Re: Cantor Confusion


*** T. Winter schrieb:


> > But whatever, you stated that a definable well-ordering of the reals would
> > lead to a contradiction in ZFC. But you have nowhere shown any proof of
> > that, and it is false. It has been proven that a definable well-ordering
> > of the reals is consistent with ZFC.
>
> Why don't you simply give the formula for the definable well ordering?
> The formula could be evaluated, and, step by step, we would get a list
> of all reals.

Wrong. It would not give a list. It would give a well-ordering. Do you
not know the difference?

Every non empty set of a well-ordering has to have a first element. If
all reals are well-ordered, then all reals are first elements in some
sets.

And I doubt whether you could apply the formula
one by one to each real.

I doubt that too, in fact it is impossible in ZFC. Therefore, there is
no well-ordering of all the reals.
=========================
Because non-distinguishable sets are not different sets. You just
proved that there is no element of a path which distinguished it from
every other path.


Right. But that does *not* mean that it can not be distinguished from every
other path.

If every edge of a path is shared by another path, how would you
distinguish them?


========================


Well, I understand why he [Leibniz] is your favourite.

He is not my special favourite. But he was very wise and he said: The
arithmetic of the infinite has to be based upon the arithmetics of the
finite.
Nach LEIBNIZ sollte das Unendliche dieselben Rechenregeln wie das
Endliche befol¬gen: Die Regeln des Endlichen behalten im Unendlichen
Geltung, wie wenn es Ato¬me (Elemente der Natur von angebbarer fester
Größe) gäbe. (Kontinuitätsprinzip).
All you know of before encountering mathematics is finite. Therefore
you cannot start with the infinite.

============================

Again, a finitistic view. There are algorithms that do calculate that
number. [pi*10^10^100]

Is it even or odd?

That they can not be implemented in a finite world is of no
concern to the mathematician. On the other hand, there *is* a natural
number that is equal to that value.

Is it even or odd?

But apparently you also eschew the proof that li(x) and pi(x) cross
each other infinitely often, because it is impossible to even calculate
the first cross-over.

I do not "eschew" the proof for li(x) and pi(x). These "numbers" seem
to eschew existence.

Regards, WM

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