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

Brian Hulley brianh at metamilk.com
Thu Jun 22 10:32:25 EDT 2006

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.


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