Re: infinity

Virgil said:
> In article <MPG.1d88e1864a974a3b98a204@xxxxxxxxxxxxxxxxxxxxxxxxx>,
> Tony Orlow (aeo6) <aeo6@xxxxxxxxxxx> wrote:
>
> > Randy Poe said:
>
> > > Empty words, no reasoning. Let's look at the actual expression you
> > > try to write.
>
> > Empty words? All lengths are finite, and for any finite length the
> > language up to that length is finite, so the language is finite.
>
> TO asserts that the number of words of finite length is finite.
>
> Since any concatenation of any set of words creates a word not in the
> original set, the TO's claim fails. There cannot be a finite set
> containing all possible finite words, since such a set cannnot contain
> any concatenation of all the words in it.
>
> Since such concatenations of infinitely many words do not create words
> of finit lengths, it appearsas if any set of ALL words of finite length
> must not be a finite set.
>
>
> > The statement applies to ALL finite strings. If ALL strings are
> > finite, then there are NO infinite lengths, and the sum can NEVER be
> > infinite.
>
> Show us any finite set of finite words that contains the finite word
> formed by any concatenation of all its members.
>
> TO can't show us any? Surprise, surprise!
>
> Come back again when you can do this impossibility, TO, but until then
> shut up about claiming things that are impossible.
>
I never claimed to be able to do what you are suggesting. I have explained how
this contradiction derives from the contradiction of the largest finite, so
your dozen or so reiterations of this "proof" by contradiction doesn't convince
me of anything but that you come up with one idea at a time. No, you cannot
specify the largest finite (although, remarkably, you have, as aleph_0!) and
you cannot sum all finite naturals without knowing this number, so that is
equally impossible. However, you CAN equate the set size with the largest
element inductively, and derive a contradiction between alpeh_0's infinity
based on your "largest finite" argument, and aleph_0's finiteness based on the
fact that the set size is always the largest member of the set and that the set
only contains finite naturals. How do you resolve this? By ignoring a valid
inductive proof? You theory WOULD appear to be internally inconsistent.
--
Smiles,

Tony
.

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