Re: infinity

Daryl McCullough said:
> Tony Orlow (aeo6) <aeo6@xxxxxxxxxxx> writes:
> >1) The size of any set of naturals from 1 through n is equal
> >to n, the largest element.
>
> True.
>
> >2) The set of naturals only contains finite elements.
>
> True.
>
> >3) the size of the set of naturals is aleph_0, an infinite number and NOT a
> >natural.
>
> True.
>
> >Do you resolve this by simply denying the existence of a valid
> >inductive proof, or do you admit a contradiction?
>
> Why do you say there is a contradiction? 1) and 3)
> are two different branches of an if then else:
>
> For any set A of consecutive naturals including 1:
>
> if A has a largest element then
> size(A) = the largest element of A
> else
> size(A) = aleph_0
Why must you have this "else", except to preserve an inconsistent system? If A
has a largest element, that is the set size, and if A has a set size, that is
the largest element. They are one and the same number. Do you know what
"equal" means?
>
> If there is a largest element, then 1) applies. If there
> is no largest element, then 3) applies. There is never a
> case where both apply.
3) is bull*** and contradicts all sense.
>
> --
> Daryl McCullough
> Ithaca, NY
>
>

--
Smiles,

Tony
.

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