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

[Brian Hulley]

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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