Integers

This chapter extends the set of natural numbers to integers. The extension has the additive inverse of each of the members. Operations of addition and multiplication are extended. The set of integers with addition and multiplication becomes a group under addition and multiplication being associative and distributive over addition, is a ring. Multiplication operation being commutative, it is a commutative ring. Some people do not consider multiplication identity mandatory for the ring. If people go by this relaxation then this structure is a commutative ring with multiplicative identity. Representation of integers is the same for positive integers. In the case of negative numbers, unsigned value with sign is used. Separate sign indication is good for humans. The addition of numbers with the same sign is simple, but the addition of different signs requires special treatment.