PEP 276 Simple Iterator for ints (fwd)

[David Eppstein]

In article <9u3uqu$bvfku$1 at fido.engr.sgi.com>, pj at sgi.com (Paul Jackson) 
wrote:

> Greg wrote:
> > ... unless "i in 5" on its own were valid and
> > had a rather unintuitive meaning.
> 
> But "i in 5" does have exactly the meaning needed here,
> for:
>     0 is the nul set
>     1 is the set containing 0
>     2 is the set containing 0 and 1
>     ...
>     5 is the set containing 0 through 4
>     ...
>     n is the set containing 0 through n-1.
> 
> Well ... to the 3 dozen people on the planet who majored
> in set theory this is all quite intuitive.

Well, except that this is only valid over the domain of natural numbers.
Here we are talking about integers not naturals.

I don't know how your set theory class defined the integers, but one 
possible way is equivalence classes of ordered pairs (a,b) (representing 
integers a-b) where a and b are naturals and (a,b) equiv (c,d) when 
a+d=b+c.  And then you have to worry about the set-theoretic definition of 
ordered pairs...but it seems unlikely that you will choose a representation 
for which "i in 5" really does have the meaning discussed here.
-- 
David Eppstein       UC Irvine Dept. of Information & Computer Science
eppstein at ics.uci.edu http://www.ics.uci.edu/~eppstein/