Reading a proof about degree oddity of odd continuous maps from $S^1$ to $S^1$, I have the following:
Let $f : S^1 → S^1$ be an odd map :
$\forall z ∈ S^1 ⊂ \mathbb{C}, f (−z) = −f (z)$ $\textbf{(**)}$
If we look at $S^1 \cong \mathbb{R}/\mathbb{Z}$, $\textbf{(**)}$ would tranlate to $ f ([x + 1/2 ]) = f ([x]) + [ 1/2 ]$.
Could you please help me understand this new expression?
Thanks!