Re: Question: Given |X|>0 and |Y|>0, can X x Y be empty?
- From: Scott <ToaTerra@xxxxxxxxx>
- Date: Wed, 08 Aug 2007 21:12:35 -0000
On Aug 8, 12:42 pm, magi...@xxxxxxxxxxxxxxxxx (Arturo Magidin) wrote:
Cantor's Argument shows that, given a function f:S->P(S), there is a
set A_f in P(S) that is not in the range of f. Change the function,
you change the set.
This is a good example of what I was talking about in the last post.
If I look at the Cantor's Proof (pg 158 in [1]), no where does it say
given a function f:S->P(S) there is a set A_f in P(S) that is not in
the range of f. It says for each function f:S -> P(S) define a set A_f
in P(S) and A_f is not in the range of f. I would say your statement
is an interpretation of the proof different from mine. Now who is
correct? Well, no matter which way I look at it, it appears I am
correct. So unless you tell me where I'm wrong I do not realize I have
a gap that needs filling.
.
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