What is ∞ + ∞ = ????

[Kernel Sohcahtoa]

Well, I found this off of Google:

"Even though infinity is not a number, it is possible for one infinite set to contain more things than another infinite set. Mathematicians divide infinite sets into two categories, countable and uncountable sets. In a countably infinite set you can 'number' the things you are counting."

So yeah.

That's referring to infinite sets of finite numbers. Not infinity + infinity.

You're talking about set theory there, that's not what your question in the OP was.

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.