I heard about it while watching a TV show, and even after reading through the wikipedia I cannot understand it. [Here](https://en.m.wikipedia.org/wiki/Cantor%27s_paradox) is the wiki for reference. I’d like to understand what the “paradox” behind this is because these sort of things bother me and I feel like I won’t be able to continue without understanding. Thanks in advance!
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Imagine a set S of all existing sets. Now what if we wanted to get, say, the power set that we would call PS. How can that set be new? It must be inside S already, so the paradox lies in the fact that no matter what you do, if you are trying to make a set that includes everything, it cannot be as infinite as the sizes of the infinite sets inside, it must be a larger infinite, the term paradox is coined here because we often think of infinite as, well, infinite, but there are different infinites. Say you were about to count all the way from 0 to infinite, it is larger than infinite for the simple reason that even the set between 0 and 1
is infinite, so counting from 0 to 1 is actually infinite, this is why the actual real set called R is an uncountable infinite and follows this kind of paradox
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