A binary operation \start : A → A → A : \start → 𝐴 𝐴 → 𝐴 \start:A\to A\to A is associative when x ⋆ ( y ⋆ z ) = ( x ⋆ y ) ⋆ z ⋆ 𝑥 ⋆ 𝑦 𝑧 ⋆ ⋆ 𝑥 𝑦 𝑧 x\star(y\star z)=(x\star y)\star z for all x , y , z 𝑥 𝑦 𝑧 x,y,z .