Re: Relative Cardinality

In article <1121607470.554070.85710@xxxxxxxxxxxxxxxxxxxxxxxxxxxx>,
mueckenh@xxxxxxxxxxxxxxxxx wrote:

> Randy Poe wrote:
>
> > > Correct. And if it cannot and never be determined which case is given,
> > > then at least one of the numbers a and b is not a real number.
> >
> > Incorrect. That is an axiom of Mueckianism, not the mathematics
> > of real numbers.
>
> If a and b are real numbers, then one of the three relations holds. If
> there is no method to find out which one it is, then we cannot prove
> which one of the relations holds. That means we cannot prove that one
> of them is true.

What is guaranteed by an axiom need not be proved as a theorem.

> >
> > I hesitate to agree with you, since your "in principle" may
> > exclude infinitely many things which are possible in principle.
> > For instance, in principle you can explore all the digits
> > up to 10^10^10^10^100 to find the difference between a and b,
> > and which one is larger. This is possible in principle even
> > though it will never happen in reality.
>
> No. This is impossible by any principle.

By what principle is it impossible? Only by assuming that physical
limitations apply to all axiom systems as hiddden axioms.
So that WM begs the question, as usual.
.

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