The following is a list of the sets of numbers in algebra. It is not comprehensive.
- Natural numbers (0, 1, 2, 3 ...)
- Integers = natural numbers and their negative counterparts.
- Rational numbers = numbers that can be expressed as ratiOS of two integers - the second being non-zero.
- Irrational Numbers = real numbers that are not rational. Irrational numbers comprise "ordinary" irrational numbers and transcendental numbers. The first are real roots of algebraic equations with rational coefficients, the second, such as pi and e, are not.
- Imaginary numbers. The square of any real number is not negative. As a result, only non-negative numbers can have real square roots. Imaginary numbers are the square roots of negative real numbers.
- complex numbers. These are numbers which consist of a real part and an imaginary part.
- quaternions: an extension of complex numbers.
There are also separate parts of algebra dealing with infinite and transfinite numbers.
