What is ∞ + ∞ = ????

[Edwardo Piet]

In a countably infinite set, the elements in it can be arranged in an infinite list (ordered sequence of terms).  Thus, any countably infinite set, say S, has the same cardinality as the set of positive integers (let's call it P), which contains an infinite number of elements, and so, we can say that there is a 1-1 correspondence between S and P: there is a function, say g, that maps P to S such that, for every element (image) b in S, there exists an element (pre-image) a in P such that g(a)=b (onto function); and, for any two elements x and y in P with x does not equal y, it follows that g(x) does not equal g(y) (one to one function).  Hence, this one to one correspondence between sets is known as a bijection (a function that is both 1-1 and onto).  Regarding uncountable sets, no bijection exists, and so, the elements in an uncountable set cannot be arranged into an infinite list.

Interesting.

I don't know much about the countable/uncountable things... but am I correct that a countable infinite set is an infinite set of finite numbers or something like that?

I didn't understand the part about math. Lol.