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. Regards, Brian. -- Logic empowers us and Love gives us purpose. Yet still phantoms restless for eras long past, congealed in the present in unthought forms, strive mightily unseen to destroy us. http://www.metamilk.com