Is cardinality a number? It's easy to find definitions such as

*

*If A and B are sets (finite or infinite) A and B have the same cardinality (written $|A|=|B|)$ if there is a bijection between them.

and equally easy to find statements such as

*

*The cardinality of a finite set is equal to the number of elements in it.

If cardinality is not a number, how is the second statement to be understood? Where and how does the transition from 'no cardinality is not a number' to 'yes cardinality is a number' occur?
 A: By definition, $|A|$ is the smallest ordinal number that is equinumerous with $A$.  The finite ordinal numbers are the natural numbers, so the cardinality of a finite set is a natural number by definition.
Infinite cardinals are analogous to natural numbers. Whether they are actually numbers is not a meaningful question, because "number" is not a well-defined term in mathematics. You could also ask whether  is a number, or whether infinitesimals are numbers, etc., and those also are not clear questions.  They are numbers in the sense that mathematicians refer to them as such, as in the phrase "cardinal number"; but I doubt you will find any formal definition of "number" that includes them.
A: Cardinality is a number when considering finite sets.
As soon as you consider infinite sets, it gets much trickier since the cardinality of an infinite set is not finite but yet all infinite sets do not have the same cardinality (see $\mathbb N$ and $\mathbb R$ for instance, or more generally countable and uncountable sets).
