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

There is only one “infinity”. It is a word, with a unique, unitary and universal *meaning*. But as with all words, that single meaning can give rise to an unlimited (potentially infinite) number of *definitions*.

In mathematics, thanks to the groundbreaking work of Georg Cantor, a German mathematician from the late Nineteenth Century, which established a domain of mathematics known as *set theory*, an unlimited number of sets, all infinite in size, can be defined. These can be grouped (as instances or members within a set invented for this purpose) into various (and, again, potentially infinite) “kinds of infinities”. The characteristic of “infinity” applies to all of them, but some kinds of infinite sets can be logically identified as being “larger” than others (a parameter named “cardinality”). This leads mathematicians to describe multiple kinds of infinity as “different” or “multiple” infinities, even though, as I said at the start, there is really only one ***infinity***.