Re: An uncountable countable set

In article <1152605227.458575.197240@xxxxxxxxxxxxxxxxxxxxxxxxxxx>,
mueckenh@xxxxxxxxxxxxxxxxx wrote:

*** T. Winter schrieb:

> And that is all you have to object against my proof? We have a fixed
> scheme of transpositions.

It is my objection to what you see as the similarity.

But it is not justified. If a fixed rule is given which determines for
each rational when it will be included in the set ordered by magnitude
(and if this is determined for every rational), then the order by
magnitude is established. Remember: You believe in the existence of a
well order, although the smallest rational larger than 1/2 and the
largest rational smaller than 1/2 and so on do not appear.

In any well ordering of all rationals, all appear, but in positions
unrelated to their magnitude as rationals.

"Mueckenh" claims to be able to well-order the rationals in such a way
that there is no first rational in that ordering. That is no more
possible than to have a natural number that is simultaneously even and
odd.

"Mueckenh" claims to do this from an arbitrary well ordering of the
rationals using a sequence of "conditional" transpositions each of which
transposes a successive pair of values if and only if they are not in
their natural order.

Since each is conditional on what has gone before, they must be executed
in sequence to have the claimed effect.

But such endless sequences never end.

If it WERE possible to finish the process and have the rationals well
ordered by magnitude. "mueckenh" should be able to produce the final
result, a well ordering by magnitude, without the bother of any
intermediate stages.

Well, can yuh, punk?
.

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