About: Integer-valued function

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In mathematics, an integer-valued function is a function whose values are integers. In other words, it is a function that assigns an integer to each member of its domain. Floor and ceiling functions are examples of an integer-valued function of a real variable, but on real numbers and generally, on (non-disconnected) topological spaces integer-valued functions are not especially useful. Any such function on a connected space either has discontinuities or is constant. On the other hand, on discrete and other totally disconnected spaces integer-valued functions have roughly the same importance as real-valued functions have on non-discrete spaces.

Attributes	Values
rdf:type	disease
rdfs:label	Zahlenfunktion (de) Integer-valued function (en)
rdfs:comment	Eine Zahlenfunktion ist eine Funktion, die Tupel von natürlichen Zahlen auf natürliche Zahlen abbildet. Der Begriff wird hauptsächlich in der theoretischen Informatik in der Berechenbarkeitstheorie verwendet und dient der Abgrenzung zu Funktionen über anderen Mengen, insbesondere Wortfunktionen. Zum Beweis der Berechenbarkeit einerZahlenfunktion dienen mathematische Modelle wie die Registermaschine, die While-Berechenbarkeit oder dieμ-Rekursion. (de) In mathematics, an integer-valued function is a function whose values are integers. In other words, it is a function that assigns an integer to each member of its domain. Floor and ceiling functions are examples of an integer-valued function of a real variable, but on real numbers and generally, on (non-disconnected) topological spaces integer-valued functions are not especially useful. Any such function on a connected space either has discontinuities or is constant. On the other hand, on discrete and other totally disconnected spaces integer-valued functions have roughly the same importance as real-valued functions have on non-discrete spaces. (en)
foaf:depiction
dcterms:subject	Types of functions
Wikipage page ID	39818965 (xsd:integer)
Wikipage revision ID	1072484968 (xsd:integer)
Link from a Wikipage to another Wikipage	Prime-counting function Primitive recursive function Partially ordered ring Real-valued function Algebra (ring theory) Types of functions Μ-recursive function Integer-valued polynomial Integer square root Computability theory Constant function Coordinate space Mathematical logic Geometric group theory Norm (mathematics) Function (mathematics) Grade (disambiguation) Multiplication Connected space Ordered ring Arithmetic function Sign function Computer programming Function of a real variable Domain of a function Gödel numbering Addition Floor and ceiling functions Non-negative Number theory Dirichlet function Formal language Graph theory Length function Discontinuity (mathematics) Well-formed formula Ring (mathematics) Ring theory Heaviside step function Codomain Discrete space Pointwise Integer Integer (computer science) Natural number Real number Set (mathematics) Metric (mathematics) Word metric Rank (disambiguation) Semi-continuity Topological space Totally disconnected space Function (programming)
sameAs	Integer-valued function Integer-valued function Integer-valued function Integer-valued function
dbp:wikiPageUsesTemplate	dbt:Math dbt:Mvar dbt:Unreferenced dbt:Functions
thumbnail	wiki-commons:Special:FilePath/Floor_function.svg?width=300
has abstract	Eine Zahlenfunktion ist eine Funktion, die Tupel von natürlichen Zahlen auf natürliche Zahlen abbildet. Der Begriff wird hauptsächlich in der theoretischen Informatik in der Berechenbarkeitstheorie verwendet und dient der Abgrenzung zu Funktionen über anderen Mengen, insbesondere Wortfunktionen. Zum Beweis der Berechenbarkeit einerZahlenfunktion dienen mathematische Modelle wie die Registermaschine, die While-Berechenbarkeit oder dieμ-Rekursion. (de) In mathematics, an integer-valued function is a function whose values are integers. In other words, it is a function that assigns an integer to each member of its domain. Floor and ceiling functions are examples of an integer-valued function of a real variable, but on real numbers and generally, on (non-disconnected) topological spaces integer-valued functions are not especially useful. Any such function on a connected space either has discontinuities or is constant. On the other hand, on discrete and other totally disconnected spaces integer-valued functions have roughly the same importance as real-valued functions have on non-discrete spaces. Any function with natural, or non-negative integer values is a partial case of integer-valued function. (en)
gold:hypernym	Function
prov:wasDerivedFrom	wikipedia-en:Integer-valued_function?oldid=1072484968&ns=0
page length (characters) of wiki page	3580 (xsd:nonNegativeInteger)
foaf:isPrimaryTopicOf	wikipedia-en:Integer-valued_function
is Link from a Wikipage to another Wikipage of	Probabilistic number theory Concrete Mathematics Floor and ceiling functions Integer Integer function Outline of mathematics Natural-valued function
is Wikipage redirect of	Natural-valued function
is foaf:primaryTopic of	wikipedia-en:Integer-valued_function

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