Theorem $4\mathrm{.}6\mathrm{.}3.$ Given $f$:$AR$ and a limit point $c$ of $A,\underset{xc}{lim}f(x)=L$ if and only if

$\underset{x{c}^{-}}{lim}f(x)=L,$ and $,\underset{x{c}^{+}}{lim}f(x)=L$

Exercise $4\mathrm{.}6\mathrm{.}4.$ Supply a proof for this proposition.