[Haskell-cafe] Functional progr., images, laziness and alltherest

[Stepan Golosunov]

On Thu, Jun 22, 2006 at 03:32:25PM +0100, Brian Hulley wrote:
> Bill Wood wrote:
> >On Thu, 2006-06-22 at 15:16 +0100, Brian Hulley wrote:
> >  . . .
> >>But how does this change the fact that y still has 1 more element
> >>than yq? yq is after all, not a circular list.
> >>I don't see why induction can't just be applied infinitely to prove
> >>this.
> >
> >The set of all non-negative integers has "one more element" than the
> >set of all positive integers, however they have the same cardinality,
> >aleph-null.  This phenomenon is the hallmark of infinite sets.
> 
> Therefore the list of non-negative integers is longer than the list of 
> positive integers. I agree they have the same cardinality but this doesn't 
> mean they have the same length.

Are you saying that some of the (0,1,2,3,4,5,...), (1,2,3,4,5,...) and
(1-1,2-1,3-1,4-1,5-1,...) lists have different lengths?