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Topic: § 432 The complete list is not a square
Replies: 10   Last Post: Feb 18, 2014 4:48 AM

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 wolfgang.mueckenheim@hs-augsburg.de Posts: 3,394 Registered: 10/18/08
Re: § 432 The complete list is not a square
Posted: Feb 14, 2014 3:13 AM

Am Freitag, 14. Februar 2014 00:03:28 UTC+1 schrieb Ben Bacarisse:
> WM <wolfgang.mueckenheim@hs-augsburg.de> writes:
>
>
>

> > Cantor's diagonalization argument.
>
>
>
> What about the other proofs?

They are as wrong as this one, but here we are debating this one.
>
>
>
> <snip>
>

> > {{Usually matheologians confuse infinities. A potentially infinits
>
> > list is always a square up to every n. But the presence of the
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> > antidiagonal cannot be excluded.
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>
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> Yes, it can.
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> Even in WMaths, every potentially infinite row, every potentially
>
> infinite column, every potentially infinite diagonal and anti-diagonal,
>
> has a value.

If it has a value, then the potentially infinite sequence can be determined up to every index n. Not the other way round. Therefore no infinite digit sequence can define a value. But it is hard to understand, because quantifier confusion and reversion of implication is inherent in matheology and gas to be assimilated by their students. Here:
A value yields an infinite digit sequence, but not the other way round.

> The sole proponent of WMaths, Prof. Mueckenheim, explains
> in his textbook how an infinite sequence of decimal digits corresponds
> to a value. If the rows do indeed correspond to real numbers, then so
> do all the other potentially infinite sequences:

If there was a complete correspondence, then you were right.Alas there is no complete correspondence. Proof: Try to recognize a value by the infinite digit sequence without having a finite construction rule. Fail.

Regards, WM