Homotopic Paths have Same Endpoints

Definition
Let $X$ be a topological space.

Let $f, g: \left[{0 \,.\,.\, 1}\right] \to X$ be paths.

Let $f$ and $g$ be homotopic.

Then $f$ and $g$ have the same endpoints.

That is:
 * $f \left({0}\right) = g \left({0}\right)$ and $f \left({1}\right) = g \left({1}\right)$.