Let $S \subseteq R$. Consider the statement:
"There exists a continuous function $f:S \rightarrow S$ such that $f(x) \neq x$ for all $x$ belongs to $S$."
This statement is false if $S$ equals
- $[2,3]$
- $[2,3]$
- $[-3,-2] \cup [2,3]$
- $(-\infty \text{ to} +\infty)$