# open interval in definition of curve

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

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If you don't give your definition you are using, you have to at least link us to it. – rschwieb Oct 8 '12 at 16:01
As much as I know closed intervals are also used: for example circle parametrisation $(r\cos\theta,r\sin\theta)$ where $\theta$ belongs to $[0,2\pi]$. Notice that circle is closed curve. – Mykolas Oct 8 '12 at 16:17
What about a line? It has no endpoints (indeed, it is an open set), so you need to parametrize it with an open set. – Christopher A. Wong Oct 8 '12 at 18:32
So I guess this is a definition that can be manipulated on a case by case basis, although the standard definition in books is the one i stated. – Vishesh Oct 9 '12 at 3:09
@Mykolas. I was wondering the same thing,partly what made me question this definition. – Vishesh Oct 9 '12 at 3:10