Re: Cantor's definition of set

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


.

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