Re: An uncountable countable set

In article <vmhjr2-085B41.11335706072006@xxxxxxxxxxxxxxxxxxxxxx> Virgil <vmhjr2@xxxxxxxxxxx> writes:
In article <1152182749.926627.310460@xxxxxxxxxxxxxxxxxxxxxxxxxxxx>,
mueckenh@xxxxxxxxxxxxxxxxx wrote:
....
Of course. But that does not exclude that these transposition can be
executed and finished (if Cantor's list can be finished).

But it prohibits them from being executed out of their prescribed order.
Since the order of execution induces a well ordering of the set of
transpositions, there would have to be a first transpostion producing
any given effect.

This is (as has been noted alread) wrong. Consider the sequence of
transpositions on N (where I use ordinal numbers for the elements):
(1, 2)(2, 3)(3, 4)(4, 5)...
This sequence places the number 0 further in the sequence of numbers at
each step. If we were to define something like a limit on it, number
0 would be greater than any other natural number (in the imposed ordering),
and so the ordered set would become:
(1, 2, 3, ..., 0)
so the ordinal number of the set is changed from w to w+1, but there is no
first transposition that performs that change.
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