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Hyperoperation

Index Hyperoperation

In mathematics, the hyperoperation sequence is an infinite sequence of arithmetic operations (called hyperoperations) that starts with the unary operation of successor (n. [1]

46 relations: Ackermann function, Addition, Alfred Tarski, ASCII, Binary operation, Bowers's operators, Commutative property, Complex number, Computable function, Conway chained arrow notation, Cristopher Moore, Division (mathematics), Donald Knuth, Exponentiation, Floating-point arithmetic, Graham's number, Grzegorczyk hierarchy, Iterated function, John Horton Conway, Knuth's up-arrow notation, Kruskal's tree theorem, Large numbers, Logarithm, Mathematics, Mathematische Annalen, Multiplication, Names of large numbers, Nth root, Numeral prefix, Operator associativity, Ordinal arithmetic, Pentation, Primitive recursive function, Recursion, Recursion (computer science), Reuben Goodstein, Scientific notation, Sequence, Skewes's number, Subtraction, Successor function, Super-logarithm, Tetration, Unary operation, Wilhelm Ackermann, Zero to the power of zero.

Ackermann function

In computability theory, the Ackermann function, named after Wilhelm Ackermann, is one of the simplest and earliest-discovered examples of a total computable function that is not primitive recursive.

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Addition

Addition (often signified by the plus symbol "+") is one of the four basic operations of arithmetic; the others are subtraction, multiplication and division.

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Alfred Tarski

Alfred Tarski (January 14, 1901 – October 26, 1983), born Alfred Teitelbaum,School of Mathematics and Statistics, University of St Andrews,, School of Mathematics and Statistics, University of St Andrews.

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ASCII

ASCII, abbreviated from American Standard Code for Information Interchange, is a character encoding standard for electronic communication.

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Binary operation

In mathematics, a binary operation on a set is a calculation that combines two elements of the set (called operands) to produce another element of the set.

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Bowers's operators

This array notation was created by Jonathan Bowers, and is known as the Bowers's operators.

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Commutative property

In mathematics, a binary operation is commutative if changing the order of the operands does not change the result.

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Complex number

A complex number is a number that can be expressed in the form, where and are real numbers, and is a solution of the equation.

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Computable function

Computable functions are the basic objects of study in computability theory.

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Conway chained arrow notation

Conway chained arrow notation, created by mathematician John Horton Conway, is a means of expressing certain extremely large numbers.

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Cristopher Moore

Cristopher David Moore, known as Cris Moore, (born March 12, 1968 in New Brunswick, New Jersey), retrieved 2012-03-10.

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Division (mathematics)

Division is one of the four basic operations of arithmetic, the others being addition, subtraction, and multiplication.

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Donald Knuth

Donald Ervin Knuth (born January 10, 1938) is an American computer scientist, mathematician, and professor emeritus at Stanford University.

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Exponentiation

Exponentiation is a mathematical operation, written as, involving two numbers, the base and the exponent.

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Floating-point arithmetic

In computing, floating-point arithmetic is arithmetic using formulaic representation of real numbers as an approximation so as to support a trade-off between range and precision.

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Graham's number

Graham's number is an enormous number that arises as an upper bound on the answer of a problem in the mathematical field of Ramsey theory.

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Grzegorczyk hierarchy

The Grzegorczyk hierarchy (pronounced), named after the Polish logician Andrzej Grzegorczyk, is a hierarchy of functions used in computability theory (Wagner and Wechsung 1986:43).

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Iterated function

In mathematics, an iterated function is a function (that is, a function from some set to itself) which is obtained by composing another function with itself a certain number of times.

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John Horton Conway

John Horton Conway FRS (born 26 December 1937) is an English mathematician active in the theory of finite groups, knot theory, number theory, combinatorial game theory and coding theory.

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Knuth's up-arrow notation

In mathematics, Knuth's up-arrow notation is a method of notation for very large integers, introduced by Donald Knuth in 1976.

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Kruskal's tree theorem

In mathematics, Kruskal's tree theorem states that the set of finite trees over a well-quasi-ordered set of labels is itself well-quasi-ordered under homeomorphic embedding.

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Large numbers

Large numbers are numbers that are significantly larger than those ordinarily used in everyday life, for instance in simple counting or in monetary transactions.

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Logarithm

In mathematics, the logarithm is the inverse function to exponentiation.

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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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Mathematische Annalen

Mathematische Annalen (abbreviated as Math. Ann. or, formerly, Math. Annal.) is a German mathematical research journal founded in 1868 by Alfred Clebsch and Carl Neumann.

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Multiplication

Multiplication (often denoted by the cross symbol "×", by a point "⋅", by juxtaposition, or, on computers, by an asterisk "∗") is one of the four elementary mathematical operations of arithmetic; with the others being addition, subtraction and division.

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Names of large numbers

This article lists and discusses the usage and derivation of names of large numbers, together with their possible extensions.

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Nth root

In mathematics, an nth root of a number x, where n is usually assumed to be a positive integer, is a number r which, when raised to the power n yields x: where n is the degree of the root.

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Numeral prefix

Numeral or number prefixes are prefixes derived from numerals or occasionally other numbers.

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Operator associativity

In programming languages, the associativity of an operator is a property that determines how operators of the same precedence are grouped in the absence of parentheses.

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Ordinal arithmetic

In the mathematical field of set theory, ordinal arithmetic describes the three usual operations on ordinal numbers: addition, multiplication, and exponentiation.

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Pentation

In mathematics, pentation is the operation of repeated tetration, just as tetration is the operation of repeated exponentiation.

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Primitive recursive function

In computability theory, primitive recursive functions are a class of functions that are defined using primitive recursion and composition as central operations and are a strict subset of the total µ-recursive functions (µ-recursive functions are also called partial recursive).

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Recursion

Recursion occurs when a thing is defined in terms of itself or of its type.

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Recursion (computer science)

Recursion in computer science is a method of solving a problem where the solution depends on solutions to smaller instances of the same problem (as opposed to iteration).

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Reuben Goodstein

Reuben Louis Goodstein (15 December 1912 – 8 March 1985) was an English mathematician with a strong interest in the philosophy and teaching of mathematics.

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Scientific notation

Scientific notation (also referred to as scientific form or standard index form, or standard form in the UK) is a way of expressing numbers that are too big or too small to be conveniently written in decimal form.

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Sequence

In mathematics, a sequence is an enumerated collection of objects in which repetitions are allowed.

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Skewes's number

In number theory, Skewes's number is any of several extremely large numbers used by the South African mathematician Stanley Skewes as upper bounds for the smallest natural number x for which where π is the prime-counting function and li is the logarithmic integral function.

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Subtraction

Subtraction is an arithmetic operation that represents the operation of removing objects from a collection.

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Successor function

In mathematics, the successor function or successor operation is a primitive recursive function S such that S(n).

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Super-logarithm

In mathematics, the super-logarithm (or tetra-logarithm) is one of the two inverse functions of tetration.

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Tetration

In mathematics, tetration (or hyper-4) is the next hyperoperation after exponentiation, and is defined as iterated exponentiation.

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Unary operation

In mathematics, a unary operation is an operation with only one operand, i.e. a single input.

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Wilhelm Ackermann

Wilhelm Friedrich Ackermann (29 March 1896 – 24 December 1962) was a German mathematician best known for the Ackermann function, an important example in the theory of computation.

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Zero to the power of zero

Zero to the power of zero, denoted by 00, is a mathematical expression with no obvious value.

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Heptation, Hexa-logarithm, Hexa-root, Hexation, Hyper operation, Hyper operator, Hyperoperater, Hyperoperations, Hyperoperator.

References

[1] https://en.wikipedia.org/wiki/Hyperoperation

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