valdiklis

Valdiklis is a term used in mathematics to describe a function that maps each element of one set to a unique element of another set. The term is derived from the Latin word "validus," meaning "strong" or "effective," reflecting the function's ability to establish a clear and unambiguous correspondence between elements of two sets. Validity of a function is determined by the following conditions:

1. For every element in the domain (input set), there is exactly one element in the codomain (output set) to which it corresponds.

2. Each element in the codomain is the image of at most one element in the domain.

Valdiklis can be represented using various notations, such as f: X → Y, where f is the function, X is the domain, and Y is the codomain. The set of all possible outputs of a function is called its range or image. A function is said to be injective (one-to-one) if distinct elements of the domain map to distinct elements of the codomain. Conversely, a function is surjective (onto) if every element of the codomain is the image of at least one element of the domain. A function that is both injective and surjective is called bijective. Validity of a function is a fundamental concept in mathematics, with applications in various fields, including computer science, physics, and engineering.