Solution
= Solution
For a closed path avoiding zero, choose a continuous lift $\gamma(t)/|\gamma(t)|=e^{i\theta(t)}$ and set $w(\gamma;0)=(\theta(1)-\theta(0))/(2\pi)$. Conjugation replaces $\theta$ by $-\theta$, as does reversing the path, so both <winding number>s are $-w(\gamma;0)$.