Re: infinity
- From: Virgil <ITSnetNOTcom#virgil@xxxxxxxxxxx>
- Date: Tue, 06 Sep 2005 11:34:38 -0600
In article <MPG.1d87825b1be803b598a1dd@xxxxxxxxxxxxxxxxxxxxxxxxx>,
Tony Orlow (aeo6) <aeo6@xxxxxxxxxxx> wrote:
> Virgil said:
> > In article <MPG.1d7fdf32b4930af698a1c3@xxxxxxxxxxxxxxxxxxxxxxxxx>,
> > Tony Orlow (aeo6) <aeo6@xxxxxxxxxxx> wrote:
> >
> > > There is no one L for all finite strings, but L for every string is
> > > finite,
> > > so
> > > S^L for every string length is finite, so sum(x=1->k: S^x) for finite k
> > > is a
> > > finite size of the language.
> >
> > Then, for s > 1, the number of finite strings is larger that any member
> > of the sequence {S^L, L in N}. Since that sequence is monotonicly
> > strictly increasing and diverges, the "number of such strings is greater
> > than any finite upper bound.
> >
> Yes, it diverges, and becomes infinite, at L=oo.
Except that it never reaches oo.
The set of finite language sizes, a set of natural numbers, has no
finite upper bound, so that there will be injections from that set to
proper subsets, thus making it infinite in the sense of Cantor. Since
What it may be in the sense of TO, who seems to have no sense, is
irrelevant.
.
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