(related to Definition: Commutativity)
Let $(X,\ast)$ be an algebraic structure with a commutative binary operation "$\ast$" and let \(x_{1},x_{2},\ldots,x_{n}\in X\) be finitely many many elements of $X$. Let \((k_1,\ldots,k_n)\) be an arbitrary permutation of the consecutive indices \(1,\ldots,n\). Then it follows \[x_{k_1}\ast x_{k_2}\ast \ldots\ast x_{k_n}=x_{1}\ast x_{2}\ast \ldots\ast x_{n}.\]
Proofs: 1
Proofs: 1