Types of Numbers

1. Natural Numbers — also called positive integers, counting numbers, or natural numbers. They are the numbers {1, 2, 3, 4, 5, …}

2. Whole Numbers — This is the set of natural numbers, plus zero, i.e., {0, 1, 2, 3, 4, 5, …}.

3. Integers —  This is the set of all whole numbers plus all the negatives (or opposites) of the natural numbers, i.e., {…, ⁻2, ⁻1, 0, 1, 2, …}

4. Rational Numbers — These is all the fractions where the top and bottom numbers are integers; e.g., 1/2, 3/4, 7/2, ⁻4/3, 4/1 [Note: The denominator cannot be 0, but the numerator can be].

5. Real Numbers — This includes all numbers that can be written as a decimal. This includes fractions written in the decimal form e.g., 0.5, 0.75 2.35, ⁻0.073, 0.3333, or 2.142857. It also includes all the irrational numbers such as π, √2, etc. Every real number corresponds to a point on the number line.

6. Irrational Numbers —  All the real numbers that are not rational numbers. An irrational number is a type of real number which cannot be represented as a simple fraction. It cannot be expressed in the form of a ratio. If N is irrational, then N is not equal to p/q where p and q are integers and q is not equal to 0. Example: √2, √3, √5, √11, √21, π(Pi) are all irrational.