I know what $\pi_1(X,\star)$ means. But what does $\pi_1(S^1,(1,0))$ mean? I came across it when wanting to solve the following problem:
“Let $I\in \pi_1(S^1,(1,0))$ be the class of the identity map. Show that $nI$ is the class of the map $f_n:S^1\rightarrow S^1$ given by $f_n(z)=z^n$.” What does this problem want?
Is $(1,0)$ the two element set consisting of $1$ and $0$, or is it an interval? But in both cases it again does not make sense to me as $0$ is not in the circle.