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.

If you want to avail Maths Assignment Help, our math experts are ready to help you.

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]