[The_Reader_David]

Actually, I think compacta as a (singular and plural (!)) for "compact sets" is quite old, although it may be just the Bing school which uses it.

I think your query is addressed in 182.

[Kyrie]

Also, I take back what I said about us being the only ones left on the thread. Still, I don't think anyone else is paying attention to us...

[Kyrie]

Your post on Cantor's diagonal argument was good. At least it worked for me. But talking real math again is so much fun I can't stop now. How about these...?

1. Cantor's theorem proves that the set of reals and the set of natural numbers, both infinite sets, have distinct cardinalities. In fact, no set has the same cardinality as its power set. So by using power sets, beginning with the set of natural numbers, we obtain an infinite ascending chain of infinite cardinals. But is there any distinct cardinal lying strictly between the (countable) cardinality of the natural numbers and the (uncountable) cardinality of the reals?
2. Is the cartesian product of nonempty sets always nonempty? (Better yet: if so, what interesting paradox does that give us?)
3. Is there any way to get mathematical notation into HTML?
4. Do you know of any more FReepers with mathematical interests?

I used to really love this stuff. The first two, anyway. I'm interested in #3 now for different reasons...