Re: wanted: mathematician

On 2008-01-04, Gene Ward Smith <gene@xxxxxxxxxxxxx> wrote:
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.

I see it is. I was hoping for a reduction showing how this is
equivalent to one of the variations that actually use the words "choice
function", seeing as it is the Axiom of Choice.

--
Aaron Denney
-><-
.

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