$f:S^1\times S^1\rightarrow S^1$ such that $f(z, w)=z^mw^n$ for some integer $m$ and $n$. Then why $f$ is smooth? By definition a smooth function is differentiable infinitely. So in order to prove $f$ is smooth we need to show it is differentiable infinitely. But from how we defined $f$ it is of course differentiable infinitely thus $f$ is a smooth function. Is there something that I am missing?
2026-03-29 13:47:07.1774792027
Showing function is smooth
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