ordered pair

An ordered pair $⟨x,y⟩$ is a mathematical object in which the order of the components matter. That is to say that $⟨x,y⟩\ne ⟨y,x⟩$. Ordered pairs can be defined in terms of sets like so: $⟨x,y⟩=\{x,\{x,y\}\}$ (note that this is the short-hand notation).