I am trying to solve an exercise in Hatcher "Algebraic Topology" but am a little confused by the terminology he is using (just so you know, it is exercise 5 in chapter 1.1). He that in the problem 'homotopic' means 'homotopic without regard to basepoints.' In general, Hatcher defines a homotopy between two paths $f, g:I\to X$ with the same endpoints as a continuous function $H:I\times I \to X$ such that $H(-, 0) = f$ and $H(-, 1)=g$ and that $H(0,t)=f(0)$ for all $t$ and $H(1, t) = f(1)$ for all $t$. So when Hatcher says 'homotopic without regard to basepoints' does he mean we can relax the requirement that $f$ and $g$ have the same endpoints in the definition of 'homotopic'?
Thanks for the help!