Editing Number (section)

===Complex numbers===
{{Main|Complex number}}
Moving to a greater level of abstraction, the real numbers can be extended to the [[complex number]]s. This set of numbers arose historically from trying to find closed formulas for the roots of [[cubic function|cubic]] and [[quadratic function|quadratic]] polynomials. This led to expressions involving the square roots of negative numbers, and eventually to the definition of a new number: a [[square root]] of&nbsp;−1, denoted by ''[[imaginary unit|i]]'', a symbol assigned by [[Leonhard Euler]], and called the [[imaginary unit]]. The complex numbers consist of all numbers of the form
:<math>\,a + b i</math>
where ''a'' and ''b'' are real numbers. Because of this, complex numbers correspond to points on the [[complex plane]], a [[vector space]] of two real [[dimension]]s. In the expression {{nowrap|''a'' + ''bi''}}, the real number ''a'' is called the [[real part]] and ''b'' is called the [[imaginary part]]. If the real part of a complex number is&nbsp;0, then the number is called an [[imaginary number]] or is referred to as ''purely imaginary''; if the imaginary part is&nbsp;0, then the number is a real number. Thus the real numbers are a [[subset]] of the complex numbers. If the real and imaginary parts of a complex number are both integers, then the number is called a [[Gaussian integer]]. The symbol for the complex numbers is '''C''' or <math>\mathbb{C}</math>.

The [[fundamental theorem of algebra]] asserts that the complex numbers form an [[algebraically closed field]], meaning that every [[polynomial]] with complex coefficients has a [[zero of a function|root]] in the complex numbers. Like the reals, the complex numbers form a [[field (mathematics)|field]], which is [[complete space|complete]], but unlike the real numbers, it is not [[total order|ordered]]. That is, there is no consistent meaning assignable to saying that ''i'' is greater than&nbsp;1, nor is there any meaning in saying that ''i'' is less than&nbsp;1. In technical terms, the complex numbers lack a [[total order]] that is [[ordered field|compatible with field operations]].