properties of integers

Summary

Basic properties

Concept

Basic properties

• closure -> product and sum are integers
• commutativity -> result of addition or multiplication is the same regardless of order of the operands
• associativity -> result of multiple operations is the same regardless of order of the operations
• distributivity -> multiplication is distributive over addition, but not the opposite
• trichotomy -> two integers are exclusively either equal to, less than or more than each other

The comes from the German word for numbers “zahlen”

Odd and even integers

assumption 1: Every integer is either odd or even, but not both

Divisibility

• n is a multiple of d

Fraction in lowest term

assumption 2: every rational number can be reduced to a faction in its lowest term