Bijekní

Bijekní is a concept in mathematics, specifically within set theory, that describes a type of function between two sets. A function is considered bijekní if it is both injective and surjective. Injectivity means that each element in the codomain is mapped to by at most one element in the domain. In simpler terms, no two different inputs produce the same output. Surjectivity, on the other hand, means that every element in the codomain is mapped to by at least one element in the domain. This implies that the function covers or "hits" every possible output. When a function is both injective and surjective, it establishes a one-to-one correspondence between the elements of the domain and the elements of the codomain. This means that for every element in the first set, there is exactly one corresponding element in the second set, and vice versa. Functions that are bijekní are also known as bijective functions or one-to-one and onto functions. The existence of a bijekní function between two sets indicates that these sets have the same cardinality, meaning they have the same "size" or number of elements. This concept is fundamental in understanding set equivalence and is crucial in various areas of mathematics, including abstract algebra and topology.