Routledge Dictionary of Language and Linguistics
1 Basic term in set theory taken from geometry: assignment to each element x of a set A (= domain) exactly one element y=f(x) of a set B (=range) (notation: f: A→B or A→B). In set theory, f frepresents a subset of the product set A ×B, namely the subset of the ordered pairs ‹x, y› with xεA and y=f(x) εB. Types of functions are as follows: (a) Injection: a function f of A into B is injective (or unidirectional), if f is left-directional, that is if the equation f(x) =f(y) consistently yields x=y.
(b) Surjection (=mapping onto): a function f of A into B is surjective if every element in B is the value of at least one element x in A under ƒ.
(c) Bijection: a function is bijective or unidirectional up if it is both injective and surjective.
References
formal logic
2 Basic term taken from mathematics and logic for describing structures and systems. Widely used synonymously with function1. ( also formal logic, set theory)
3 In Hjelmslev’s (1943) glossematics, ‘function’ refers to the concept of relation. Hjelmslev uses ‘function’ ‘in a meaning that lies intermediately between the logicalmathematical and the etymological’ (p.
33), i.e. function relates both to the different forms of dependencies of various quantities amongst themselves (which he calls interdependence, determination, or constellation) as well as to the fact that these quantities ‘function’ in certain ways and occupy a certain role in the text.
References
Hjelmslev, L. 1943. Omkring sprogteoriens grundlaeggelse. Copenhagen. 1961. Prolegomena to a theory of language, trans. F.J.Whitfield. Madison, WI.
glossematics
4 syntactic function
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