Re: Cantor Confusion

In article <1178878942.895369.182760@xxxxxxxxxxxxxxxxxxxxxxxxxxxx>,
WM <mueckenh@xxxxxxxxxxxxxxxxx> wrote:

On 10 Mai, 22:30, Virgil <vir...@xxxxxxxxxxx> wrote:

In fact, to establish the difference between the diagonal and any
one
other only requires finitely many digits, which WM knows but
chooses to
ignore.

This is also true for the numbers 1.000... and 0.999...

Why must this case be excluded from the proof?

Because they are both excluded from appearing after the point in the
diagonal. The diagonal rule excludes both 0's and 9's after the decimal
point, so automatically cannot be equal to any number whose decimal
expansion can have them there.

I ask: Why must this case be excluded from the proof?
You answer: Because they are excluded.

It was Cantor, or someone of his time, who created that rule, not me.

No, it was not Cantor. It was someone who recognized that lim[n-->oo]
10^-1 = 0 in case of dual representation, i.e., 1.000... = 0.999...

As Cantor DID recognize dual representations, that is insufficient
reason to be sure it was not Cantor.

Unfortunately he did not recognize that he same holds for the
difference between the diagonal number and a list entry in case of
this limit. The reason is clear. Nobody ever considered the case that
a real number is changed in the limit lim[n-->oo] except the natural
"dual representation".

Whatever does it mean to say that " a real number is changed in the
limit"?

Wm seems t be losing what little contact with actuallity he still has to
propound such a footless argument.






And Cantor's proof deceives the reader by
stating that every digit has a finite index. In fact, that is true

So WM accuses Cantor of confusing the reader by stating the truth.

That is far, far better than WM's practice of trying to confuse the
reader by a compilation of falsehoods and nonsense.


nt to yield one and the same number.

The various Cantor-type rules for proper decimals all say, among other
things, that the diagonal shall be made up digits other than 0 or 1.

This is specifically to avoid the problem of dual representations.


Why is there a problem if only digits at finite places are changed?

Why is there a problem with lim[n-->oo] 10^-1 = 0 in one case but not
in another one?

If WM cannot see why on his own, then he has no grasp of the meaning of
Cantor's proofs.
.

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