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- {{short description|Subset of real numbers that are greater than zero}} ...hose [[real number]]s that are greater than zero. The '''non-negative real numbers''', <math>\R_{\geq 0} = \left\{ x \in \R \mid x \geq 0 \right\},</math> als ...9 KB (1,332 words) - 23:37, 8 July 2024
- ...string of decimal digits is actually a [[decimal representation]] for some real number. Depending on the [[construction of the real numbers]] used, completeness may take the form of an [[axiom]] (the '''completeness ...11 KB (1,670 words) - 12:05, 6 January 2025
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- In [[real analysis]], a branch of [[mathematics]], a '''modulus of convergence''' is ...> converges to a real number <math>x</math>, then by definition, for every real <math>\varepsilon > 0</math> there is a [[natural number]] <math>N</math> s ...2 KB (276 words) - 13:38, 22 May 2022
- {{Short description|The real numbers or their cardinality}} ...{\aleph_0}\!</math>, the cardinality of the [[power set]] of the [[natural numbers]]. ...2 KB (337 words) - 21:47, 11 March 2024
- ...n|title=The Classical Fields: Structural Features of the Real and Rational Numbers|volume=112|series=Encyclopedia of Mathematics and its Applications|first=H. ...eal numbers have two square classes, the positive numbers and the negative numbers.<ref name="salzmann"/> ...3 KB (429 words) - 06:38, 13 May 2024
- ...al]] [[coefficient]]s is the largest ideal containing ''I'' with the same (real) vanishing locus. It plays a similar role in [[real algebraic geometry]] that the [[radical of an ideal]] plays in [[algebraic ...2 KB (318 words) - 02:56, 28 April 2024
- ...[[complex number]]s, and [[complete valued field]]s (such as the [[p-adic numbers|''p''-adic number]]s). ===Real and complex numbers=== ...3 KB (534 words) - 23:53, 6 September 2024
- ...collection with [[rational number|rational]] coefficients. A collection of numbers which is not rationally independent is called '''rationally dependent'''. F The [[real number]]s ω<sub>1</sub>, ω<sub>2</sub>, ... , ω<sub>''n''</sub> are said to ...2 KB (294 words) - 20:51, 2 April 2022
- | caption = spiral figure representing both finite and transfinite ordinal numbers ...ity with the [[cardinality of the continuum|cardinality of the set of real numbers]] can neither be proved nor disproved within the standard version of [[axio ...4 KB (553 words) - 05:05, 20 December 2020
- {{short description|How well a certain kind of real number can be approximated by another kind}} ...pecifically it tells us that we can get a good approximation to irrational numbers that are not quadratic by using either [[quadratic irrational]]s or simply ...2 KB (356 words) - 22:51, 27 November 2022
- {{short description|Space formed by the ''n''-tuples of complex numbers}} ...math> \Complex^n</math> is a [[topological vector space]] over the complex numbers. ...2 KB (289 words) - 17:10, 4 September 2024
- ...e [[sequence]] <math>\{f(x_i) \}_{i=1}^\infty</math> is also [[computable real number|computable]]. A [[real function]] is ''computable'' if it is both sequentially computable and effe ...2 KB (300 words) - 21:47, 27 April 2020
- {{Short description|Identity for real numbers}} ...|Geometric interpretation of the Candido identity for sequential Fibonacci numbers. The white area equals the grey area and each of them equals half of the ou ...3 KB (431 words) - 05:46, 16 September 2024
- ...]] and <math>\mathbb K</math> either the [[real numbers]] or the [[complex numbers]], such that for any given <math>f \in \mathcal C(X, \mathbb K)</math> ther ...988 bytes (138 words) - 03:26, 9 January 2025
- ...generalises the idea of exponential functions on the ordered field of real numbers. ...s decidable.<ref>A.J. Macintyre, A.J. Wilkie, ''On the decidability of the real exponential field'', Kreisel 70th Birthday Volume, (2005).</ref> ...6 KB (859 words) - 12:55, 12 February 2022
- ...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, ...}. ...9 KB (1,334 words) - 19:40, 24 January 2025
- [[Image:Floor function.svg|thumb|right|288px|The floor function on real numbers. Its discontinuities are pictured with white discs outlines with blue circl ...ed space]]s integer-valued functions have roughly the same importance as [[real-valued function]]s have on non-discrete spaces. ...4 KB (523 words) - 22:50, 8 October 2024
- ...ssengruppe". Here "Strahl" is German for ray, and often means the positive real line, which appears in the positivity conditions defining ray class groups. ...ing of integers]] of a [[number field]] ''K'' and ''S'' is a subset of the real places, then the ray class group of ''m'' and ''S'' is the [[quotient group ...5 KB (814 words) - 13:34, 10 February 2025
- ...of a [[Topological space#topology|topology]] given to the set '''R''' of [[real number]]s. ...1,018 bytes (149 words) - 00:10, 5 June 2023
- {{Short description|System of numbers with non-finite quantities}} ...795–1815}}</ref> is a [[non-Archimedean ordered field]]; i.e., a system of numbers containing infinite and [[infinitesimal]] quantities. It is usually denoted ...8 KB (1,143 words) - 04:38, 3 December 2024
- The fields of [[rational number]]s and [[real number]]s, with their usual orderings, satisfy the Archimedean property. ...e [[Dehn planes|Dehn field]], and the field of [[rational function]]s with real coefficients (where we define {{math|''f'' > ''g''}} to mean that {{math|'' ...4 KB (567 words) - 06:05, 2 March 2024
- Interesting examples of multiplicatively closed harmonious sets of real numbers arise in the theory of [[diophantine approximation]]. * Let ''G'' be the additive group of [[real number]]s, ''θ'' >1, and the set ''Λ'' consist of all finite s ...4 KB (664 words) - 01:55, 2 April 2016