Re: wanted: mathematician

From: Gene Ward Smith <gene@xxxxxxxxxxxxx>
Date: Fri, 04 Jan 2008 20:15:12 GMT

Aaron Denney <wnoise@xxxxxxx> wrote in
news:slrnfnt0o6.elb.wnoise@xxxxxxx:

If you multiply together a finite number of finite positive integers
the result is never zero. The Axiom of Choice says an arbitrary
Cartesian product of non-empty sets is non-empty. This means if you
multiply any number, including an infinite number, of nonzero
cardinals, including infinite cardinals, the result is never zero. I
find the idea of multiplying an infinite number of infinities
together and getting zero as a result objectionably
counter-intuitive.

Can you show me the reduction to one of the more standard definitions?
Thanks.

"An arbitrary Cartesian product of non-empty sets is non-empty" is a
standard definition. That means an arbitrary Cartesian product of nonzero
cardinals is not empty, which is the direction I require above.

.

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Re: wanted: mathematician
... Cartesian product of non-empty sets is non-empty. ... cardinals, including infinite cardinals, the result is never zero. ... Can you show me the reduction to one of the more standard definitions? ...
(rec.arts.sf.written)
Re: wanted: mathematician
... Cartesian product of non-empty sets is non-empty. ... cardinals, including infinite cardinals, the result is never zero. ... Can you show me the reduction to one of the more standard definitions? ...
(rec.arts.sf.written)
Re: wanted: mathematician
... Because the way multiplication is defined, the product can't be zero unless ... "If you pick one member from each of the non-empty sets, ... infinite cardinals, ...
(rec.arts.sf.written)
Re: wanted: mathematician
... Cartesian product of non-empty sets is non-empty. ... cardinals, including infinite cardinals, the result is never zero. ... find the idea of multiplying an infinite number of infinities ...
(rec.arts.sf.written)
Re: wanted: mathematician
... Cartesian product of non-empty sets is non-empty. ... cardinals, including infinite cardinals, the result is never zero. ... standard definition. ...
(rec.arts.sf.written)