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
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