In the definition of continuity the interval $I$ may be replaced by an arbitrary finite union of intervals. Consider $X = (-1, 0) \cup (0, 1)$ and the function $f:X \to \mathbb{R}$ defined by $$ f(x)=\begin{cases} 1 &\text{if $x \in (0, 1)$}\\ -1 &\text{if $x \in (-1, 0)$} \end{cases} $$ Decide whether or not the function f is continuous and prove it using epsilon-delta.
My initial thoughts were that this was continuous by allowing epsilon = delta, though now I'm not sure...
Edit:
Thank you very much for editing it! I'm still quite new to this math jax business