What is cardinality of $P(\mathbb{R})$? And $P(P(\mathbb{R}))$?
P is a Power Set, $\mathbb{R}$ is set of real numbers.
In general - how can find cardinality of different sets? Is/are there a good method(s)? And is there some kind of handout, that provides list of cardinality of popular sets ($\mathbb{R}$, $\mathbb{Q}$, $P(\mathbb{Q})$) etc.?
And, how to find cardinality of sets of functions? For example, what is the cardinality of set that contains all functions? What about set of functions $f: \mathbb{N} \to \mathbb{R}$?