On Mon, May 23, 2016 at 9:30 AM, Rustom Mody <rustompm...@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. -- https://mail.python.org/mailman/listinfo/python-list