Natural numberNatural numbers can be used for counting: one apple plus two apples equals three apples.In mathematics, the natural numbers are the numbers used for counting up, starting from 0 or 1. The first few natural numbers are 0 (if included), 1, 2, 3, and so on. The terms positive integers, non-negative integers, whole numbers, and counting numbers are also used. The set of the natural numbers is commonly denoted by a bold N or a blackboard boldN{\displaystyle \mathbb {N} }.
Metric spaceIn mathematics, a metric space is a set together with a notion of distance between its points. The distance is measured by a function called a metric or distance function. Metric spaces are a general setting for studying many of the concepts of mathematical analysis and geometry. The most familiar example of a metric space is 3-dimensional Euclidean space with its usual notion of distance.
SubsetIn mathematics, a setA is a subset of a set Bif and only if all elements of A are also elements of B; B is then a superset of A. It is possible for A and B to be equal; if they are unequal, then A is a proper subset of B. The relationship of one set being a subset of another is called inclusion (or sometimes containment). A is a subset of B may also be expressed as B includes (or contains) A or A is included (or contained) in B. A k-subset is a subset with k elements.
Real numberIn mathematics, a real number is a number that can be used to measure a continuous one-dimensionalquantity such as a length, duration or temperature. Here, continuous means that pairs of values can have arbitrarily small differences. Every real number can be almost uniquely represented by an infinite decimal expansion.
Formal languageIn logic, mathematics, computer science, and linguistics, a formal language is a set of strings whose symbols are taken from a set called "alphabet". The alphabet of a formal language consists of symbols that concatenate into strings (also called "words"). Words that belong to a particular formal language are sometimes called well-formed words. A formal language is often defined by means of a formal grammar such as a regular grammar or context-free grammar.
SequenceIn mathematics, a sequence is a collection of objects possibly with repetition, that come in a specified order. Like a set, it contains members (also called elements, or terms). Unlike a set, the same elements can appear multiple times at different positions in a sequence, and unlike a set, the order does matter. The notion of a sequence can be generalized to an indexed family, defined as a function from an arbitrary index set.
Ordinal numberIn set theory, an ordinal number, or ordinal, is a generalization of ordinal numerals (first, second, nth, etc.) aimed to extend enumeration to infinite sets. Usually Greek letters are used for ordinal number variables to help distinguish them from natural number variables. A finite set can be enumerated by successively labeling each element with the least natural number that has not been previously used.
Theoretical computer scienceTheoretical computer science is a subfield of computer science and mathematics that focuses on the abstract and mathematical foundations of computation. It is difficult to circumscribe the theoretical areas precisely.
Set (mathematics)In mathematics, a set is a collection of different things; the things are called elements or members of the set and are typically mathematical objects: numbers, symbols, points in space, lines, other geometric shapes, variables, functions, or even other sets. Mathematics typically does not define precisely what constitutes a "set" or "collection", because such a definition would have to be in terms of something else previously defined.
Symbol (formal)A formal symbol is a fundamental concept in logic, tokens of which may be marks or a configuration of marks which form a particular pattern.
Infimum and supremumGreatest lower bound and least upper boundA set P{\displaystyle P} of real numbers (hollow and filled circles), a subset S{\displaystyle S} of P{\displaystyle P} (filled circles), and the infimum of S.{\displaystyle S.} Note that for totally ordered finite sets, the infimum and the minimum are equal.A set A{\displaystyle A} of real numbers (blue circles), a set of upper bounds of A{\displaystyle A} (red diamond and circles), and the smallest such upper bound, that is, the supremum of A{\displaystyle A} (red diamond).In mathematics, the infimum (abbreviated inf; pl.: infima) of a subsetS{\displaystyle S} of a partially ordered setP{\displaystyle P} is the greatest element in P{\displaystyle P} that is less than or equal to each element of S,{\displaystyle S,} if such an element exists.*As an Amazon Associate I earn from qualifying purchases.