Re: infinity

In article <MPG.1d8f52f4d88d036398a263@xxxxxxxxxxxxxxxxxxxxxxxxx> Tony Orlow (aeo6) <aeo6@xxxxxxxxxxx> writes:
> David Kastrup said:
> > Tony Orlow (aeo6) <aeo6@xxxxxxxxxxx> writes:
....
> > >> No, it does not follow. *If* there is a maximal length L, then
> > >> there are finitely many strings with length less than or equal to
> > >> L. There is however no L such that all strings are in length less
> > >> than that L, so it does not follow.
....
> > > To get an infinite set of all string less than or equal to L you
> > > need infinite L.
> >
> > But the set of all strings is not a set of strings less than or equal
> > to some L.
>
> For ANY finite length L, there are a finite set of strings of length L or
> less. For which L in N is the set of all strings up to that length an
> infinite set? For NONE of them. There is not ONE finite string which, in
> the ordered set of strings, has an infinite set of predecessors. Therefore
> the set is finite, since any infinite ordered set MUST have some members
> (an infinite number) which have an infinite number of predecessors.

The therefore does not follow, and the since part is what you are trying
to prove.
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