Re: An uncountable countable set

In article <1152133786.204995.294260@xxxxxxxxxxxxxxxxxxxxxxxxxxxx>,
mueckenh@xxxxxxxxxxxxxxxxx wrote:

Virgil schrieb:

Wrong. The scheme is a fixed matrix and each line can be applied
simultaneously.

(1,2), (3,4), (5,6), ...
1, (2,3), (4,5), (6,7), ...
(1,2), (3,4), (5,6), ...
1, (2,3), (4,5), (6,7), ...
(1,2), (3,4), (5,6), ...
1, (2,3), (4,5), (6,7), ...

Since any line and the following line both act on the same elements,
they cannot be applied simultaneously, and they do not "commute", but
must be applied sequentially.

What has commutation to do with this proof?

Absence of commutativity, which is the case with certain transpositions
and sequences of transpostions, means that they must be applied in
sequence and not simultaneously as "mueckenh"'s theory requires.
.

Relevant Pages

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