In the game of
rock paper scissors, let M := \{ r, p, s \} , standing for the "rock", "paper" and "scissors" gestures respectively, and consider the
binary operation \cdot : M \times M \to M derived from the rules of the game as follows: : For all x, y \in M: :* If x \neq y and x beats y in the game, then x \cdot y = y \cdot x = x :* x \cdot x = x I.e. every x is
idempotent. : So that for example: :* r \cdot p = p \cdot r = p "paper beats rock"; :* s \cdot s = s "scissors tie with scissors". This results in the
Cayley table: as shown by: :r \cdot (p \cdot s) = r \cdot s = r but :(r \cdot p) \cdot s = p \cdot s = s i.e. :r \cdot (p \cdot s) \neq (r \cdot p) \cdot s It is the simplest non-associative magma that is
conservative, in the sense that the result of any magma operation is one of the two values given as arguments to the operation. == Applications ==