Algebraic number: Difference between revisions
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An algebraic number is a root of a polynomial with rational coefficients. It can be complex. Any polynomial with rational coefficients can be converted to one with integer coefficients by multiplying through by the least common multiple of the denominators, so an algebraic number is also a root of a polynomial with integer coefficients. Thus, <math> \sqrt{2}</math> is an algebraic number. The algebraic numbers include all rational numbers, and both sets of numbers, rational and algebraic, are [[countable set|countable]]. | An '''algebraic number''' is a root of a [[polynomial]] with rational coefficients. It can be complex. Any polynomial with rational coefficients can be converted to one with integer coefficients by multiplying through by the least common multiple of the denominators, so an algebraic number is also a root of a polynomial with integer coefficients. Thus, <math> \sqrt{2}</math> is an algebraic number. The algebraic numbers include all rational numbers, and both sets of numbers, rational and algebraic, are [[countable set|countable]]. | ||
[[Category:CZ Live]] | [[Category:CZ Live]] | ||
[[Category:Mathematics Workgroup]] | [[Category:Mathematics Workgroup]] | ||
Revision as of 14:51, 3 April 2007
An algebraic number is a root of a polynomial with rational coefficients. It can be complex. Any polynomial with rational coefficients can be converted to one with integer coefficients by multiplying through by the least common multiple of the denominators, so an algebraic number is also a root of a polynomial with integer coefficients. Thus, is an algebraic number. The algebraic numbers include all rational numbers, and both sets of numbers, rational and algebraic, are countable.
