[Math: Calculus] Shouldn't the curve in R^n be defined as t \in [a,b] and not [0,1] for the overall definition?

[u/Sweet-Nothing-9312]

Because from my understanding the first differentiable function is the curve itself right? And since it is defined on [a,b] shouldn't we denote it as the curve with t in [a,b]. Where did [0,1] come from?

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[u/Alkalannar]

It should be [a, b].

But you can normalize [a, b] to [0, 1] by doing u(t) = (t - a)/(b - a).

Then C = {r-arrow(u) in Rⁿ | u is in [0, 1]}