Re: infinity
- From: Tony Orlow (aeo6) <aeo6@xxxxxxxxxxx>
- Date: Tue, 6 Sep 2005 13:53:06 -0400
Daryl McCullough said:
> Tony Orlow wrote:
> >
> >Daryl McCullough said:
>
> >> >> [1] For all s a string, exists L a length s.t. L > len(s)
> >> >>
> >> >> [2] Exists L a length s.t. for all s a string, L > len(s)
>
> >> So are you saying that [2] means the same thing as [1], even though
> >> the quantifiers are reversed?
>
> >No, I am saying that [1] implies [2].
>
> But [1] is true even if we restrict L and s to be *finite*:
>
> [1'] For all s a finite string, exists L a finite length
> s.t. L > len(s)
>
> In contrast, [2] is certainly *false* if we restrict s and L to be
> finite:
>
> [2'] Exists L a finite length s.t. for all s a finite
> string, L > len(s)
>
> --
> Daryl McCullough
> Ithaca, NY
>
>
True. I'll concede this point, that there is no largest finite length, but if
all lengths are finite, then none are infinite, and the language cannot be
infinite. The only way to get sum(x=1->k: S^x) to be infinite for finite k is
to claim that there are an infinite number of finite k, so you are summing an
infinite number of finite terms. However, there cannot be an infinite number of
finite k, since k is incremented each iteration, and after being incremented
infinite times, becomes infinite.
--
Smiles,
Tony
.
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