The well-ordering theorem says every set can be well-ordered. In a set theory
where "set" is undefined, how can we be sure the order isn't already there?
The
disorder may be only in our notation, where we use {0,1} and {1,0} for the same
set. In any event, once a well-ordering is established for a given set, you
can
pick out the 0th element, the 1th element, and so on. I agree this picking is
an operation on an ordered set, and that in set theory we usually ignore any
order that may be available for a set. We think of the elements as being
"jumbled in a paper bag." We say, "it's the same club no matter in what order
the members are listed," and "we know the club when we know who the members
are." (Real clubs aren't like that, but sets are.)
...and I prefer well-ordered sets, a generalization of sequences, so we are
together in preference.
Have you figured out the element of A =: set a: ?
Raul Miller wrote:
> On Thu, Jul 30, 2009 at 10:49 PM, Kip Murray<[email protected]> wrote:
>> 1 get S n T
>> 4
>
> This looks like an operation on ordered sets,
> and not an operation simply on sets.
>
> (And, personally, I prefer using sequences
> instead of sets.)
>
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