TITLE: Is it viable to ask in an infinite set about the Cardinality?
QUESTION [5 upvotes]: Can you ask given an infinite set about its cardinality? Does an infinite set have a cardinality? So, for example, what would be the cardinality of $+\infty$?

REPLY [2 votes]: But... "$\infty$" isn't a set. A cardinality is the number of elements in a set. For example, the cardinality of $\{3,4,5\}$ is three.
Yes, infinite sets can also have cardinalities. The rigorous definition is a bit of heavy machinery that you probably don't know about yet. 

To give you an idea though of what the definition will look like: it will say that everything in this world is a set hence $3$ is also a set. Hence when we define cardinality of a set to a set in bijection with the set. To give you an example, the cardinality of the natural numbers $\mathbb N$ is $\mathbb N$ itself. But the cardinality of the integers $\mathbb Z$ is also $\mathbb N$. And the cardinality of the rationals $\mathbb Q$ is also $\mathbb N$. In fact, every countable infinite set you can think of has cardinality $\mathbb N$.
I will stop here since going on into details will only be confusing at this stage.