I want to know all the possibilities for a combination of $n$ elements when taking their signs into consideration.
If $n=1$, meaning that we consider the set $\{a_1\}$, there are $N=2$ options:$$a_1 > 0 \quad \text{or} \quad a_1 < 0.$$
If $n=2$, meaning that we consider the set $\{a_1, a_2\}$, there are $N=4$ options:$$(a_1 > 0, a_2 > 0), \quad (a_1 < 0, a_2 < 0), \quad (a_1 < 0, a_2 > 0), \quad (a_1 > 0, a_2 < 0).$$
Is it true that the number of possibilities is $2^n$?