obscure

Not so obscure that it wasn't referenced on this board, this very day.

billytea "Spike's Bitches 21 Gunn Salute" Jan 10, 2005 12:33:02 am PST

eta²: There are infinitely many integers > 0, but there are infinitely many real numbers between 0 and 1. So the number of real numbers is a higher order infinity (or something) than the number of integers.

Yes, there are more real numbers than integers, but that argument doesn't really work. There's also infinitely many rational numbers between 0 and 1, but in fact there are an equal number of integers and rational numbers.

Also? What would transcendental or surreal boobies be like? Discrete/continuous/differentiable/analytic boobies?

Do you want me to explain why there are more real numbers than integers? 'Cause I'll do it, don't think I won't.

What would transcendental or surreal boobies be like? Discrete/continuous/differentiable/analytic boobies?

A boobie is a boobie is a boobie. Unless it's blue-footed and then it's a bird.

I'm wondering how it ended up in this thread...

Well, you know, once the boobies invade, you can never go back. Take Janet Jackson, for example...

I wanna see this:

in fact there are an equal number of integers and rational numbers.

explained. Because it seems to me that the set of all integers would be a non-trivial subset of the set of all rational numbers.

eta: Oh, I found a proof: [link]

eta2: It says

The set Q of all rational numbers is equivalent to the set N of all integers.

Does "equivelent" here mean the same thing as "there are an equal number"? I don't think so....

Whew, saved me from typing out a whole lot of stuff. They're just using lazy notation. Usually, equivalent in mathematics means isomorphic, which has different meanings in different contexts.

Now, if you really want to get your mind blown, look at the Banach-Tarski Paradox or the Continuum Hypothesis.

Does "equivelent" here mean the same thing as "there are an equal number"? I don't think so....

You can put them into a one-to-one correspondence, which can be thought of as having the same number. Counting things is just a matter of putting the things in question into a one-to-one corespondence with a set of known ordinality (like the natural numbers less than or equal to 10, for example). This is an extension of that concept into the infinite realm. One definition of an infinite set is a set that can be put into a one-to-one correspondence with a proper subset of itself.

My unfinished master's thesis was on Georg Cantor. I can go on and on.

One definition of an infinite set is a set that can be put into a one-to-one correspondence with a proper subset of itself.

Leading to this your mama's joke I found here: your mama's so fat she has a proper subgroup isomorphic to herself

∞∈{things that are cool}