This document defines properties of integers under binary operations. It discusses six properties: commutative, associative, distributive, additive identity, multiplicative identity, and additive inverse. Examples are given for each property using addition and multiplication of integers. The commutative property states that the order of operands does not matter, the associative property concerns grouping of operations, and the distributive property relates multiplication and addition. Additive and multiplicative identities refer to identity elements, and additive inverse is the opposite element under addition.