Some [[Binary Operation]] / [[Function]] is [[Associative]] if changing the order of *evaluation* does not change result. $\huge x \circ y \circ z = (x \circ y )\circ z = x\circ(y\circ z) $ >[!note] >Note that this is not to be confused with [[Commutative|Commutative Properties]], where the result is sensitive to left-right ordering >[!example]- Example with $\R$ The [[Binary Operation]] $+$ upon all [[Real Numbers]] $\R$ is [[Associative]]. >$ \forall p,q,r\in \R: (p+q)+r=p+(q+r) $ >$ (5+3)+1=5+(3+1) $ > >However, $-$ is not [[Associative]]. >$ \begin{align} >(5-3) - 1 &= 1 \\ >5-(3-1) &= 3\\ >3 \neq 1 \end{align} $