The Real Number Axioms

Dr. Holly Hirst
Appalachian State University
The Shodor Education Foundation
June 1998

The real numbers follow the basic field axioms we know and love.

• Additive "Group"
  • Closure
  • Commutativity
  • Associativity
  • Identity
  • Inverse
  
  
• Multiplicative "Group"
  • Closure
  • Commutativity
  • Associativity
  • Identity
  • Inverse
  
  
• Distributivity of Multiplication over Addition

What's left for the Floating Point Axioms

Many of these properties have trouble when the finiteness of the floating point numbers is considered.

• Additive
  • Commutativity
  • Identity - if we're careful
  • Inverse
  
  
• Multiplicative
  • Commutativity
  • Identity - if we're careful