Re: Question: Given |X|>0 and |Y|>0, can X x Y be empty?

On Aug 8, 8:08 pm, G. Frege <nomail@invalid> wrote:
On Wed, 08 Aug 2007 23:54:28 -0000, Scott <ToaTe...@xxxxxxxxx> wrote:

I told you 5 times already to STOP writing (Ex)(whatever) and START
writing [what HE -george- prefers].


Franz, seriously, if you're not part of the solution, you're part of
the
problem. The issue here is pedagogical. The student has revealed
that he is prone to confusion. One of the first steps in attacking
that
is to decrease OPPORTUNITIES for confusion and one of the first paths
to that is to reduce AMBIGUITY AND OVERLOADING. If the same symbol
is interpretable in more than 1 way then it greatly increases the
probability
that the student will pick the wrong way. You will recall that when
I asked Scott to interpret
Ex[exists(x)], he said it was the same as (Ex)(Ex)(x).
UNDER HIS NOTATION, THE (Ex) IN THE MIDDLE IS AMBIGUOUS,
and the string as a whole doesn't even parse. It was ONLY because he
was
TRYING to go into a notation that IS FLAWED in that it OVERLOADS
parentheses
unreasonably, that that lesson went untaught.
*I* am teaching here; this is MY class; you can be SUPPORTIVE or you
can
GET OUT.


[You see, the only CORRECT notation is the one HE uses,
of course.] :-)


That is NOT funny.
THERE OBVIOUSLY IS A GOOD REASON for preferring THIS notation in THIS
context. EVERYbody who knows how this stuff works knows that ANY
notation
whatSOEVER is "correct" as long as you USE it correctly and
consistently!
I myself make that point every time anyone is fool enough to talk
about "the language
of arithmetic" or to insist on an "interpreted theory" in a context
where it is in fact
the LANGUAGE AND NOT the theory that is getting interpreted and where
that interpretation
WAS IN FACT IRRELEVANT, since ANY interpretation that SATISFIED the
theory would
do.

(Sometimes discussions with GG are rather cumbersome.)

And sometimes YOU are a complete jerk. What's new?


But (Ex)(whatever) *is* correct notation.

Sure.

Wrong.



See:http://en.wikipedia.org/wiki/Quantification#Notation_for_quantifiers

That is DEscriptive, NOT PREscriptive, idiot.

The brute weight of usage may suffice to make something tolerable but
it cannot
make it reasonable.

.

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