Re: Cantor Confusion


Franziska Neugebauer schrieb:


All elements that can be shown to exist in the diagonal can be
shown to exist in one single line. [(P1)]

This proposition P1 has _not_ yet been proved (shown).

This proposition is the definition of the diagonal.

You misinterpret L_D. L_D is that line which contains all numbers
contained in the diagonal.

The Diagonal is unbounded thus any _assumed_ L_D is not bounded, too.

Correct is:
If the diagonal is unbounded then any _assumed_ L_D is not bounded,
too.

From the finiteness of any L_D we obtain: The diagonal is not
unbounded.

Hence L_D cannot be a line of the list (meaning: cannot be _in_ the
list) for any line in the list is bounded (proof by induction).

Hence contradiction to P1. P1 must be dropped.

If your L_D does not contain them, then you have the wrong L_D.

Upto now we have no line L_D at all since P1 has not been proved.

There is nothing to prove in a definition. I remember you said a
definition cannot be wrong. So it cannot be proved.

Regards, WM

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