## Numbers

*See also: prime numbers, GCD and LCM, significant figures and scientific notation*

In Mathematics, a number can be classified into different types. They are complex numbers, imaginary numbers, real numbers, rational numbers, irrational numbers, integers and natural numbers.

- Natural Number (ℕ)
- Also called
**counting number**or**whole number**. There are two definitions of natural number.- an element of the set { 1, 2, 3, 4, ... }
- an element of the set { 0, 1, 2, 3, 4, ... }

*positive integers*(without 0) and*nonnegative integers*(includes 0) are recommended.

Example: 1, 2, 4, 7, etc. - Integer (ℤ)
- Number that can be written without a fractional or decimal component. The set of integers consists of natural numbers, their negatives and the number zero.

ℤ = { ..., -2, -1, 0, 1, 2, ... }. The symbol ℤ stands for Zahlen (German for numbers).

Example: -12,-3, 0, 4, 5 etc. - Rational Number (ℚ)
- Number that can be expressed as a fraction. The symbol ℚ stands for quotient.

Example: -23,-3.5, 0, 2, 2¾, 4.7, etc. - Irrational Number
- Number that cannot be expressed as a fraction.

Example: √2, √3, π, e, etc. - Real Number (ℝ)
- Number that is in one-to-one correspondence with the points on the infinite number line. The set of real numbers consists of rational and irrational numbers.

Example: √2, -3.4, 1, etc. - Imaginary Number
- Number whose square is a negative real number. It's denoted by the symbol i, where i = √-1.

Example: 2i, -4i, 5i, etc. - Complex Number (ℂ)
- Number of the form a + bi, where a and b are real numbers and i is the imaginary unit (i = √-1).

Example: 2 + 3i.

*See also: prime numbers, GCD and LCM, significant figures and scientific notation*