Re: Cantor Confusion
- From: Virgil <virgil@xxxxxxxxxxx>
- Date: Sun, 01 Apr 2007 13:42:47 -0600
In article <1175414674.648660.163490@xxxxxxxxxxxxxxxxxxxxxxxxxxxx>,
mueckenh@xxxxxxxxxxxxxxxxx wrote:
On 30 Mrz., 21:07, Virgil <vir...@xxxxxxxxxxx> wrote:
Thus the order of application of transpositions makes a difference.
That is not a problem at all. We can work like the cleaning service of
Hilbert hotel: For the first sequence of transposition use half an
hour, for the second sequence use quarter an hour and so on.
If, for example, the nth transposition exchanges the current occupants
of positions n and n+1, what is the final position of the object
originally in first position?
If it does not have a final position, then what you have constructed is
not a permutation of the members of the list.
The replacement of members of a sequence by a rule depending only on the
value and not position of the member being replaced is independent of
the order of operations. let the rule be to replace any lower case
letter by its upper case equivalent.
abc-> Abc -> ABc -> ABC is the same as abc -> abC -> AbC -> ABC
even though the operations were differently ordered.
So the Cantor rule for building an antidiagonal for a list of binary
sequences can be applied independently to different digits
Nevertheless it cannot be applied to the n-th digit unless the
positions 1 to n-1 are known.
It can be applied, as shown above, before anything is /applied/ to prior
positions, which is all that is needful for the validity of the Cantor
proof.
WM's pseudo-permutation is, unlike Cantor's rule, dependent on order of
application.
.
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