitimately exists was a minority view -- Cantor,=
Dedekind,
>  Weierstrass...

I'm not sure where =E2=84=9D comes into this in the first place. Existing
Python numeric types only represent various subsets of =E2=84=9A (in the ca=
se
of fractions.Fraction, the entirety of =E2=84=9A).

> On the other side Kronecker belligerently declared:
> "The good Lord made the natural numbers (Zahlen in German)
> All the rest is the work of man"
>
> This was the MAINSTREAM view in the 1880s.
>
> As late as 1918 Weyl and Polya took a bet that math concepts such as
> real numbers, sets, countability etc would be relegated to history as a b=
ad
> dream and the pristine purity of constructive math would be firmly establ=
ished
> -- where "constructive math" basically means =E2=84=95 is the only reason=
able infinite set and that =E2=84=9D is anything but real!
>
> https://en.wikipedia.org/wiki/Hermann_Weyl#Foundations_of_mathematics

I'm rather skeptical that this bet would have extended to fractions.