x2

x infinity

You all suck at set theory.

Georg Cantor is ashamed.

Aleph-null squared stars.

That's one major snoozer. They typically go down slowly.

Aleph-null squared is still aleph-null. Back to discrete math with you!

Aleph-null squared=c (the continuum)

To change the magnitude of aleph-null in a mathematically meaningful way, you would need to do something like 2^(aleph-null). This is not "the continuum" (I don't think you really understand the continuum hypothesis), but "aleph-one".

This is still a humorously small (countably) infinite magnitude when compared against something like the cardinality of the set of real numbers.

Somebody didn't do well in discrete.

You're right, you're right, I should have said aleph-null^aleph-null, or 2^aleph-null.

Whether aleph-one (which is uncountably infinite)=c or not is undecidable. (c being the cardinality of the set of real numbers)

Correct me if I'm wrong, I never took discrete math.

That all sounds about right.

If you're genuinely interested in set theory and counting, you should try taking some classes at a local college (assuming they have a halfway decent mathematics or computer science department). Single classes aren't terribly expensive (and if you don't care about credits profs will almost always let you audit them, even if you're not an actually enrolled student), and it's a good way to get some real exposure to the concepts and what they can be used for. Algorithm analysis and complexity theory are some of my favorites (I've done a PhD course in the latter, and a several undergrad/masters level courses in the former). I would recommend some books, but really there is no substitute for a person who knows their shit and is willing to help you puzzle out some of the more inscrutable stuff (and there is a lot of that).

If you're interested in complexity theory I CAN suggest a book, though. "Computers and Intractibility" by Garey/Johnson. You can probably pick it up on amazon.com, and it is fantastic.

Thanks!

Possibly the most unexpected direction ever for a kitty video comment thread to go.

Well said!

Seconded!