Real Uniform Continuity
Definition
Let $f: \R \to \R $. Then $f$ is
uniformly continuous at $x
\in \R $ if
\[
(\forall \epsilon > 0)(\exists \delta > 0)(\forall x \in
\R )
(\abs{x - y} < \delta \Rightarrow \abs{f(x) - f(y)} <
\epsilon )
\]