\begin{definition}[Definition:Left Difference Quotient]
Let $V$ be a vector space over the real numbers $\R$.
Let $f: \R \to V$ be a function.
A '''left difference quotient''' is an expression of the form:
:$\dfrac {\map f {x + h} - \map f x} h$
where $h < 0$ is a strictly negative real number.
\end{definition}