Jon Fairbairn wrote:
On 2006-06-22 at 15:16BST "Brian Hulley" wrote:
minh thu wrote:
y and yq are infinite...
But how does this change the fact that y still has 1 more element
than yq? yq is after all, not a circular list.
infinity+1 = infinity
Surely this is just a mathematical convention, not reality! :-)
I don't see why induction can't just be applied infinitely
to prove this.
because (ordinary) induction won't go that far.
I wonder why?
For any finite list yq, |y| == |yq| + 1
So considering any member yq (and corresponding y) of the set of all finite
lists, |y| == |yq| + 1
Couldn't an infinite list just be regarded as the maximum element of the
(infinite) set of all finite lists?
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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