Just wanted to brush up on my definitions.
The question states:
Let $r :\mathbb{R}^1\rightarrow \mathbb{R}^n$ be a representation of a curve. Whats the definition for $r$ to be smooth?
My definition is: A curve $r :\mathbb{R}^1\rightarrow \mathbb{R}^n$ is smooth iff it's $C^\infty$.
Is this a correct statement ?
Sometimes only $C^1$ is required. Or... some authors write the expression like smooth enough. What does it mean? If you want to compute, say, a curvature, you need $C^2$, so in th is context smoooth enough means $C^2$. And so on...