--- title: Integer-valued function slug: integer-valued-function qid: snapshot: enwiki-001250171425 content_hash: license: CC BY-SA 4.0 source: https://en.wikipedia.org/w/index.php?oldid=1250171425 tags: [22991881, 24043274, 29176689] --- # Integer-valued function > [!note] Provenance > Snapshot `enwiki-001250171425` · content root `…` > Derived from · Licensed CC BY-SA 4.0 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. The floor and ceiling functions are examples of integer-valued functions 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 an integer-valued function. 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. The floor and ceiling functions are examples of integer-valued functions 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 an integer-valued function. ==Further reading== https://webusers.imj-prg.fr/~michel.waldschmidt/articles/pdf/SurveyIntegerValuedEntireFunctions.pdf