(related to Proposition: Multiplication of Real Numbers Is Commutative)
Let the numbers \(x_{1},x_{2},\ldots,x_{n}\in\mathbb R\) be given and let \((k_1,\ldots,k_n)\) be an arbitrary permutation of the consecutive indices \(1,\ldots,n\).
Then it is \[x_{k_1}\cdot x_{k_2}\cdot \ldots\cdot x_{k_n}=x_{1}\cdot x_{2}\cdot \ldots\cdot x_{n}.\]
Proofs: 1