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...ree [[field extension]] of the field <math>\mathbb{Q}</math> of [[Rational number|rational numbers]]. ...rs, is the central topic of [[:en:Algebraic_number_theory|algebraic number theory]]. ...

== Algebraic over <math>k</math> == ...math>K</math> is called algebraic over <math>k</math> if it satisfies some algebraic equation with coefficients in <math>k</math>, and transcendental otherwise. ...

In elementary math, the main example is f(x) = x with the [[Real number|set of numbers]]. == Algebraic properties == ...

[[Category:Algebraic geometry]] [[Category:Number theory]] ...

...lled a '''transcendental number''' if it cannot be found as a result of an algebraic equation with [[integer]] coefficients. ...ental can be very hard. Each transcendental number is also an [[irrational number]]. The first people to see that there were transcendental numbers were [[Go ...

...mbol <math>\Delta</math>, is an algebraic expression used to determine the number of roots a [[polynomial]] have.<ref>{{Cite web|date=2020-03-01|title=Compen ...iminant is larger than zero, then the polynomial has two (distinct) [[real number]]s as roots. ...

#Can all solutions be found in theory? [[Category:Number theory]] ...

...able]], or a product of a number and several variables. When an [[algebra|algebraic]] expression contains letters mixed with numbers and arithmetic, like <math ...ession is not a polynomial. Polynomials are often easier to use than other algebraic expressions. ...

...and ''c'' are 2, 3, and 1, respectively. From a set of ''n'' elements, the number of ''r''-element multisets is written as <math>\textstyle \left(\!\binom{n} ...et of elements is the set of prime [[divisor]]s of ''n''. For example, the number ''120'' has the [[factorisation|prime factorisation]] ...

...n of two numbers can produce a [[negative number]], which is not a natural number, but is an integer. ...nomial has a root in the complex numbers, the complex numbers are also the algebraic closure of the real numbers. One can express this relationship as <math>\ov ...

...humb|right|150px|The plus and minus symbols are used to show the sign of a number. Plus means positive and minus means negative.]] ...ded before the number to indicate that the number is a negative of another number.<ref>{{Cite web|date=2020-03-17|title=List of Arithmetic and Common Math Sy ...

...thematics)|matrices]]. One example of a matrix function occurs with the [[Algebraic Riccati equation]], which is used to solve certain [[optimal control]] prob ...atrices]].<ref name="fm">Higham, Nicholas J. (2008). Functions of matrices theory and computation. Philadelphia: [[Society for Industrial and Applied Mathema ...

:''This article is about the basic notions. For advanced topics, see [[Group theory]].'' In [[mathematics]], a '''group''' is a kind of [[algebraic structure]]. A group is a [[set]] with an [[Binary operation|operation]]. T ...

People who do algebra use the rules of [[number]]s and mathematical [[Operation (mathematics)|operations]] used on numbers. Algebra was first used to solve [[Algebraic equation|equations]] and [[Inequality|inequalities]]. Two examples are [[li ...

A '''number''' is a mathematical object used to '''count''', '''measure''', and '''labe ...rial number]]s, or to put a unique identifier, as in an [[ISBN]], a unique number that can identify a [[book]]. ...

This is a list of [[Number|numbers]]. This list will always be not finished. This happens because ther ...that can also make the number important. This is called the [[interesting number paradox]]. ...

...ny equations and many variables, not just two or three. In many cases, the number of equations and variables in the system are the same. In some cases, ther ...ds on the properties of the field. In many cases there will be an infinite number of solutions. ...

...[[Algebraic solution|solution]]s when ''x'', ''y'' and ''z'' are [[natural number]]s. ...eger|whole numbers]] larger than zero, and where <math>n</math> is a whole number bigger than 2. [[Pierre de Fermat]] wrote about it in 1637 inside his copy ...

[[Cardinality]] is the ''number'' of elements in a set. The cardinality of ''A''={X,Y,Z,W} is 4. This can b ...<math>x^{-1}=\frac{1}{x}</math> denotes the [[reciprocal]] value of the '''number''' ''x''. ...