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The Collatz conjecture is an unsolved problem in mathematics that asks whether repeating two simple arithmetic operations will eventually transform every positive integer into 1. The operations are: if the number is even, divide it by 2; if the number is odd, multiply it by 3 and add 1.
Division is one of the four basic operations of arithmetic, which involves calculating the number of times one number is contained within another. Learn about different types, properties, and notations of division, as well as its applications in algebra and other fields.
A multiplicative inverse or reciprocal for a number x is a number which when multiplied by x yields 1. Learn the definition, examples, properties and applications of multiplicative inverses in different mathematical domains and contexts.
A division algebra is an algebra over a field in which division, except by zero, is always possible. Learn about the definitions, examples, properties and classifications of associative and non-associative division algebras over various fields.
Restoring division is a slow division method that operates on fixed-point fractional numbers and depends on the assumption that the divisor is not zero. It produces the quotient and remainder of Euclidean division using a recurrence equation and a partial remainder.
Learn about the concept of split, a cut whose cut-set forms a complete bipartite graph, and its applications in graph algorithms. Find out how to construct the split decomposition tree and recognize graph classes such as circle graphs and distance-hereditary graphs.
Learn about Moser's circle problem, which asks how to divide a circle into the most regions by an inscribed polygon. See the solution by an inductive method, the combinatorics and topology method, and the formula for the Euler characteristic.
A fraction is a number that represents a part of a whole or a ratio of equal parts. Fractions are not integers, but they can be converted to decimals or percentages. Learn more about the types, properties, and uses of fractions in mathematics and education.