From: "Mauricio Fernández" <batsman.geo@...>
Date: 2003-02-13T17:33:54+09:00
Subject: Re: Range#length?

On Thu, Feb 13, 2003 at 01:07:37PM +0900, William Djaja Tjokroaminata wrote:
> Hi Matz,
> 
> I was taking the point from ahoward, which said
> 
>     "what would be the last_member of (0.0 ... 42.0) ??"
> 
> In any Advanced Calculus or Real Analysis course, they introduced the
> concept of "Supremum" (sup) which is the smallest upper bound and
> "Infinum" (inf) which is the greatest lower bound.  A smallest upper bound
> that belongs to the set is also called Maximum, and similarly, a greatest
> lower bound that belongs to the set is also called Minimum.
> 
> Therefore, (0.0 .. 42.0).max == 42.0 but (0.0 ... 42.0).max does not
> exist.  However, (0.0 .. 42.0).sup and (0.0 ... 42.0).sup both exist and
> are equal to 42.0.
> 
> For a quick, more formal treatment of the subject, we can read e.g.
> 
>     http://www.math.purdue.edu/~rcp/11_sup-inf_public.pdf
> 
> I am sorry if I am being too formal mathematically; I was only responding
> to ahoward's points.

This is mathematically sound, but in which context would you use it?

All our problems come from trying to define ranges over compact metric
spaces (although floats really aren't). A way to differentiate would be
introducing a new notation
 
  'a'..'b'    'a'...'b'         
  1.0 -- 2.0   1.0 --- 2.0     compact 
and warnings when Ruby realizes you're mistaken in your choice of range.
They easiest way to find whether '..' or '--' are right would be testing
for #succ. 

This is however ugly and I'd stay with what we have now.

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