Let $f$ be a real-valued function whose domain is the set of all real
numbers. Suppose that $f$ is {\bf NOT} continuous at~$a$. Which one of the
following statements is then necessarily true?
\correct There exists $\epsilon>0$ such that for any $\delta>0$ there
exists an~$x$ with $\abs{x-a}<\delta$ and
$\abs{f(x)-f(a)}\ge\epsilon$.
\wrong For any sequence $(x_n)$ with $\lim x_n=a$, $\lim f(x_n)\ne
f(a)$.
\wrong For any $\epsilon>0$ there exists $\delta>0$ such that
$\abs{x-a}<\delta$ implies $\abs{f(x)-f(a)}\ge\epsilon$.
\wrong For any $\epsilon>0$ and $\delta>0$ there exists an $x$ such
that $\abs{x-a}<\delta$ and $\abs{f(x)-f(a)}\ge\epsilon$.
\wrong There exists a sequence $(x_n)$ such that $\lim x_n=a$ and
$\lim f(x_n)=\infty$.
