Re: A new definition of natural numbers

Eckard Blumschein wrote:
On 11/15/2006 9:40 PM, Virgil wrote:

I do not deny possible progress in mathematics. On the contrary.
Abandoning an Utopia will not create that huge heap of rubble which was
warned of by Fraenkel. I see it a new chance. Proficient mathematicians
will not be affected at all from critical evaluation.

Is there any need to use Cantor's transfinite set theory, any example of
useful application of aleph_2 or even more nonsensical phantasmagoria?

Measure theory, among other mathematical developments, requires more
than countable sets.

This might be a wrong interpretation. I will look at the matter. Can you
point me to an example?

Eckard Blumschein

http://en.wikipedia.org/wiki/Measure_theory
http://mathworld.wolfram.com/LebesgueMeasure.html
http://mathworld.wolfram.com/BorelMeasure.html
http://mathworld.wolfram.com/ProbabilityMeasure.html

I did not expect to find a useful application aleph_2 via these links.
I did not even find aleph_2.

You asked for a use of Cantor's transfinite set theory. That is what you
were given.

--
David Marcus
.