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?