# Numbers

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 () Integer is a number that can be written without a fractional component ... –1, 0, 1, 2, ...
Rational () Rational number is a number that can be expressed as the quotient or fraction mn of two integers, a numerator m and a non-zero denominator n. 5; 10; 23; 367
Irrational Irrational numbers are numbers that cannot be expressed as a fraction of two integers. $$\pi, \phi, \sqrt{2}$$
Real () 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 () 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.