Re: Cantor Confusion


Virgil schrieb:

In article <1162828907.384237.5300@xxxxxxxxxxxxxxxxxxxxxxxxxxxx>,
mueckenh@xxxxxxxxxxxxxxxxx wrote:

Virgil schrieb:

In article <1162563567.735020.246810@xxxxxxxxxxxxxxxxxxxxxxxxxxxx>,
mueckenh@xxxxxxxxxxxxxxxxx wrote:

Virgil schrieb:

In article <1162470874.593282.36250@xxxxxxxxxxxxxxxxxxxxxxxxxxxx>,
mueckenh@xxxxxxxxxxxxxxxxx wrote:

WM merely repeated his automatic error several more times here.

WM claims that a list in which the nth listed element is a string of
length at least n characters cannot produce a diagonal of length
greater that any finite number of characters.


The diagonal needs an element from every line, the n-th element from
the n-th line. Therefore it cannot be longer than every line.

The "diagonal"must be longer than every finite "line".

But it cant, because each of its elements stems from a line.

Which line(s) is the diagonal NOT longer than when line n is at least of
length n?

The only way it
will ever fail to be longer than some "line" is if that line is itself
infiitely long.

Which is impossible, because each of its elements stems from a line.

When for all n in N, line n is of length n, which is quite possible,
then for all n in N, the diagonal is of length >= n.

That looks like an infinite diagonal to me.

Actually infinitely long and potentially infinitely broad.

WM is assuming that since every natural is finite, there must be a
largest natural, but in ZF and NBG, that is specifically false.

Intermingling of actual infinity and potential infinity kept these
systems alive, until now.

Regards, WM

.

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