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...restrictions on possible values of [[L2 cohomology|<math>l^2</math>-Betti numbers]]. ...ed if it is possible for <math>l^2</math>-Betti numbers to be [[irrational numbers|irrational]]. ...

...and ''b'' is a real [[quadratic irrational]], are [[transcendental number|transcendental]]. In particular, this result implies that [[Gelfond–Schneider constant]] :is transcendental. See [[Gelfond–Schneider theorem]] for later developments. ...

...urnal|last=Feldman|first=Naum|date=2000|title=Algebraic and transcendental numbers|url=http://static.nsta.org/pdfs/QuantumV10N6.pdf|journal=Quantum|volume=10| ...9|bibcode=1967RuMaS..22....1F}}</ref><ref>{{cite book|title=Transcendental Numbers|url=https://archive.org/details/numbertheorytran00pars|url-access=limited|l ...

| title = Expression of real numbers with the help of infinite series {{harvtxt|Hančl|1996}} has defined a transcendental sequence to be an integer sequence ''a''_''n'' such that, for eve ...

...ion|Dirichlet {{mvar|L}}-function]] for the field of [[Gaussian rational]] numbers. This formula is a special case of the [[analytic class number formula]], a ...anscendental" number (regardless of whether it is currently possible for [[transcendental number theory]] to provide a proof of the transcendence); and</li> ...

...hat is, it is generally the sum of [[unit fraction]]s. If infinitely many numbers have their reciprocals summed, generally the terms are given in a certain s If only finitely many numbers are included, the key issue is usually to find a simple expression for the ...

...first part and 22 chapters in the second. It has [[Eneström index|Eneström numbers]] E101 and E102.<ref>{{Cite web|url=https://scholarlycommons.pacific.edu/eu ...ifferentiation or integration. In particular, he introduced the elementary transcendental functions, the logarithm, the exponential function, the trigonometric funct ...

...ral numbers. Natural numbers including 0 are also sometimes called ''whole numbers''.<ref> ...ath>\mathbb{Z}</math>): Positive and [[negative number|negative]] counting numbers, as well as zero: {..., −3, −2, −1, 0, 1, 2, 3, ...}. ...

...no formal statement as such but refers to a general problem prevalent in [[transcendental number theory]]. Often proofs in transcendence theory are [[Reductio ad ab ...example, if ''x''₁,&nbsp;...,&nbsp;''x''_''n'' are [[real number]]s, then there is an algorithm<ref>{{Cite journal | first=David H. | ...

[[file:Cosine_fixed_point.svg|thumb|The Dottie number is the unique real [[fixed point (mathematics)|fixed point]] of the [[cosine]] function.]] ...' is a [[mathematical constant|constant]] that is the unique [[real number|real]] root of the equation ...

...onentiation]] on the [[real number]]s, where the base is a chosen positive real number. ...Bays, Jonathan Kirby, A.J. Wilkie, ''A Schanuel property for exponentially transcendental powers'', (2008), {{arxiv|0810.4457}}</ref> ...

{{Short description|Function from the limited hyperreal to the real numbers}} ...obinson standard part.|arxiv=1104.0375 }}</ref> as well as [[Leibniz]]'s [[Transcendental law of homogeneity]]. ...

...he [[real number]]s that are not [[rational number]]s. That is, irrational numbers cannot be expressed as the ratio of two [[integer]]s. When the [[ratio]] of ...s/mathematical-gazette/article/abs/9542-irrational-square-roots-of-natural-numbers-a-geometrical-approach/6B9D8EBFDCC016013D303AA78973429F |journal=The Mathem ...

...th> \alpha </math>-covariant [[modular form|modular function]] Jimm on the real line <math> \mathbf{R}</math> is defined via the codenominator. Jimm relate ...moduli space of rank-2 pseudolattices and is related to the arithmetic of real [[Quadratic irrational number|quadratic irrationals]]. ...

...ion|compass and straight edge]], and the values are called [[constructible numbers]]. ...], whereas if the codomain is taken to be the [[projectively extended real numbers]], these entries take the value <math>\infty</math> (see [[division by zero ...

...]], [[Goldbach's conjecture]], and the [[twin prime]] conjecture for prime numbers.<ref name="blms"/><ref name="laa"/> ...ditions for the existence of matrices of various types ([[symmetric matrix|real symmetric matrices]], [[orthogonal matrix|orthogonal matrices]], [[Hermitia ...

All named mathematical constants are [[Definable real number|definable numbers]], and usually are also [[computable number]]s ([[Chaitin's constant]] bein ...s' constant''', and written as {{math|{{sqrt|2}}}}, is the unique positive real number that, when multiplied by itself, gives the number [[2]]. It is more ...

In [[mathematics]], the '''natural logarithm of 2''' is the unique [[real number]] argument such that the [[exponential function]] equals two. It app ...(more generally, of any positive [[algebraic number]] other than 1) is a [[transcendental number]]. It is also contained in the ring of [[Period (algebraic geometry) ...

Kepler's equation is a [[transcendental equation]] because [[sine]] is a [[transcendental function]], and it cannot be solved for <math>E</math> [[algebraic function |title=Rootfinding for a transcendental equation without a first guess: Polynomialization of Kepler's equation thro ...

{{About||the real numbers used in descriptive set theory|Baire space (set theory)}} ...the other real numbers have one decimal expansion.}}<ref>{{Cite web|title=Real number |url=https://www.oxfordreference.com/view/10.1093/oi/authority.20110 ...