Injektyvi

Injektyvi is a term found in some linguistic and mathematical texts to describe a one-to-one correspondence, a concept more commonly referred to as injective in English. Its exact meaning and usage can vary by language and author, but the core idea is that a mapping preserves distinctness: different inputs yield different outputs.

In mathematics, a function f from a set A to a set B is injective if x1 ≠ x2 implies f(x1) ≠ f(x2) for all x1, x2 in A. Equivalently, f(x1) = f(x2) only when x1 = x2. Injective functions are sometimes described as one-to-one mappings. Examples include f(x) = 2x on the real numbers, which is injective, while f(x) = x^2 is not injective on all real numbers because f(1) = f(-1). Injectivity is a key property for embeddings and for ensuring that a left inverse exists on the image of the function.

Outside pure mathematics, the term is sometimes used in computer science, data modeling, and logic to denote a one-to-one relationship between elements of different sets or representations. It should not be confused with surjective (onto) or bijective (one-to-one and onto) mappings, which describe different levels of coverage between domains and codomains.

Etymologically, injektyvi appears to be a regional or language-specific variant of the term injective, adapted to local spelling and pronunciation. When encountering the word, consult the surrounding text to confirm whether it is intended as a direct synonym of injective or as a broader or context-specific notion. See also: injective function, one-to-one correspondence, bijection.