Finittiset

Finittiset is a term used in Finnish-language mathematics to describe objects that have a finite number of elements or components. It is applied as an adjective or noun to indicate finiteness in sets, structures, and processes.

Formally, a set S is finittiset if its cardinality |S| is a finite natural number. More generally, a mathematical structure or system is described as finittiset when it contains only finitely many elements, states, or components. This property can be extended to various constructions: a finite sequence has finite length, a finite graph has finitely many vertices and edges, and a finite group has a finite number of elements.

Key properties follow from finiteness: any subset of a finittiset set is finittiset; the union of finitely many finittiset sets is finittiset; and the Cartesian product of a finite collection of finittiset sets is finittiset. The set of all functions from a finite domain to another finite codomain is itself finite. Finittiset structures often enable concrete enumeration and algorithmic treatment, which is central in areas such as combinatorics and computer science.

In computer science, finite automata are a common example: they have a finite set of states and operate on finite sequences of inputs. In broader mathematics, finittiset objects are contrasted with infinite structures, where cardinalities are not bounded by a finite number.

See also: cardinality, finite set, finite automaton, discrete mathematics.