Difference between revisions of "Space"
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| + | In [[w:mathematics|mathematics]], the [[w:fundamental theorem of algebra|fundamental theorem of algebra]] states that every complex [[w:polynomial|polynomial]] <math>p(z)</math> in one variable and of [[w:degree of a polynomial|degree]] <math>n</math> ≥ <math>1</math> has some complex [[w:root (mathematics)|root]]. In other words, the [[w:field (mathematics)|field]] of [[w:complex number|complex number]]s is [[w:algebraically closed field|algebraically closed]] and therefore, as for any other algebraically closed field, the equation <math>p(z)=0</math> has <math>n</math> roots ([[w:multiple roots of a polynomial|not necessarily distinct]]). | ||
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| + | The name of the theorem is now considered a [[w:misnomer|misnomer]] by many mathematicians, since it is an instance of [[w:mathematical analysis|analysis]] rather than [[w:algebra|algebra]]. | ||
Revision as of 03:01, 26 October 2006
- Organising some notes about spacetime fundamentals from pedia
- The fundamental theorem of algebra
In mathematics, the fundamental theorem of algebra states that every complex polynomial [math]p(z)[/math] in one variable and of degree [math]n[/math] ≥ [math]1[/math] has some complex root. In other words, the field of complex numbers is algebraically closed and therefore, as for any other algebraically closed field, the equation [math]p(z)=0[/math] has [math]n[/math] roots (not necessarily distinct).
The name of the theorem is now considered a misnomer by many mathematicians, since it is an instance of analysis rather than algebra.
