Symbols:P

Power Set
$$\mathcal{P} \left({S}\right)$$ is the power set of the set $$S$$.

It is defined as: $$\mathcal{P} \left({S}\right) = \left\{ {T: T \subseteq S}\right\}$$.

Its LaTeX code is \mathcal{P} \left({S}\right).

$$\mathfrak {P} \left({S}\right)$$ is an alternative notation, but the "fraktur" font, of which $$\mathfrak {P}$$ is an example, is falling out of use, probably as a result of its difficulty in being both read and written.