\begin{definition}[Definition:Linearly Dependent Real Functions]
Let $f \left({x}\right)$ and $g \left({x}\right)$ be real functions defined on a closed interval $\left[{a \,.\,.\, b}\right]$.
Let $f$ and $g$ be constant multiples of each other:
:$\exists c \in \R: \forall x \in \left[{a \,.\,.\, b}\right]: f \left({x}\right) = c g \left({x}\right)$
or:
:$\exists c \in \R: \forall x \in \left[{a \,.\,.\, b}\right]: g \left({x}\right) = c f \left({x}\right)$
Then $f$ and $g$ are '''linearly dependent'''.
\end{definition}