properties of integers


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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”

Application

Definition of odd and even integers

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

Definition of divisibility, d divides n if d is a factor of n

Definiton of fraction in lowest term,

Assumption 2: Every rational number can be reduced to a faction in its lowest term

Definition of colorful for #cs1231s