injektiivsed

Injektiivsed is the Estonian term used to describe injective or one-to-one mappings. A function f: A → B is injektiivne if different inputs map to different outputs: for all x1, x2 in A, f(x1) = f(x2) implies x1 = x2. Equivalently, if x1 ≠ x2 then f(x1) ≠ f(x2).

Examples help illustrate the concept. The function f(x) = 2x from the real numbers to the real numbers is injective. The function f(x) = x^2 from R to R is not injective, since f(1) = f(-1). On the domain [0, ∞), however, f(x) = x^2 is injective.

In relation to other properties, a function can be injective without being surjective; surjectivity means the image of the function equals its codomain. If a function is both injective and surjective, it is bijective and has a two-sided inverse.

In finite settings, an injective function from A to B satisfies |A| ≤ |B|. If |A| = |B|, then an injective function is automatically bijective.

In broader mathematics and computer science, injektiivsed functions are used to model processes that preserve distinctness of inputs, such as encoding schemes and data mappings. In the category of sets, injective functions correspond to monomorphisms, reflecting their role as structure-preserving embeddings.