Re: infinity

Virgil said:
> In article <MPG.1dbef246af19279e98a4c8@xxxxxxxxxxxxxxxxxxxxxxxxx>,
> Tony Orlow <aeo6@xxxxxxxxxxx> wrote:
>
> > David R Tribble said:
> > > Tony Orlow wrote:
>
>
> > > So how are your N and R related? Is R = N^N? Or is there no
> > > defined relation between them?
> > >
> > >
> > In my theory, R is definitely not 2^N.
>
> But is Card(R) = Card(2^N) = Card(P(N)) ?
Probably in your system. I don;t use "cardinality", so that statement has no
meaning in my system.
>
>
>
>
>
> >
> > So, you are thinking, "see? his stuff sucks." But, this question is
> > probably not properly answerable. Between discrete and continuous
> > infinities, there is really no quantitative comparison.
>
> There is the ultimately quantitative Card(N) < Cardf(R), for which there
> exists several excellent proofs other than the Cantor "diagonal" one.
I am not saying that N is not less than R. I am saying it is so much less than
R that neither can be expressed formulaically in terms of the other. Based on
the inverse function rule, R>2^N.
>
> > If there
> > were, then we wouldn't need R. We could simply express it reliably in
> > terms of N. However, this is almost certainly not possible.
>
> Except that Card(P(N)) = Card(R) has been proved to hold outside of
> TOmatics.
Only according to axioms that basically state this fact with no justification.
There is no justification for any such statement. If you disagree, please
explain exactly why this is so. Can you? I doubt you'll even attempt it. You
seem so much more to like insults than math.
>

--
Smiles,

Tony
.

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