In exercise 10, page 26 of Manfredo's Differentiable Geometry of Curves and Surfaces, we are asked to look at the following differentiable curve: $$\alpha(t)=\left\{\begin{array}{ll} (t,0,e^{-\frac{1}{t^2}}) &, \mbox{if}\, t>0 \\ (t,e^{-\frac{1}{t^2}},0)&, \mbox{if}\, t<0\\ (0,0,0) &, \mbox{if}\, t=0 \end{array} \right.$$ The d part of this question asks
Show that τ can be defined so that τ ≡ 0, even though α is not a plane curve.
I have calculated the binormal vector to be $b(t)=(0,1,0)$ for $t>0$ and $(0,0,1)$ for $t<0$, and in both these cases the torsion $\tau=1$. What might he mean when saying that it can defined to be zero?