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29 relations: Algorithm, Apartness relation, Axiom of choice, Cauchy sequence, Constructivism (mathematics), Coq, Curry–Howard correspondence, Equality (mathematics), Equivalence class, Equivalence relation, Errett Bishop, Extension (semantics), Foundations of mathematics, Groupoid, Intension, Intuitionistic type theory, Lambda calculus, Mathematical proof, Mathematics, Partial equivalence relation, Per Martin-Löf, Proof theory, Quotient type, Rational number, Real analysis, Real number, Set (mathematics), Theorem, Type theory.
Algorithm
In mathematics and computer science, an algorithm is an unambiguous specification of how to solve a class of problems.
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Apartness relation
In constructive mathematics, an apartness relation is a constructive form of inequality, and is often taken to be more basic than equality.
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Axiom of choice
In mathematics, the axiom of choice, or AC, is an axiom of set theory equivalent to the statement that the Cartesian product of a collection of non-empty sets is non-empty.
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Cauchy sequence
In mathematics, a Cauchy sequence, named after Augustin-Louis Cauchy, is a sequence whose elements become arbitrarily close to each other as the sequence progresses.
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Constructivism (mathematics)
In the philosophy of mathematics, constructivism asserts that it is necessary to find (or "construct") a mathematical object to prove that it exists.
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Coq
In computer science, Coq is an interactive theorem prover.
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Curry–Howard correspondence
In programming language theory and proof theory, the Curry–Howard correspondence (also known as the Curry–Howard isomorphism or equivalence, or the proofs-as-programs and propositions- or formulae-as-types interpretation) is the direct relationship between computer programs and mathematical proofs.
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Equality (mathematics)
In mathematics, equality is a relationship between two quantities or, more generally two mathematical expressions, asserting that the quantities have the same value, or that the expressions represent the same mathematical object.
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Equivalence class
In mathematics, when the elements of some set S have a notion of equivalence (formalized as an equivalence relation) defined on them, then one may naturally split the set S into equivalence classes.
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Equivalence relation
In mathematics, an equivalence relation is a binary relation that is reflexive, symmetric and transitive.
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Errett Bishop
Errett Albert Bishop (July 14, 1928 – April 14, 1983) was an American mathematician known for his work on analysis.
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Extension (semantics)
In any of several studies that treat the use of signs—for example, in linguistics, logic, mathematics, semantics, and semiotics—the extension of a concept, idea, or sign consists of the things to which it applies, in contrast with its comprehension or intension, which consists very roughly of the ideas, properties, or corresponding signs that are implied or suggested by the concept in question.
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Foundations of mathematics
Foundations of mathematics is the study of the philosophical and logical and/or algorithmic basis of mathematics, or, in a broader sense, the mathematical investigation of what underlies the philosophical theories concerning the nature of mathematics.
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Groupoid
In mathematics, especially in category theory and homotopy theory, a groupoid (less often Brandt groupoid or virtual group) generalises the notion of group in several equivalent ways.
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Intension
In linguistics, logic, philosophy, and other fields, an intension is any property or quality connoted by a word, phrase, or another symbol.
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Intuitionistic type theory
Intuitionistic type theory (also known as constructive type theory, or Martin-Löf type theory) is a type theory and an alternative foundation of mathematics.
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Lambda calculus
Lambda calculus (also written as λ-calculus) is a formal system in mathematical logic for expressing computation based on function abstraction and application using variable binding and substitution.
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Mathematical proof
In mathematics, a proof is an inferential argument for a mathematical statement.
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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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Partial equivalence relation
In mathematics, a partial equivalence relation (often abbreviated as PER, in older literature also called restricted equivalence relation) R on a set X is a relation that is symmetric and transitive.
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Per Martin-Löf
Per Erik Rutger Martin-Löf (born May 8, 1942) is a Swedish logician, philosopher, and mathematical statistician.
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Proof theory
Proof theory is a major branchAccording to Wang (1981), pp.
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Quotient type
In type theory, a kind of foundation of mathematics, a quotient type is an algebraic data type that represents a type whose equality relation has been redefined by a given equivalence relation such that the elements of the type are partitioned into a set of equivalence classes whose cardinality is less than or equal to that of the base type.
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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 analysis
In mathematics, real analysis is the branch of mathematical analysis that studies the behavior of real numbers, sequences and series of real numbers, and real-valued functions.
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Real number
In mathematics, a real number is a value of a continuous quantity that can represent a distance along a line.
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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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Theorem
In mathematics, a theorem is a statement that has been proven on the basis of previously established statements, such as other theorems, and generally accepted statements, such as axioms.
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Type theory
In mathematics, logic, and computer science, a type theory is any of a class of formal systems, some of which can serve as alternatives to set theory as a foundation for all mathematics.
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References
[1] https://en.wikipedia.org/wiki/Setoid
