Corollary: General Associative Law

(related to Definition: Associativity)

Let $(X,\ast)$ be an algebraic structure with an associative binary operation \(\ast\). When we repeatedly apply the operation on a finite number of elements of $X$, the result does not depend on the way we put the parantheses. In other words, we can also omitt the parantheses:

\[x_1\ast x_2\ast x_3\ast \ldots\ast x_n:=(\ldots((x_1\ast x_2)\ast x_3)\ast \ldots)\ast x_n\]

Proofs: 1

Proofs: 1 2

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  1. Knauer Ulrich: "Diskrete Strukturen - kurz gefasst", Spektrum Akademischer Verlag, 2001