Number is one of the basic concepts of mathematics; it includes the concept of a natural number obtained by counting or comparing finite quantities, as well as its various generalizations, including integers, rational numbers, irrational numbers, real numbers, and complex numbers.
| Number system | Description | Example |
|---|---|---|
| Natural (ℕ; ℕ0) | Natural numbers are 1, 2, ... or 0, 1, 2, ... | (0), 1, 2, 3, ... |
| Integer (ℤ) | Integer is a number that can be written without a fractional component | ... –1, 0, 1, 2, ... |
| Rational (ℚ) | Rational number is a number that can be expressed as the quotient or fraction m⁄n of two integers, a numerator m and a non-zero denominator n. | 5; 10; 2⁄3; 36⁄7 |
| Irrational | Irrational numbers are numbers that cannot be expressed as a fraction of two integers. | $$\pi, \phi, \sqrt{2}$$ |
| Real (ℝ) | Real numbers are all rational and irrational numbers i.e all positive and negative numbers and zero i.e all algebraic numbers and transcendental numbers (Nt. π, e). | |
| Complex (ℂ) | complex number is a number that can be expressed in the form$$a+ib,$$ where a and b are real numbers, and i is a symbol called the imaginary unit, and satisfying the equation $$i^{2}=-1.$$ Real numbers can be viewed as complex numbers with an imaginary part equal to 0. |