Difference between revisions of "Space"
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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]]. | 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]]. | ||
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| + | In mathematics, a [[w:field (mathematics)|field]] <math>F</math> is said to be [[w:algebraically closed|algebraically closed]] if every polynomial in one variable of degree at least <math>1</math>, with [[w:coefficient|coefficient]]s in <math>F</math>, has a zero ([[w:root (mathematics)|root]]) in <math>F</math>. | ||
Revision as of 03:05, 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.
- Algebraically closed field
In mathematics, a field [math]F[/math] is said to be algebraically closed if every polynomial in one variable of degree at least [math]1[/math], with coefficients in [math]F[/math], has a zero (root) in [math]F[/math].
