Lemma 3.2.3.9. Let $\alpha $ and $\beta $ be elements of $\pi _{n}(X,x)$. For $2 \leq i \leq n$, we have $m_{i}(\alpha , \beta ) = m_{i-1}( \beta , \alpha )$.
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Lemma 3.2.3.9. Let $\alpha $ and $\beta $ be elements of $\pi _{n}(X,x)$. For $2 \leq i \leq n$, we have $m_{i}(\alpha , \beta ) = m_{i-1}( \beta , \alpha )$.
Proof. Combining Lemma 3.2.3.8 with Example 3.2.3.6, we obtain