for / while else doesn't make sense

[Rustom Mody]

On Monday, May 23, 2016 at 7:59:47 PM UTC+5:30, Ben Bacarisse wrote:
> Ian Kelly  writes:
> 
> > On Mon, May 23, 2016 at 2:09 AM, Steven D'Aprano wrote:
> >> Are you saying that the Egyptians, Babylonians and Greeks didn't know how to
> >> work with fractions?
> >>
> >> http://mathworld.wolfram.com/EgyptianFraction.html
> >>
> >> http://nrich.maths.org/2515
> >>
> >> Okay, it's not quite 4000 years ago. Sometimes my historical sense of the
> >> distant past is a tad inaccurate. Shall we say 2000 years instead?
> >
> > Those links give dates of 1650 BC and 1800 BC respectively, so I'd say
> > your initial guess was closer.
> 
> Right, but this is to miss the point.  Let's say that 4000 years have
> defined 1/3 to be one third, but Python 3 (as do many programming
> languages) defines 1/3 to be something very very very very close to one
> third, and *that* idea is very very very very new!  It's unfortunate
> that the example in this thread does not illustrate the main problem of
> shifting to binary floating point, because 1/2 happens to be exactly
> representable.

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

That the set ℝ legitimately exists was a minority view -- Cantor,Dedekind,
 Weierstrass...

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

For a conspectus showing that:
- our current views are fairly recent (compared to Egypt, Babylon etc)
- that far from being universally accepted they were hotly disputed
- And thence gave rise to our field of CS
see http://blog.languager.org/2015/03/cs-history-0.html