Real Number Axioms

Real Number Axioms

Mathematics is an interesting subject because it is the base for modern technology. It controls and governs trades of modern society.

The study of real numbers is important because it helps us to understand advanced concepts.

Axioms are facts and validated truth about the algebraic relation between mathematical entities. Here we are describing real numbers.

Axiom 1: Associative law
Axiom 2: Communicative law
Axiom 3: Distributive law
Axiom 4: Existence of identities
Axiom 6: Existence of subtraction
Axiom 6: Existence of division
Axiom 7: Transitive law
Axiom 8: Law of Trichotomy

These are the fundamental truth about real number and algebraic operations on them. This leads to exploration of other interesting properties.
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Some interesting questions based on these properties are :

  • Prove that a is positive (negative) if and only if 1/a is positive(negative)
  • If 0<a<b , prove that [latex]1/b < 1/a [/latex]

Real Number Axioms

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