Injective

Part of speech: adjective

Pronunciation: /ɪnˈd͡ʒɛktɪv/

Definitions

1. A mathematical function where each element of the range corresponds to at most one element of the domain, ensuring no two different inputs produce the same output
2. A type of function in mathematics where every distinct input has a unique output, meaning no two different inputs will yield the same result in the range
3. Referring to a function in which each element in the output is paired with a single, unique input from the domain, so different inputs always give different outputs

Etymology: "Injective" is a mathematical term, and its history runs through French. It was borrowed from French "injectif", the adjective built on the same Latin base as "inject" (from "iniectus", the past participle of "inicere", "to throw into"). The sense of throwing something into a place carries over into the mathematical idea: an injective function is one that throws each input to its own distinct output, so that no two inputs land on the same target. The mathematical sense is itself the main thing the word is known for. It is a technical coinage from modern algebra rather than an ordinary everyday word, and it sits alongside its companions "surjective" and "bijective", which together describe how a function's inputs and outputs match up. Used this way, the word preserves the Latin image of projecting something into a specific spot, now applied to the pairing of elements between two sets.