\begin{definition}[Definition:Linearly Independent 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 such that they are not linearly dependent.
Then $f$ and $g$ are '''linearly independent'''.
\end{definition}