Re: Cantor's definition of set

On Tue, 30 Oct 2007 12:16:07 -0700, MoeBlee <jazzmobe@xxxxxxxxxxx>
wrote:


Not the definition of ordered pair, in the sense that

{{x} {x y}} =
{{x} {y x}} =
{{x y} {x}} =
{{y x} {x}}.

Of course, though, we do stipulate that printed formulas are read from
left to right. But we could as well stipulate the opposite.


Moreover, we can define the notions of /First_Coordinate/ and
/Second_Coordinate/, then we can show for any ordered pairs P_1 and P2,
that

P_1 = P_2 <-> First_Coordinate(P_1) = First_Coordinate(P_2) &
Second_Coordinate(P_1) = Second_Coordinate(P_2).

And this equivalence is independent of any direction of reading. (We may
for example decide to consider the element in the singleton set {x} to
be the /first coordinate/ of the pair {{x}, {x, y}}.)


F.

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