for / while else doesn't make sense

[Ian Kelly]

On Mon, May 23, 2016 at 9:30 AM, Rustom Mody <rustompmody at gmail.com> wrote:
> Yes the point is being missed but in a different direction:
> The SET (as a completed whole) of real numbers (ℝ) is no more than 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 archaeological
> 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 ℝ legitimately exists was a minority view -- Cantor,Dedekind,
>  Weierstrass...

I'm not sure where ℝ comes into this in the first place. Existing
Python numeric types only represent various subsets of ℚ (in the case
of fractions.Fraction, the entirety of ℚ).

> 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 bad
> dream and the pristine purity of constructive math would be firmly established
> -- where "constructive math" basically means ℕ is the only reasonable infinite set and that ℝ 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.