noun
Meaning 1
A function whose domain is a subset of the set on which it is formally defined; i.e., a function f: X→Y for which values f(x) are defined only for x ∈ W, where W ⊆ X.
Definition source: English Wiktionary via Wiktextract
Topics: mathematics, sciences
Examples
- 1967 [John Wiley & Sons], Stephen Cole Kleene, Mathematical Logic, 2002, Dover, page 244, The Church-Turing thesis applies to partial functions on the same grounds as to total functions (§ 41).
- 1991, Michel Bidoit, Hans-Jörg Kreowski, Pierre Lescanne, Fernando Orejas, Donald Sannella (editors), Algebraic System Specification and Development: A Survey and Annotated Bibliography, Springer, LNCS 501, page 15, Nowadays it seems quite clear that if algebraic specifications are to be used as a powerful and realistic tool for the development of complex systems they should permit the specification of partial functions. [...] There are essentially two ways of specifying partial functions.
- 2006, Paulo Oliva, Understanding and Using Spector's Bar Recursive Interpretation of Classical Analysis, Arnold Beckmann, Ulrich Berger, Benedikt Löwe, John V. Tucker (editors), Logical Approaches to Computational Barriers: 2nd Conference on Computability in Europe, Proceedings, Springer, LNCS 3988, page 432, In the following σ and τ will denote finite partial functions from N to N , i.e. partial functions which are defined on a finite domain. A partial function which is everywhere undefined is denoted by ⟨⟩, whereas a partial function defined only at position k (with value n) is denoted by ⟨k,n⟩.
Meaning relationships
Synonyms: none provided
Antonyms: none provided