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}

A boobie meara (not to be confused in any way with a meara boobie):

A positive boobie + a negative boobie does not cancel out to zero boobies. The sum would be two boobies. and the world rejoices.

Good thing boobies aren't like matter/anti-matter or the universe would explode.

They must be evil twins.

They do tend to come in pairs.

A boobie is a boobie is a boobie.

"Sometimes a boobie is just a boobie." I think Freud came up with that around the time he came up with the theory of "bosom envy".

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

Heh. "Your mama's pegleg got a kick stand on it / Yer mama, yer mama, yer mama, yer mama..."

t nerd

This is the best thread EVER.

Also, I totally knew that ∞ + 1 was countable. But the context clearly implied that he wanted something bigger for Out of Gass than Objects in Space, so I did the only thing my math allowed and elevated the cardinalities.

And now I'm trying to remember the proof that real numbers are uncountable. I think I may have done something before that proved that the irrational numbers between 0 and 1 were uncountable, which is clearly a sufficient proof, but I don't remember how I did it exactly.

Internet!

And now I'm trying to remember the proof that real numbers are uncountable. I think I may have done something before that proved that the irrational numbers between 0 and 1 were uncountable, which is clearly a sufficient proof, but I don't remember how I did it exactly.

The simplest proof that I can remember right now is to assume that they are countable, and give some enumeration of them. Then you can make a real number by putting in the tenths place any digit but what's there in the first real number in your enumeration, putting in the hundredths place anything but the hundredths digit in your second real number, and so on. You end up creating a real number between 0 and 1 that can't possibly be in your enumeration.