Believe it or not - in general - it's still infinity.......to see this........consider the set of positive even integers on the number line and the set of positive odd integers on the number line. Both sets are infinite. And if we add them together, the result is just another infinite set - the set of ALL positive integers. This set is also "countable" because we can assign a number to each member. There are also "uncountable" infinite sets. The set of all real numbers that exist between 0 and 1 is an example of an "uncountable" set....!!!!
Georg Cantor may take exception to your answer.
The answer is infinity if both infinities are the same. It is not double infinity! (duh!)
(This posted about one minute after CPhill -- didn't intend to step on your post).