- Introduction to Rational Numbers
- Closure law of Whole Numbers Addition and Multiplication
- Closure law of Whole Numbers Subtraction and Division
- Closure law of Integers Addition, Multiplication & Subtraction
- Closure law of Integers Division
- Closure Law of Rational Numbers
- Closure law of Rational Numbers Subtraction and Division
- Closure law of Irrational Numbers Addition and Subtraction
- Closure law of Irrational Numbers Multiplication and Division
- Commutative Law
- Commutative law under Subtration and Division
- Associative Law
- Associative law of Subtraction and Division
- Additive Identity & Additive Inverse
- Multiplicative Identity & Inverse
- Distributive Law
- Distributive Property of Multiplication over Subtraction
- Introduction to Irrational Numbers
- Decimal Representation of Rational Number
- Decimal Representation of Irrational Number
- Square Root
- Properties of Square Root
- More on Properties of Square Root

- Introduction to Real Numbers
- Commutative Law
- Commutative law under Subtration and Division
- Associative Law
- Associative law of Subtraction and Division
- Additive Identity & Additive Inverse
- Multiplicative Identity & Inverse
- Distributive Law
- Distributive Property of Multiplication over Subtraction
- Order of a Surd
- Order of a Surd

- Reflexive And Symmetric Property of Equality
- Transitive Property of Equality
- Additive Property of Equality
- Multiplicative Property of Equality
- Cancellation Property of Equality
- Trichotomy Property of Inequality
- Transitive Property of Inequality
- Additive Property of Inequality
- Multiplicative Property of Inequality
- Inequality Multiplicative Inverse

- Law of Sum of Power of Exponents
- Law of Power of Product of Exponent
- Law of Power of Power of Exponent
- Law of Quotient of Power with Same Base
- Law of Power of a Fraction