The torsion at $\gamma(s)$ for a unit-speed curve $\gamma$ in $\Bbb R^3$ is the value $\tau \in\Bbb R$ such that $\textbf{b'(s)}= -\tau(s)\textbf{n(s)}$ where $\textbf{b(s)}=\textbf{t(s)}\times\textbf{n(s)}$ is the binormal vector of $\gamma$ at $\gamma(s)$ and $\textbf{n(s)}= \frac{1}{k(s)}\textbf{t'(s)}$ is the principal normal vector of $\gamma$ at $\gamma(s)$ with curvature $k(s)$.
I understand the torsion will not be defined unless our curvature $k(s)$ doesn't equal zero, however I'm not sure how to word it in a mathematical proof/explanation of a sort.