Re: Cantor Confusion

Virgil wrote:
In article <1165421742.266029.197420@xxxxxxxxxxxxxxxxxxxxxxxxxxx>,
mueckenh@xxxxxxxxxxxxxxxxx wrote:

Bob Kolker schrieb:

mueckenh@xxxxxxxxxxxxxxxxx wrote:

I have understood the concept and its failure. (That is the parallel
between those who have not yet arrived and those who have already left:
Both are not there.)

What failure?

One of many examples: The set {2,4,6,...,2n} has a cardinal number less
than some numbers in the set. This does not change when n grows (yes,
it can grow!) over all upper bounds. Therefore the assertion that the
set of all even natural numbers has a cardinal number gretaer than any
even number is false.

It appears that the negation of "the set of all even numbers has
cardinal greater than any even number" would have to be " there is an
even natural number as great as the cardinality of the set of all even
natural numbers."

If I am misunderstanding, WM, let him state his own understanding of
what that negations wold be, but without merely appending "is false".

WM is just repeating his incorrect use of limits. Start with

|{2,4,...,2n}| < 2n.

Letting n go to infinity, WM gets

|{2,4,...}| < w.

Or, something like that. It is hard for me to keep track of all of his
wrong arguments. He really is very inventive in coming up with
fallacies.

--
David Marcus
.

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