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Encyclopedia > Finite

In mathematics, a set is called finite if and only if there is a bijection between the set and some set of the form {1, 2, ..., n} where n is a natural number. It is a theorem that a set is finite if and only if there exists no bijection between the set and any of its proper subsets. Equivalently, a set is finite if its cardinality, i.e. the number of its elements, is a natural number. For instance, the set of integers between -15 and 3 is finite, since it has 17 elements. The set of all prime numbers is not finite. Sets that are not finite are called infinite.

In physics, finite additionally means "non-zero", for instance in a sentence like "if the distance of the two objects is finite...". Results from FactBites:

 Finite - Wikipedia, the free encyclopedia (175 words) In mathematics, a set is called finite if and only if there is a bijection between the set and some set of the form {1, 2,..., n} where n is a natural number. All finite sets are countable, but not all countable sets are finite. It is a theorem (assuming the axiom of choice) that a set is finite if and only if there exists no bijection between the set and any of its proper subsets.
 Finite state machine - Wikipedia, the free encyclopedia (1085 words) A finite state machine (FSM) or finite automaton is a model of behaviour composed of states, transitions and actions. Finite state machines are one type of the automata studied in automata theory and the theory of computation. In computer science, finite state machines are widely used in modelling of application behaviour, design of hardware digital systems, software engineering, compilers, study of computation and languages.
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