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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]]. ...

...hat neither this hypothesis nor its negation contradicts the tenets of set theory itself.<ref>{{Cite web|last=Weisstein|first=Eric W.|title=Continuum|url=htt * [[Continuum (theory)]] ...

{{Groups}}In [[group theory]], a branch of [[mathematics]], given a group <math>G</math> under a [[bina For example, the [[even number]]s are a subgroup of the [[integer]]s, with [[addition]] as the binary oper ...

...e number|prime]]s. It says that if ''a'' is a number, and ''p'' is a prime number, then in the notation of modular Arithmetic, it can be expressed as, [[Category:Theorems in number theory]] ...

...' be any [[natural number]]. Wilson's theorem says that ''n'' is a [[prime number]] if and only if: ...uation is correct. Also, if the equation is correct, then ''n'' is a prime number. The equation says that the [[factorial]] of ''(n - 1)'' is one less than a ...

...'''Cantor's paradox''' refers to two related [[paradox]]es in [[naive set theory]]: * The set of all [[cardinal number]]s does not exist. ...

...any elements are in H, called the order of H) divides |G|. Moreover, the number of distinct left (right) [[coset]]s of H in G is |G|/|H|. This theorem is [[Category:Group theory]] ...

In [[graph theory]], a '''directed graph''' (or '''digraph''') is a [[Graph (mathematics)|gra For a normal graph, the degree of a vertex <math>v</math> is the number of edges touching <math>v</math>. ...

In [[number theory]] a '''Carmichael number''' is a [[composite number|composite]] positive [[integer]] <math>n</math>, which satisfies the [[cong ...are composite numbers that behave a little bit like they would be a prime number. ...

...t Theory Symbols|url=https://mathvault.ca/hub/higher-math/math-symbols/set-theory-symbols/|access-date=2020-10-07|website=Math Vault|language=en-US}}</ref> * [[Cardinal number]] ...

...F, the system is called '''ZFC'''. It is the system of axioms used in set theory by most [[mathematician]]s today. ...t did not have contradictions. [[Ernst Zermelo]] proposed a theory of set theory in 1908. In 1922, [[Abraham Fraenkel]] proposed a new version based on Zer ...

...t theory]] (particularly in the theory of [[Infinity|infinite]] [[Cardinal number|cardinal numbers]]), the <math>\gimel</math> symbol is used to represent th ...

...'') states that if ''n'' and ''a'' are [[coprime]], (meaning that the only number that divides ''n'' and ''a'' is 1), then the following [[equivalence relati [[Category:Theorems in number theory]] ...

[[Category:Number theory]] ...

[[Category:Number theory]] ...

...e '''totient''' of a [[positive number|positive]] [[integer]] ''n'' is the number of positive integers smaller than ''n'' which are [[coprime]] to ''n'' (the ...}/n\mathbb{Z}</math>. This fact, together with [[Lagrange's theorem (group theory)|Lagrange's theorem]], provides a proof for [[Euler's theorem]]. ...

A [[real number|real]] or [[complex number]] is called a '''transcendental number''' if it cannot be found as a result of an algebraic equation with [[intege ...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 ...

'''Ordinal numbers''' (or '''ordinals''') are [[number]]s that show something's [[order]], for example: 1st, 2nd, 3rd, 4th, 5th. ...ega</math> + 1).<ref>{{Cite web|last=Weisstein|first=Eric W.|title=Ordinal Number|url=https://mathworld.wolfram.com/OrdinalNumber.html#:~:text=In%20formal%20 ...

[[Category:Number theory]] ...

...number''' is a [[Mathematical model|mathematical method]] to obtain from a number another written in the opposite way to the first. ...st2=Barry|date=2021|title=Numbers and properties|journal=Journal of Number Theory}}</ref> ...