\begin{definition}[Definition:Anticommutative/Structure with One Operation]
Let $\struct {S, \circ}$ be an algebraic structure
Then $\circ$ is '''anticommutative on $S$''' {{iff}}:
:$\forall x, y \in S: x \circ y = y \circ x \iff x = y$
Equivalently, it can be defined as:
:$\forall x, y \in S: x \ne y \iff x \circ y \ne y \circ x$
The word can also be applied to the structure itself: $\struct {S, \circ}$ is referred to as an '''anticommutative structure''', or described as being '''anticommutative'''.
\end{definition}