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58 relations: American Mathematical Monthly, Axiom schema of specification, Bijection, Binary number, Bit, Cantor's theorem, Cardinal number, Cardinality, Cardinality of the continuum, Classical mathematics, Complexity class, Constructive proof, Constructivism (mathematics), Continuum hypothesis, Controversy over Cantor's theory, Countable set, Diagonal lemma, Diagonalization, Entscheidungsproblem, Enumeration, Function (mathematics), Function composition, Gödel's incompleteness theorems, Georg Cantor, Georg Cantor's first set theory article, German Mathematical Society, Halting problem, Image (mathematics), Infinite set, Injective function, Interval (mathematics), Irrational number, Linear function, Mathematical proof, Naive set theory, Natural number, New Foundations, Ones' complement, P versus NP problem, Power set, Proof by contradiction, Radix, Radix point, Real number, Richard's paradox, Russell's paradox, Sequence, Series (mathematics), Set (mathematics), Set theory, ..., Subcountability, Subset, Surjective function, Trigonometric functions, Type theory, Uncountable set, Universal set, Willard Van Orman Quine. Expand index (8 more) »
American Mathematical Monthly
The American Mathematical Monthly is a mathematical journal founded by Benjamin Finkel in 1894.
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Axiom schema of specification
In many popular versions of axiomatic set theory the axiom schema of specification, also known as the axiom schema of separation, subset axiom scheme or axiom schema of restricted comprehension is an axiom schema.
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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 number
In mathematics and digital electronics, a binary number is a number expressed in the base-2 numeral system or binary numeral system, which uses only two symbols: typically 0 (zero) and 1 (one).
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Bit
The bit (a portmanteau of binary digit) is a basic unit of information used in computing and digital communications.
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Cantor's theorem
In elementary set theory, Cantor's theorem is a fundamental result that states that, for any set A, the set of all subsets of A (the power set of A, denoted by \mathcal(A)) has a strictly greater cardinality than A itself.
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Cardinal number
In mathematics, cardinal numbers, or cardinals for short, are a generalization of the natural numbers used to measure the cardinality (size) of sets.
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Cardinality
In mathematics, the cardinality of a set is a measure of the "number of elements of the set".
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Cardinality of the continuum
In set theory, the cardinality of the continuum is the cardinality or “size” of the set of real numbers \mathbb R, sometimes called the continuum.
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Classical mathematics
In the foundations of mathematics, classical mathematics refers generally to the mainstream approach to mathematics, which is based on classical logic and ZFC set theory.
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Complexity class
In computational complexity theory, a complexity class is a set of problems of related resource-based complexity.
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Constructive proof
In mathematics, a constructive proof is a method of proof that demonstrates the existence of a mathematical object by creating or providing a method for creating the object.
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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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Continuum hypothesis
In mathematics, the continuum hypothesis (abbreviated CH) is a hypothesis about the possible sizes of infinite sets.
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Controversy over Cantor's theory
In mathematical logic, the theory of infinite sets was first developed by Georg Cantor.
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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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Diagonal lemma
In mathematical logic, the diagonal lemma or fixed point theorem establishes the existence of self-referential sentences in certain formal theories of the natural numbers—specifically those theories that are strong enough to represent all computable functions.
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Diagonalization
In mathematics, diagonalization may refer to.
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Entscheidungsproblem
In mathematics and computer science, the Entscheidungsproblem (German for "decision problem") is a challenge posed by David Hilbert in 1928.
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Enumeration
An enumeration is a complete, ordered listing of all the items in a collection.
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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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Function composition
In mathematics, function composition is the pointwise application of one function to the result of another to produce a third function.
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Gödel's incompleteness theorems
Gödel's incompleteness theorems are two theorems of mathematical logic that demonstrate the inherent limitations of every formal axiomatic system containing basic arithmetic.
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Georg Cantor
Georg Ferdinand Ludwig Philipp Cantor (– January 6, 1918) was a German mathematician.
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Georg Cantor's first set theory article
Georg Cantor's first set theory article was published in 1874 and contains the first theorems of transfinite set theory, which studies infinite sets and their properties.
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German Mathematical Society
The German Mathematical Society (Deutsche Mathematiker-Vereinigung – DMV) is the main professional society of German mathematicians.
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Halting problem
In computability theory, the halting problem is the problem of determining, from a description of an arbitrary computer program and an input, whether the program will finish running (i.e., halt) or continue to run forever.
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Image (mathematics)
In mathematics, an image is the subset of a function's codomain which is the output of the function from a subset of its domain.
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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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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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Irrational number
In mathematics, the irrational numbers are all the real numbers which are not rational numbers, the latter being the numbers constructed from ratios (or fractions) of integers.
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Linear function
In mathematics, the term linear function refers to two distinct but related notions.
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Mathematical proof
In mathematics, a proof is an inferential argument for a mathematical statement.
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Naive set theory
Naïve set theory is any of several theories of sets used in the discussion of the foundations of mathematics.
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Natural number
In mathematics, the natural numbers are those used for counting (as in "there are six coins on the table") and ordering (as in "this is the third largest city in the country").
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New Foundations
In mathematical logic, New Foundations (NF) is an axiomatic set theory, conceived by Willard Van Orman Quine as a simplification of the theory of types of Principia Mathematica.
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Ones' complement
The ones' complement of a binary number is defined as the value obtained by inverting all the bits in the binary representation of the number (swapping 0s for 1s and vice versa).
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P versus NP problem
The P versus NP problem is a major unsolved problem in computer science.
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Power set
In mathematics, the power set (or powerset) of any set is the set of all subsets of, including the empty set and itself, variously denoted as, đť’«(), ℘() (using the "Weierstrass p"),,, or, identifying the powerset of with the set of all functions from to a given set of two elements,.
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Proof by contradiction
In logic, proof by contradiction is a form of proof, and more specifically a form of indirect proof, that establishes the truth or validity of a proposition.
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Radix
In mathematical numeral systems, the radix or base is the number of unique digits, including zero, used to represent numbers in a positional numeral system.
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Radix point
In mathematics and computing, a radix point (or radix character) is the symbol used in numerical representations to separate the integer part of a number (to the left of the radix point) from its fractional part (to the right of the radix point).
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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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Richard's paradox
In logic, Richard's paradox is a semantical antinomy of set theory and natural language first described by the French mathematician Jules Richard in 1905.
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Russell's paradox
In the foundations of mathematics, Russell's paradox (also known as Russell's antinomy), discovered by Bertrand Russell in 1901, showed that some attempted formalizations of the naïve set theory created by Georg Cantor led to a contradiction.
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Sequence
In mathematics, a sequence is an enumerated collection of objects in which repetitions are allowed.
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Series (mathematics)
In mathematics, a series is, roughly speaking, a description of the operation of adding infinitely many quantities, one after the other, to a given starting quantity.
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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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Set theory
Set theory is a branch of mathematical logic that studies sets, which informally are collections of objects.
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Subcountability
In constructive mathematics, a collection is subcountable if there exists a partial surjection from the natural numbers onto 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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Surjective function
In mathematics, a function f from a set X to a set Y is surjective (or onto), or a surjection, if for every element y in the codomain Y of f there is at least one element x in the domain X of f such that f(x).
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Trigonometric functions
In mathematics, the trigonometric functions (also called circular functions, angle functions or goniometric functions) are functions of an angle.
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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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Uncountable set
In mathematics, an uncountable set (or uncountably infinite set) is an infinite set that contains too many elements to be countable.
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Universal set
In set theory, a universal set is a set which contains all objects, including itself.
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Willard Van Orman Quine
Willard Van Orman Quine (known to intimates as "Van"; June 25, 1908 – December 25, 2000) was an American philosopher and logician in the analytic tradition, recognized as "one of the most influential philosophers of the twentieth century." From 1930 until his death 70 years later, Quine was continually affiliated with Harvard University in one way or another, first as a student, then as a professor of philosophy and a teacher of logic and set theory, and finally as a professor emeritus who published or revised several books in retirement.
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References
[1] https://en.wikipedia.org/wiki/Cantor's_diagonal_argument
