Parity Party

For any $n \in \N$ , let $S$ be a set of real numbers such that: $S = \bigcup\limits_{i=1}^{n} S_i$ , where $S_i = [l_i, r_i)$ , $l_1 \geq 0$ and $l_i < r_i \leq l_{i+1}$ . Let: $\overline{S} = \bigcup\limits_{i=1}^{n} \overline{S_i}$ , where $\overline{S_i} = (-r_i, -l_i]$ . Now, let: $X = S \cup \overline{S}$ . Any function $f(x)$ defined on $X$ such that $f : X \to \{0\}$ is both odd and even, since $f(x) = f(-x) = -f(-x) = 0$ , $\forall x \in X$ .

If we set the function to be $f(x)=0$ , it is as even as odd function