Let $f(x)$ be defined on $[0,1]$ such that $f(x) = 0$ if $x \in \mathbb{Q} \cap [0,1]$ and $f(x) = 1$ if $x \notin \mathbb{Q} \cap [0,1]$. Which of the following is true regarding the limit $\lim_{x \to c} f(x)$?