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...all positive [[real number]]s that are not positive [[Natural number|whole numbers]].<ref name=SS7778>Steen & Seebach (1978) pp.77 – 78</ref> ...his topology are taken to be the whole set ''S'', the empty set ∅, and the sets generated by ...

...oncepts are '''model sets''', '''[[Meyer set]]s''', and '''cut-and-project sets'''. ...screte topology]]. A '''weak character''' is a restriction to ''&Lambda;'' of an algebraic homomorphism from ''&Lambda;''_''d'' into the [[circ ...

...ce|sequence]] {{nowrap|(1, 2, 3, ...)}} in the [[ultrapower]] construction of the hyperreals. ...s the greatest integer not exceeding ''x''. By the [[transfer principle]] of nonstandard analysis, there exists a natural extension: ...

....1506-1511 (1964).</ref> Although it was originally stated in the language of [[category theory]], as Leinster pointed out, the axioms can be stated with ...ory that emphasizes sets as abstract structures (as opposed to collections of elements). ...

...of a [[Topological space#topology|topology]] given to the set '''R''' of [[real number]]s. ...]]s {''x_k''} with the property that {''x_k''} [[Limit of a sequence|converge]]s to ''x'' with respect to the [[Euclidean topology]]. ...

{{short description|On decreasing nested sequences of non-empty compact sets}} ...rsections of decreasing nested [[sequence|sequences]] of non-empty compact sets. ...

...ric and decreasing, and whose [[level sets]] are of the same size as those of the original function.<ref name=liebloss>{{cite book|last1=Lieb|first1=Elli ==Definition for sets== ...

...(logic)|decidability]] of the [[theory (mathematical logic)|theory]] of [[real-closed field]]s. ...al, as there are examples where the output has a double exponential number of connected components. This algorithm is therefore fundamental, and it is wi ...

...counterexamples in basic topology. In particular, it provides an example of a [[Hausdorff space]] that is not [[Regular space|regular]]. ...collection of all open intervals <math>(a,b)</math> together with all sets of the form <math>(a,b)\setminus K.</math>{{sfn|Munkres|2000|p=82}} ...

{{short description|Mathematical function that takes real values}} ...nction from this collection of weight to [[positive number|positive]] real numbers. The term "[[weight function]]", an allusion to this example, is used in pu ...

...n a set <math>X</math> is a collection <math>\mathcal{B}</math> of subsets of <math>X</math> that satisfy all the following conditions: ...ed {{em|'''<math>\mathcal{B}</math>-bounded'''}} or simply {{em|'''bounded sets'''}} if <math>\mathcal{B}</math> is understood. ...

{{Short description|Type of totally ordered set}} ...er 6 section 8}} that generalizes the [[order type]] ''η'' of the rational numbers. ...

...the second addendum to problem 43 of the [[Scottish book]] as a variation of the [[Banach–Mazur game]].<ref name="The Scottish Book">{{cite book|last1=M ...e 50th Anniversary of the Banach–Mazur Game|journal=Rocky Mountain Journal of Mathematics|date=Spring 1987|volume=17|issue=2|pages=227–276|url=http://www ...

{{distinguish|Family of sets}} {{Short description|Collection of objects, each associated with an element from some index set}} ...

{{see also|List of numeral systems}} ...ral numbers. Natural numbers including 0 are also sometimes called ''whole numbers''.<ref> ...

...s|mathematical]] [[set theory]], '''Baumgartner's axiom (BA)''' can be one of three different [[axiom]]s introduced by [[James Earl Baumgartner]]. ...n's axiom does not imply that every two <math>\aleph_{1}</math>-dense sets of reals are isomorphic|volume=38|year=1981}}</ref> ...

...finite.<ref>{{Cite book |last=Trench |first=William |title=Introduction to Real Analysis |isbn=0-13-045786-8 |page=21 |language=en}}</ref> [[Half-space (ge ...n] (accessed November 2010).</ref> For instance, one might study solutions of the heat equation in an idealised semi-infinite metal bar. ...

{{Short description|Type of internal set in nonstandard analysis}} ...te book|title=Truth, possibility, and probability: new logical foundations of probability and statistical inference|url=https://archive.org/details/truth ...

...ally zero such functions may exist was a problem that arose in the context of early-1900s research on functional differentiability and [[Integrable funct ...]] {{math|[0, 1]}}. Let <math>\{a_j\}_{j \isin \N}</math> be positive real numbers with <math>\sum_j a_j < \infty</math>. Define <math>g\colon [0, 1] \rarr \R ...

...ity presented here is used in [[game theory]] to investigate the existence of an equilibrium. ...[[geometric mean]] and [[arithmetic mean]] of two sets of [[real number]]s of the [[unit interval]]. ...