Why the hell are there so many “infinities”, in the field of mathematics specifically, and what do they mean and their differences?

Question

I saw a yt vid on largest numbers etc, and extremely baffled by how many versions of infinities are. Didnt know it has premium version like absolute and the regular infinity. lol

In: 0

Answer 1

Ok so the first infinity, what most people think of when they think infinity is countable infinity. That’s the infinity of the whole numbers, you just keep adding one.

beyond that there are two kinds of infinity cardinal infinity and ordinal infinity.

Ordinal infinity omega is just the regular counting number that come after countable infinity. from there you can have omega + 1, omega +2 etc. when you get to the number that is after all the omega + somethings you get to 2 x omega. You can use this scheme to get to really big levels of ordinal inifinty. We use ordinal infinity when the order of the numbers matter.

Cardinal infinity is often used when the order of the numbers doesn’t matter just the size of the infinity. We say that countable infinity, the smallest infinity, is aleph 0. aleph 1 is the next biggest infinity, Omega, beyond this my math isn’t strong enough to really talk about higher alephs.