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114 relations: Acta Mathematica, Alain Connes, Asymmetric relation, Automorphism, Base (topology), Bijection, Binary relation, Bulletin of the American Mathematical Society, Cardinal direction, Cartesian product, CC system, Centrum Wiskunde & Informatica, Chromatic circle, Chromatic scale, Circadian rhythm, Circle, Circle group, Circle of fifths, Clockwise, Completeness (order theory), Configuration space (physics), Conjugacy class, Convex set, Countable set, Covering space, Currying, Cut (cards), Cycle graph, Cycles and fixed points, Cyclic category, Cyclic group, Cyclic homology, Cyclically ordered group, Cyclohedron, Dedekind–MacNeille completion, Degree of a continuous mapping, Dense order, Directed algebraic topology, Dynamical system (definition), Element (mathematics), Embedding, Finitary relation, Finite set, Formal power series, Free group, Function (mathematics), Fundamenta Mathematicae, Gene, Greatest and least elements, Group (mathematics), ..., Group action, Group of rational points on the unit circle, Hans Freudenthal, Harold Scott MacDonald Coxeter, Inclusion map, Infinite set, Injective function, Integer, Interval (mathematics), Jean Piaget, Journal of Combinatorial Theory, Knot invariant, Ladislav Rieger, Line (geometry), Linearly ordered group, Longitude, Lorentz surface, Manifold, Mathematics, Monomial, Monotonic function, Morphism, Names of the days of the week, O-minimal theory, Omega-categorical theory, Open set, Order (journal), Order theory, Order topology, Order type, Ordered geometry, Partial cyclic order, Partially ordered set, Pencil (mathematics), Permutation, Pitch class, Polytope, Prime meridian, Principal homogeneous space, Rational number, Real closed field, Real projective line, Rewriting, Rock–paper–scissors, Rotation number, Royal Bohemian Society of Sciences, Scientific pitch notation, Separation relation, Serial relation, Set (mathematics), Simply connected space, Strongly minimal theory, Structure (mathematical logic), Subset, Symmetric function, Ternary relation, Topological space, Total order, Transitive relation, Unit circle, Weakly o-minimal structure, 12-hour clock, 180th meridian, 24-hour clock. Expand index (64 more) »
Acta Mathematica
Acta Mathematica is a peer-reviewed open-access scientific journal covering research in all fields of mathematics.
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Alain Connes
Alain Connes (born 1 April 1947) is a French mathematician, currently Professor at the Collège de France, IHÉS, Ohio State University and Vanderbilt University.
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Asymmetric relation
In mathematics, an asymmetric relation is a binary relation on a set X where.
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Automorphism
In mathematics, an automorphism is an isomorphism from a mathematical object to itself.
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Base (topology)
In mathematics, a base (or basis) B for a topological space X with topology T is a collection of open sets in T such that every open set in T can be written as a union of elements of B.We are using a convention that the union of empty collection of sets is the empty set.
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Bijection
In mathematics, a bijection, bijective function, or one-to-one correspondence is a function between the elements of two sets, where each element of one set is paired with exactly one element of the other set, and each element of the other set is paired with exactly one element of the first set.
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Binary relation
In mathematics, a binary relation on a set A is a set of ordered pairs of elements of A. In other words, it is a subset of the Cartesian product A2.
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Bulletin of the American Mathematical Society
The Bulletin of the American Mathematical Society is a quarterly mathematical journal published by the American Mathematical Society.
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Cardinal direction
The four cardinal directions or cardinal points are the directions north, east, south, and west, commonly denoted by their initials N, E, S, and W. East and west are at right angles to north and south, with east being in the clockwise direction of rotation from north and west being directly opposite east.
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Cartesian product
In set theory (and, usually, in other parts of mathematics), a Cartesian product is a mathematical operation that returns a set (or product set or simply product) from multiple sets.
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CC system
In computational geometry, a CC system or counterclockwise system is a ternary relation introduced by Donald Knuth to model the clockwise ordering of triples of points in general position in the Euclidean plane.
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Centrum Wiskunde & Informatica
The Centrum Wiskunde & Informatica (abbr. CWI; English: "National Research Institute for Mathematics and Computer Science") is a research center in the field of mathematics and theoretical computer science.
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Chromatic circle
The chromatic circle is a geometrical space that shows relationships among the 12 equal-tempered pitch classes making up the familiar chromatic scale on a circle.
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Chromatic scale
The chromatic scale is a musical scale with twelve pitches, each a semitone above or below its adjacent pitches.
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Circadian rhythm
A circadian rhythm is any biological process that displays an endogenous, entrainable oscillation of about 24 hours.
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Circle
A circle is a simple closed shape.
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Circle group
In mathematics, the circle group, denoted by T, is the multiplicative group of all complex numbers with absolute value 1, that is, the unit circle in the complex plane or simply the unit complex numbers The circle group forms a subgroup of C×, the multiplicative group of all nonzero complex numbers.
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Circle of fifths
In music theory, the circle of fifths (or circle of fourths) is the relationship among the 12 tones of the chromatic scale, their corresponding key signatures, and the associated major and minor keys.
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Clockwise
Two-dimensional rotation can occur in two possible directions.
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Completeness (order theory)
In the mathematical area of order theory, completeness properties assert the existence of certain infima or suprema of a given partially ordered set (poset).
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Configuration space (physics)
In classical mechanics, the parameters that define the configuration of a system are called generalized coordinates, and the vector space defined by these coordinates is called the configuration space of the physical system.
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Conjugacy class
In mathematics, especially group theory, the elements of any group may be partitioned into conjugacy classes; members of the same conjugacy class share many properties, and study of conjugacy classes of non-abelian groups reveals many important features of their structure.
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Convex set
In convex geometry, a convex set is a subset of an affine space that is closed under convex combinations.
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Countable set
In mathematics, a countable set is a set with the same cardinality (number of elements) as some subset of the set of natural numbers.
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Covering space
In mathematics, more specifically algebraic topology, a covering map (also covering projection) is a continuous function p from a topological space, C, to a topological space, X, such that each point in X has an open neighbourhood evenly covered by p (as shown in the image); the precise definition is given below.
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Currying
In mathematics and computer science, currying is the technique of translating the evaluation of a function that takes multiple arguments (or a tuple of arguments) into evaluating a sequence of functions, each with a single argument.
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Cut (cards)
In many card games, to cut the cards (or to cut the deck) is a procedure used just prior to the cards being dealt to the players.
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Cycle graph
In graph theory, a cycle graph or circular graph is a graph that consists of a single cycle, or in other words, some number of vertices connected in a closed chain.
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Cycles and fixed points
In mathematics, the cycles of a permutation π of a finite set S correspond bijectively to the orbits of the subgroup generated by π acting on S. These orbits are subsets of S that can be written as, such that The corresponding cycle of π is written as (c1 c2... cn); this expression is not unique since c1 can be chosen to be any element of the orbit.
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Cyclic category
In mathematics, the cyclic category or cycle category or category of cycles is a category of finite cyclically ordered sets and degree-1 maps between them.
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Cyclic group
In algebra, a cyclic group or monogenous group is a group that is generated by a single element.
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Cyclic homology
In noncommutative geometry and related branches of mathematics, cyclic homology and cyclic cohomology are certain (co)homology theories for associative algebras which generalize the de Rham (co)homology of manifolds.
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Cyclically ordered group
In mathematics, a cyclically ordered group is a set with both a group structure and a cyclic order, such that left and right multiplication both preserve the cyclic order.
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Cyclohedron
In geometry, the cyclohedron or Bott–Taubes polytope is a certain (n − 1)-dimensional polytope that is useful in studying knot invariants.
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Dedekind–MacNeille completion
In order-theoretic mathematics, the Dedekind–MacNeille completion of a partially ordered set (also called the completion by cuts or normal completion) is the smallest complete lattice that contains the given partial order.
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Degree of a continuous mapping
In topology, the degree of a continuous mapping between two compact oriented manifolds of the same dimension is a number that represents the number of times that the domain manifold wraps around the range manifold under the mapping.
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Dense order
In mathematics, a partial order or total order.
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Directed algebraic topology
In mathematics, directed algebraic topology is a refinement of algebraic topology for directed spaces, topological spaces and their combinatorial counterparts equipped with some notion of direction.
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Dynamical system (definition)
The dynamical system concept is a mathematical formalization for any fixed "rule" which describes the time dependence of a point's position in its ambient space.
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Element (mathematics)
In mathematics, an element, or member, of a set is any one of the distinct objects that make up that set.
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Embedding
In mathematics, an embedding (or imbedding) is one instance of some mathematical structure contained within another instance, such as a group that is a subgroup.
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Finitary relation
In mathematics, a finitary relation has a finite number of "places".
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Finite set
In mathematics, a finite set is a set that has a finite number of elements.
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Formal power series
In mathematics, a formal power series is a generalization of a polynomial, where the number of terms is allowed to be infinite; this implies giving up the possibility of replacing the variable in the polynomial with an arbitrary number.
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Free group
In mathematics, the free group FS over a given set S consists of all expressions (a.k.a. words, or terms) that can be built from members of S, considering two expressions different unless their equality follows from the group axioms (e.g. st.
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Function (mathematics)
In mathematics, a function was originally the idealization of how a varying quantity depends on another quantity.
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Fundamenta Mathematicae
Fundamenta Mathematicae is a peer-reviewed scientific journal of mathematics with a special focus on the foundations of mathematics, concentrating on set theory, mathematical logic, topology and its interactions with algebra, and dynamical systems.
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Gene
In biology, a gene is a sequence of DNA or RNA that codes for a molecule that has a function.
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Greatest and least elements
In mathematics, especially in order theory, the greatest element of a subset S of a partially ordered set (poset) is an element of S that is greater than every other element of S. The term least element is defined dually, that is, it is an element of S that is smaller than every other element of S. Formally, given a partially ordered set (P, ≤), an element g of a subset S of P is the greatest element of S if Hence, the greatest element of S is an upper bound of S that is contained within this subset.
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Group (mathematics)
In mathematics, a group is an algebraic structure consisting of a set of elements equipped with an operation that combines any two elements to form a third element and that satisfies four conditions called the group axioms, namely closure, associativity, identity and invertibility.
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Group action
In mathematics, an action of a group is a formal way of interpreting the manner in which the elements of the group correspond to transformations of some space in a way that preserves the structure of that space.
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Group of rational points on the unit circle
In mathematics, the rational points on the unit circle are those points (x, y) such that both x and y are rational numbers ("fractions") and satisfy x2 + y2.
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Hans Freudenthal
Hans Freudenthal (17 September 1905 – 13 October 1990) was a Jewish-German-born Dutch mathematician.
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Harold Scott MacDonald Coxeter
Harold Scott MacDonald "Donald" Coxeter, FRS, FRSC, (February 9, 1907 – March 31, 2003) was a British-born Canadian geometer.
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Inclusion map
In mathematics, if A is a subset of B, then the inclusion map (also inclusion function, insertion, or canonical injection) is the function \iota that sends each element, x, of A to x, treated as an element of B: A "hooked arrow" is sometimes used in place of the function arrow above to denote an inclusion map; thus: \iota: A\hookrightarrow B. (On the other hand, this notation is sometimes reserved for embeddings.) This and other analogous injective functions from substructures are sometimes called natural injections.
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Infinite set
In set theory, an infinite set is a set that is not a finite set.
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Injective function
In mathematics, an injective function or injection or one-to-one function is a function that preserves distinctness: it never maps distinct elements of its domain to the same element of its codomain.
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Integer
An integer (from the Latin ''integer'' meaning "whole")Integer 's first literal meaning in Latin is "untouched", from in ("not") plus tangere ("to touch").
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Interval (mathematics)
In mathematics, a (real) interval is a set of real numbers with the property that any number that lies between two numbers in the set is also included in the set.
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Jean Piaget
Jean Piaget (9 August 1896 – 16 September 1980) was a Swiss psychologist and epistemologist known for his pioneering work in child development.
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Journal of Combinatorial Theory
The Journal of Combinatorial Theory, Series A and Series B, are mathematical journals specializing in combinatorics and related areas.
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Knot invariant
In the mathematical field of knot theory, a knot invariant is a quantity (in a broad sense) defined for each knot which is the same for equivalent knots.
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Ladislav Rieger
Ladislav Svante Rieger (1916–1963) was a Czech mathematician who worked in the areas of algebra, mathematical logic, and axiomatic set theory.
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Line (geometry)
The notion of line or straight line was introduced by ancient mathematicians to represent straight objects (i.e., having no curvature) with negligible width and depth.
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Linearly ordered group
In abstract algebra a linearly ordered or totally ordered group is a group G equipped with a total order "≤", that is translation-invariant.
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Longitude
Longitude, is a geographic coordinate that specifies the east-west position of a point on the Earth's surface.
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Lorentz surface
In mathematics, a Lorentz surface is a two-dimensional oriented smooth manifold with a conformal equivalence class of Lorentzian metrics.
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Manifold
In mathematics, a manifold is a topological space that locally resembles Euclidean space near each point.
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Mathematics
Mathematics (from Greek μάθημα máthēma, "knowledge, study, learning") is the study of such topics as quantity, structure, space, and change.
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Monomial
In mathematics, a monomial is, roughly speaking, a polynomial which has only one term.
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Monotonic function
In mathematics, a monotonic function (or monotone function) is a function between ordered sets that preserves or reverses the given order.
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Morphism
In mathematics, a morphism is a structure-preserving map from one mathematical structure to another one of the same type.
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Names of the days of the week
The names of the days of the week in many languages are derived from the names of the classical planets in Hellenistic astrology, which were in turn named after contemporary deities, a system introduced by the Roman Empire during Late Antiquity.
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O-minimal theory
In mathematical logic, and more specifically in model theory, an infinite structure (M,<,...) which is totally ordered by Knight, Pillay and Steinhorn (1986), Pillay and Steinhorn (1988).
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Omega-categorical theory
In mathematical logic, an omega-categorical theory is a theory that has exactly one countably infinite model up to isomorphism.
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Open set
In topology, an open set is an abstract concept generalizing the idea of an open interval in the real line.
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Order (journal)
Order (subtitled "A Journal on the Theory of Ordered Sets and its Applications") is a quarterly peer-reviewed academic journal on order theory and its applications, published by Springer Science+Business Media.
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Order theory
Order theory is a branch of mathematics which investigates the intuitive notion of order using binary relations.
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Order topology
In mathematics, an order topology is a certain topology that can be defined on any totally ordered set.
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Order type
In mathematics, especially in set theory, two ordered sets X,Y are said to have the same order type just when they are order isomorphic, that is, when there exists a bijection (each element matches exactly one in the other set) f: X → Y such that both f and its inverse are strictly increasing (order preserving i.e. the matching elements are also in the correct order).
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Ordered geometry
Ordered geometry is a form of geometry featuring the concept of intermediacy (or "betweenness") but, like projective geometry, omitting the basic notion of measurement.
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Partial cyclic order
In mathematics, a partial cyclic order is a ternary relation that generalizes a cyclic order in the same way that a partial order generalizes a linear order.
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Partially ordered set
In mathematics, especially order theory, a partially ordered set (also poset) formalizes and generalizes the intuitive concept of an ordering, sequencing, or arrangement of the elements of a set.
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Pencil (mathematics)
In projective geometry, a pencil is a family of geometric objects with a common property, for example the set of lines that pass through a given point in a projective plane.
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Permutation
In mathematics, the notion of permutation relates to the act of arranging all the members of a set into some sequence or order, or if the set is already ordered, rearranging (reordering) its elements, a process called permuting.
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Pitch class
In music, a pitch class (p.c. or pc) is a set of all pitches that are a whole number of octaves apart, e.g., the pitch class C consists of the Cs in all octaves.
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Polytope
In elementary geometry, a polytope is a geometric object with "flat" sides.
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Prime meridian
A prime meridian is a meridian (a line of longitude) in a geographic coordinate system at which longitude is defined to be 0°.
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Principal homogeneous space
In mathematics, a principal homogeneous space, or torsor, for a group G is a homogeneous space X for G in which the stabilizer subgroup of every point is trivial.
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Rational number
In mathematics, a rational number is any number that can be expressed as the quotient or fraction of two integers, a numerator and a non-zero denominator.
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Real closed field
In mathematics, a real closed field is a field F that has the same first-order properties as the field of real numbers.
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Real projective line
In geometry, a real projective line is an extension of the usual concept of line that has been historically introduced to solve a problem set by visual perspective: two parallel lines do not intersect but seem to intersect "at infinity".
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Rewriting
In mathematics, computer science, and logic, rewriting covers a wide range of (potentially non-deterministic) methods of replacing subterms of a formula with other terms.
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Rock–paper–scissors
Rock-paper-scissors (also known as scissors-paper-rock or other variants) is a hand game usually played between two people, in which each player simultaneously forms one of three shapes with an outstretched hand.
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Rotation number
In mathematics, the rotation number is an invariant of homeomorphisms of the circle.
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Royal Bohemian Society of Sciences
Royal Bohemian Society of Sciences (Regia Societas Scientiarum Bohemica; Königliche böhmische Gesellschaft der Wissenschaften; Královská česká společnost nauk) was established in 1784 – originally without adjective "royal" which was granted as late as in 1790 by King and Emperor Leopold II – to be the scientific center for Czech Crown lands.
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Scientific pitch notation
Scientific pitch notation (or SPN, also known as American Standard Pitch Notation (ASPN) and International Pitch Notation (IPN)) is a method of specifying musical pitch by combining a musical note name (with accidental if needed) and a number identifying the pitch's octave.
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Separation relation
In mathematics, a separation relation is a formal way to arrange a set of objects in an unoriented circle.
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Serial relation
In set theory, a serial relation is a binary relation R for which every element of the domain has a corresponding range element (∀ x ∃ y x R y).
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Set (mathematics)
In mathematics, a set is a collection of distinct objects, considered as an object in its own right.
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Simply connected space
In topology, a topological space is called simply connected (or 1-connected, or 1-simply connected) if it is path-connected and every path between two points can be continuously transformed (intuitively for embedded spaces, staying within the space) into any other such path while preserving the two endpoints in question.
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Strongly minimal theory
In model theory—a branch of mathematical logic—a minimal structure is an infinite one-sorted structure such that every subset of its domain that is definable with parameters is either finite or cofinite.
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Structure (mathematical logic)
In universal algebra and in model theory, a structure consists of a set along with a collection of finitary operations and relations that are defined on it.
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Subset
In mathematics, a set A is a subset of a set B, or equivalently B is a superset of A, if A is "contained" inside B, that is, all elements of A are also elements of B. A and B may coincide.
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Symmetric function
In mathematics, a symmetric function of n variables is one whose value given n arguments is the same no matter the order of the arguments.
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Ternary relation
In mathematics, a ternary relation or triadic relation is a finitary relation in which the number of places in the relation is three.
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Topological space
In topology and related branches of mathematics, a topological space may be defined as a set of points, along with a set of neighbourhoods for each point, satisfying a set of axioms relating points and neighbourhoods.
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Total order
In mathematics, a linear order, total order, simple order, or (non-strict) ordering is a binary relation on some set X, which is antisymmetric, transitive, and a connex relation.
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Transitive relation
In mathematics, a binary relation over a set is transitive if whenever an element is related to an element and is related to an element then is also related to.
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Unit circle
In mathematics, a unit circle is a circle with a radius of one.
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Weakly o-minimal structure
In model theory, a weakly o-minimal structure is a model theoretic structure whose definable sets in the domain are just finite unions of convex sets.
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12-hour clock
The 12-hour clock is a time convention in which the 24 hours of the day are divided into two periods: "The use of AM or PM to designate either noon or midnight can cause ambiguity.
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180th meridian
The 180th meridian or antimeridian is the meridian 180° east or west of the Prime Meridian, with which it forms a great circle dividing the earth into the Western and Eastern Hemispheres.
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24-hour clock
The 24-hour clock is the convention of time keeping in which the day runs from midnight to midnight and is divided into 24 hours, indicated by the hours passed since midnight, from 0 to 23.
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Circular order, Circular ordering, Circularly ordered set, Complete cyclic order, Cyclic ordering, Cyclic sequence, Cyclically ordered set, L-cyclic order, Linear cyclic order, Total cyclic order.
References
[1] https://en.wikipedia.org/wiki/Cyclic_order
