Re: Question: Given |X|>0 and |Y|>0, can X x Y be empty?
- From: magidin@xxxxxxxxxxxxxxxxx (Arturo Magidin)
- Date: Thu, 9 Aug 2007 17:10:10 +0000 (UTC)
In article <1186678707.264315.81580@xxxxxxxxxxxxxxxxxxxxxxxxxxxx>,
Scott <ToaTerra@xxxxxxxxx> wrote:
Thanks, especially too you Arturo. I really appreciate you taking the
time to explain things. Even if it takes severals hits to sink in. :)
It would be far better, far less frustrating for everyone, and far less
time consuming, if you took a better approach.
You read Cantor's Theorem. You misunderstood it, and you could not
figure out how to reconcile that misunderstanding with some other
facts. Fine. It happens.
But you did not post something like: "I read the
proof of Cantor's Theorem; I think I understand it. But I do not
understand why it says that given f:S->P(S) there exists A_f in P(S)
which is not in the range of any function from S to P(S)" (which would
have resulted in many a precise, short, and clear
response). No. Instead, you started by asking "How could I prove a set
does not exist?" and made the question even more vague and useless by
asking that the usual axioms be ignored or discarded. Then you started
asking about functions. Then you asked about cartesian products of two
sets.
None of that was really germain to your confusion, and got you no
closer to figuring out that confusion. It wasn't until you posted
exactly what it was you concluded and you got replies that addressed
that and only that, apparently, that it finally got through your
skull.
->That<- is the main source of the frustration.
It would save you a lot of time if you stopped reading set theory and
learned some basic mathematical logic first. Again, your alleged A in
Logic 101 notwithstanding, you are painfully incompetent at it. And
if, when you find yourself confused, you ask about the confusion
simply and plainly, instead of all this dancing around. You flatter
yourself thinking you are going "beyond the textbook" or are
"exploring the cracks". What you are doing instead of floundering
because you don't know what you are doing.
--
======================================================================
"It's not denial. I'm just very selective about
what I accept as reality."
--- Calvin ("Calvin and Hobbes" by Bill Watterson)
======================================================================
Arturo Magidin
magidin-at-member-ams-org
.
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