This is the second soft question I am asking today, so I apologise for that. This question, though probably a bit silly has been bugging me for a while and I have not come up with a satisfactory answer. Question is the reason as to why a open interval is used as the domain in the definition of a curve. One reason I can think of is the fact that this ensures a finite speed for the curves at every point which might not be the case at the endpoints of a closed interval. Is there something else to this??Again, my apologies if the question seems a bit too silly.
Edit: My bad, I thought this was common knowledge, so I didnt bother to mention the definition. A curve $ \alpha $ in $ \mathbb R^3 $ is defined as the differentiable function $ \alpha : I \rightarrow \mathbb R^3 $ where $ I $ is an open interval