Re: Cantor's definition of set

On Oct 29, 5:41?pm, MoeBlee <jazzm...@xxxxxxxxxxx> wrote:
On Oct 27, 4:23 pm, John Jones <jonescard...@xxxxxxx> wrote:

What dictates the 'order' in an ordered pair? The way it is written
down?

Any number of methods that work, though usually the Kuratowski
definition is used.

Def: <x y> = {{x} {x y}}.

Then we prove <x y> = <z w> iff x=z and y=w.

And for any ordered pair <x y> we can define 1st(<x y>) = x and 2nd(<x
y>) = y.

And to top it off we prove p is an ordered pair iff p = <1st(p)
2nd(p)>

An ordered pair is ordered by a function.

Not with the usual menthod just mentioned.

It is not ordered by
the set

It is an ordered pair.

MoeBlee

I must be honest with you. This is my stance: there is no formal
procedure for establishing order. The beer is on me for anyone who
could derive order or sequence. An ordered pair is an impossibility.
Just log that and forget it. But Frege had some problems with the
metaphysics of sequence, but I think the problems are fatal to any
mathematical enterprise that needs to employ order or sequence.

.

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