\begin{definition}[Definition:Homotopy/Path]
Let $X$ be a topological space.
Let $f, g: \left[{0 \,.\,.\, 1}\right] \to X$ be paths.
We say that $f$ and $g$ are '''path-homotopic''' if they are homotopic relative to $\left\{ {0, 1}\right\}$.
\end{definition}