Finite set information

mathematics, particularly set theory, a finite set is a set that has a finite number of elements. Informally, a finite set is a set which one could in principle...

mathematics and set theory, hereditarily finite sets are defined as finite sets whose elements are all hereditarily finite sets. In other words, the set itself...

numbers. While the cardinality of a finite set is just the number of its elements, extending the notion to infinite sets usually starts with defining the...

cofinite subset of a set X {\displaystyle X} is a subset A {\displaystyle A} whose complement in X {\displaystyle X} is a finite set. In other words, A...

In set theory, an infinite set is a set that is not a finite set. Infinite sets may be countable or uncountable. The set of natural numbers (whose existence...

algebraic geometry, Galois theory, finite geometry, cryptography and coding theory. A finite field is a finite set that is a field; this means that multiplication...

z}, {y, z}, {x, y, z}}. If S is a finite set with the cardinality |S| = n (i.e., the number of all elements in the set S is n), then the number of all the...

deterministic finite automaton (DFA)—also known as deterministic finite acceptor (DFA), deterministic finite-state machine (DFSM), or deterministic finite-state...

(first, second, nth, etc.) aimed to extend enumeration to infinite sets. A finite set can be enumerated by successively labeling each element with the least...

term "discrete mathematics". The set of objects studied in discrete mathematics can be finite or infinite. The term finite mathematics is sometimes applied...

Look up finite, finitely, or finiteness in Wiktionary, the free dictionary. Finite is the opposite of infinite. It may refer to: Finite set, a set whose...

a set. In the case of a finite set, its cardinal number, or cardinality is therefore a natural number. For dealing with the case of infinite sets, the...

used in combinatorics, orders subsets of a given finite set by assigning a total order to the finite set, and converting subsets into increasing sequences...

mathematics, a set is countable if either it is finite or it can be made in one to one correspondence with the set of natural numbers. Equivalently, a set is countable...

elements of finite sets, usually grouped into infinite families, such as the family of sets each consisting of all permutations of some finite set. There are...

sum of the elements of a finite set, one is inevitably led to the convention that the sum of the elements of the empty set (the empty sum) is zero. The...

In automata theory, a finite-state machine is called a deterministic finite automaton (DFA), if each of its transitions is uniquely determined by its...

of determining the number of elements of a finite set of objects; that is, determining the size of a set. The traditional way of counting consists of...

(which is actually an indirect reference to types in Typed Set Theory). The axioms in a finite axiomatization correspond to natural basic constructions...

In mathematics, a finite topological space is a topological space for which the underlying point set is finite. That is, it is a topological space which...

condition. In other contexts, only chains that are finite sets are considered. In this case, one talks of a finite chain, often shortened as a chain. In this...

B . {\displaystyle A\subseteq B{\text{ if and only if }}A\cup B=B.} A finite set A is a subset of B, if and only if the cardinality of their intersection...

fuzzy set A = ( U , m ) {\displaystyle A=(U,m)} . For a finite set U = { x 1 , … , x n } , {\displaystyle U=\{x_{1},\dots ,x_{n}\},} the fuzzy set ( U ...

II-finite, III-finite, IV-finite, V-finite, VI-finite and VII-finite. I-finiteness is the same as normal finiteness. IV-finiteness is the same as Dedekind-finiteness...