Re: Question: Given |X|>0 and |Y|>0, can X x Y be empty?
- From: george <greeneg@xxxxxxxxxx>
- Date: Tue, 07 Aug 2007 14:47:41 -0700
On Aug 7, 2:47 pm, Scott <ToaTe...@xxxxxxxxx> wrote:
Prop 4A: (AS != emptyset)(Ap)( p in P(S) -> (Eg_p)(g_p:S -> P(S) & p
in range(g_p) ) ).
Convoluted, but clearly, if the domain is non-empty then the range
must
be too, so you can map everything in the domain to the thing that must
be in the range.
Prop 5A: (AS != emptyset)(Ep)( p in P(S) -> ~(Ef_p)(f_p:S -> P(S) & p
in range(f_p) ) ).
Since this contradicts 4A, this is obviously going to be false.
f_p is, OBVIOUSLY, the function that maps everything in s to p.
You can't say that this function does not exist.
The range of f_p is {p}.
Proof: Let S be any non-empty set. Let A_{f_A} = { x in S : x notin f_A(x) } so A_{f_A} in P(S).
This is already incoherent since you HAVE NOT DEFINED EITHER
of A *or* f_A. You have to stop right here. Nothing else you wrote
matters.
The next two lines after "Let S be any non-empty set" have to be
"Let A be" whatever and "Let f_A be" whatever. Whatever you thought
you meant. Which is of course using "thought" very loosely.
But what does any of this have to do with whether XxY can be empty?
This seems a lot more like the other thread's question about whether a
subset can be proven not to exist.
.
- References:
- Re: Question: Given |X|>0 and |Y|>0, can X x Y be empty?
- From: Scott
- Re: Question: Given |X|>0 and |Y|>0, can X x Y be empty?
- From: Arturo Magidin
- Re: Question: Given |X|>0 and |Y|>0, can X x Y be empty?
- From: Scott
- Re: Question: Given |X|>0 and |Y|>0, can X x Y be empty?
- From: Arturo Magidin
- Re: Question: Given |X|>0 and |Y|>0, can X x Y be empty?
- From: Scott
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