Numbers can be categorized into different sets or groups. Some sets of numbers are subsets of others.
Natural Numbers
Natural numbers are your common counting numbers. These are all the positive numbers from 1 and on.
{1, 2, 3, 4, 5, … n}
Among the Natural numbers are the Prime and Composite numbers.
- Prime Numbers: A prime number (or a prime) is a natural number greater than 1 that is not a product of two smaller natural numbers. A prime number has exactly 2 factors.
- Composite Numbers: A composite number is any number that is not a prime number. Composite numbers contain more than 2 positive factors.
Whole Numbers
Whole numbers are all of the Natural numbers and Zero (0).
{0, 1, 2, 3, 4, 5, … n}
Integer Numbers
Integers are the positive and negative Natural numbers and Zero (0).
{-n, … -5, -4, -3, -2, -1, 0, 1, 2, 3, 4, 5, … n}
Rational Numbers
Rational numbers are all numbers that can be expressed as the ratio of two Integers.
Examples of Rationals are:
{-5/3, 3/7, 0, 2}
Irrational Numbers
Irrational numbers on the other hand, cannot be expressed as the ratio of two Integers.
Examples of Irrationals are:
{pi, e, phi, sqrt(2)}
Real Numbers
Real numbers are all numbers that can be found on a number line, positive, negative or Zero.
Examples of Real numbers:
{-3.12341, -3.10, -1, 0, 0.235, sqrt(2), 1.95832, 2/3, 3}
Imaginary Numbers
Imaginary numbers are equal the product of a real number and the square root of −1 or i.
Examples of Imaginary numbers:
{-2i, 0, sqrt(-1)}
Complex Numbers
Complex numbers include all real numbers, imaginary numbers, and sums and differences of real and imaginary numbers.
Examples of Complex numbers:
{-1 + 3i, 0, 1}