Re: Relative Cardinality



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. That implies that a or b or both are not real numbers.

But it is uninteresting to further discuss this if you want to believe
in things we can never know. Stay with your mathelogy erroneously
called mathematics. I want to propagate the truth but not to convince
by any means. If you are not willing to exchange truth for your false
belief than further talking is useless.

>
> > > It does not say anything
> > > about requiring a simple rule to be able to determine that
> > > truth.
> >
> > It must not be possible by a simple rule. But it must be possible in
> > principle.
>
> 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. Otherwise you should show how
it could be done. it is a part of your religion erroneously called
mathematics.
>
> > > > This principle is strict
> > >
> > > This principle may be strict in Mueckism, but in mathematics
> > > it is not only not strict, it is nonexistent.
> >
> > The axioms are valid in mathematics.
>
> But the "simple rule axiom" is not a valid axiom of the real
> number system. It leaves gaps in the real numbers which will
> cause us all kinds of problems and inconsistencies.

I agree that there will be probems. But that does not help. The "simple
rule" means simply: Not requiring more information than can be stored
in the universe.
>
> > What should axioms be good for if they did not apply?
>
> The verb "apply" in my language requires an object, which you
> have not provided. Therefore I can not answer this incomplete
> question.

"Apply" is only to be used transitive? Is "applicable" better?
I meant: Axioms mst be applicable to real numbers. Numbers must obey
the rules set by the axioms.

Regards, WM

.

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