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Collatz conjecture

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The Collatz conjecture is a conjecture in mathematics that concerns a sequence defined as follows: start with any positive integer n. Then each term is obtained from the previous term as follows: if the previous term is even, the next term is one half the previous term. [1]

54 relations: Abstract machine, Almost surely, American Mathematical Monthly, American Mathematical Society, Arithmetical hierarchy, Berkeley Open Infrastructure for Network Computing, Binary number, Binary relation, Bit, Conjecture, Counterexample, Directed graph, Distributed computing, Fractal, Function (mathematics), Function composition, Gödel, Escher, Bach, Graph (discrete mathematics), Hail, Halting problem, Helmut Hasse, If and only if, Iterated function, Jeffrey Lagarias, John Horton Conway, Lothar Collatz, Mathematics, Mertens conjecture, Modular arithmetic, Natural number, P-adic number, Parity (mathematics), Paul Erdős, Pólya conjecture, Power of two, Precomputation, Providence, Rhode Island, Remainder, Repeating decimal, Residue-class-wise affine group, Sequence, Shizuo Kakutani, Skewes's number, Space–time tradeoff, Springer Science+Business Media, Stanislaw Ulam, String (computer science), Syracuse University, Theory of computation, Tree (graph theory), ..., Undecidable problem, University of Strasbourg, Wolfram Demonstrations Project, 3x + 1 semigroup. Expand index (4 more) »

Abstract machine

An abstract machine, also called an abstract computer, is a theoretical model of a computer hardware or software system used in automata theory.

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Almost surely

In probability theory, one says that an event happens almost surely (sometimes abbreviated as a.s.) if it happens with probability one.

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American Mathematical Monthly

The American Mathematical Monthly is a mathematical journal founded by Benjamin Finkel in 1894.

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American Mathematical Society

The American Mathematical Society (AMS) is an association of professional mathematicians dedicated to the interests of mathematical research and scholarship, and serves the national and international community through its publications, meetings, advocacy and other programs.

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Arithmetical hierarchy

In mathematical logic, the arithmetical hierarchy, arithmetic hierarchy or Kleene–Mostowski hierarchy classifies certain sets based on the complexity of formulas that define them.

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Berkeley Open Infrastructure for Network Computing

The Berkeley Open Infrastructure for Network Computing (BOINC, pronounced – rhymes with "oink"), an open-source middleware system, supports volunteer and grid computing.

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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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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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Bit

The bit (a portmanteau of binary digit) is a basic unit of information used in computing and digital communications.

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Conjecture

In mathematics, a conjecture is a conclusion or proposition based on incomplete information, for which no proof has been found.

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Counterexample

In logic, and especially in its applications to mathematics and philosophy, a counterexample is an exception to a proposed general rule or law.

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Directed graph

In mathematics, and more specifically in graph theory, a directed graph (or digraph) is a graph that is a set of vertices connected by edges, where the edges have a direction associated with them.

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Distributed computing

Distributed computing is a field of computer science that studies distributed systems.

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Fractal

In mathematics, a fractal is an abstract object used to describe and simulate naturally occurring objects.

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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, Escher, Bach

Gödel, Escher, Bach: An Eternal Golden Braid, also known as GEB, is a 1979 book by Douglas Hofstadter.

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Graph (discrete mathematics)

In mathematics, and more specifically in graph theory, a graph is a structure amounting to a set of objects in which some pairs of the objects are in some sense "related".

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Hail

Hail is a form of solid precipitation.

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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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Helmut Hasse

Helmut Hasse (25 August 1898 – 26 December 1979) was a German mathematician working in algebraic number theory, known for fundamental contributions to class field theory, the application of p-adic numbers to local class field theory and diophantine geometry (Hasse principle), and to local zeta functions.

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If and only if

In logic and related fields such as mathematics and philosophy, if and only if (shortened iff) is a biconditional logical connective between statements.

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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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Jeffrey Lagarias

Jeffrey Clark Lagarias (born November 16, 1949 in Pittsburgh, Pennsylvania, United States) is a mathematician and professor at the University of Michigan.

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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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Lothar Collatz

Lothar Collatz (July 6, 1910 – September 26, 1990) was a German mathematician, born in Arnsberg, Westphalia.

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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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Mertens conjecture

In mathematics, the Mertens conjecture is the disproven statement that the Mertens function M(n) is bounded by \sqrt, which implies the Riemann hypothesis.

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Modular arithmetic

In mathematics, modular arithmetic is a system of arithmetic for integers, where numbers "wrap around" upon reaching a certain value—the modulus (plural moduli).

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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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P-adic number

In mathematics, the -adic number system for any prime number extends the ordinary arithmetic of the rational numbers in a different way from the extension of the rational number system to the real and complex number systems.

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Parity (mathematics)

In mathematics, parity is the property of an integer's inclusion in one of two categories: even or odd.

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Paul Erdős

Paul Erdős (Erdős Pál; 26 March 1913 – 20 September 1996) was a Hungarian mathematician.

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Pólya conjecture

In number theory, the Pólya conjecture stated that "most" (i.e., 50% or more) of the natural numbers less than any given number have an odd number of prime factors.

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Power of two

In mathematics, a power of two is a number of the form where is an integer, i.e. the result of exponentiation with number two as the base and integer as the exponent.

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Precomputation

In algorithms, precomputation is the act of performing an initial computation before run time to generate a lookup table that can be used by an algorithm to avoid repeated computation each time it is executed.

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Providence, Rhode Island

Providence is the capital and most populous city of the U.S. state of Rhode Island and is one of the oldest cities in the United States.

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Remainder

In mathematics, the remainder is the amount "left over" after performing some computation.

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Repeating decimal

A repeating or recurring decimal is decimal representation of a number whose digits are periodic (repeating its values at regular intervals) and the infinitely-repeated portion is not zero.

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Residue-class-wise affine group

In mathematics, specifically in group theory, residue-class-wise affine groups are certain permutation groups acting on \mathbb (the integers), whose elements are bijective residue-class-wise affine mappings.

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Sequence

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

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Shizuo Kakutani

was a Japanese-American mathematician, best known for his eponymous fixed-point theorem.

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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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Space–time tradeoff

A space–time or time–memory trade-off in computer science is a case where an algorithm or program trades increased space usage with decreased time.

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Springer Science+Business Media

Springer Science+Business Media or Springer, part of Springer Nature since 2015, is a global publishing company that publishes books, e-books and peer-reviewed journals in science, humanities, technical and medical (STM) publishing.

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Stanislaw Ulam

Stanisław Marcin Ulam (13 April 1909 – 13 May 1984) was a Polish-American scientist in the fields of mathematics and nuclear physics.

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String (computer science)

In computer programming, a string is traditionally a sequence of characters, either as a literal constant or as some kind of variable.

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Syracuse University

Syracuse University (commonly referred to as Syracuse, 'Cuse, or SU) is a private research university in Syracuse, New York, United States.

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Theory of computation

In theoretical computer science and mathematics, the theory of computation is the branch that deals with how efficiently problems can be solved on a model of computation, using an algorithm.

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Tree (graph theory)

In mathematics, and more specifically in graph theory, a tree is an undirected graph in which any two vertices are connected by exactly one path.

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Undecidable problem

In computability theory and computational complexity theory, an undecidable problem is a decision problem for which it is known to be impossible to construct a single algorithm that always leads to a correct yes-or-no answer.

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University of Strasbourg

The University of Strasbourg (Université de Strasbourg, Unistra or UDS) in Strasbourg, Alsace, France, is the second largest university in France (after Aix-Marseille University), with about 46,000 students and over 4,000 researchers.

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Wolfram Demonstrations Project

The Wolfram Demonstrations Project is an organized, open-source collection of small (or medium-size) interactive programs called Demonstrations, which are meant to visually and interactively represent ideas from a range of fields.

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3x + 1 semigroup

In algebra, the 3x + 1 semigroup is a special subsemigroup of the multiplicative semigroup of all positive rational numbers.

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References

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

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