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Dyadic rational

Index Dyadic rational

In mathematics, a dyadic fraction or dyadic rational is a rational number whose denominator, when the ratio is in minimal (coprime) terms, is a power of two, i.e., a number of the form \frac where a is an integer and b is a natural number; for example, 1/2 or 3/8, but not 1/3. [1]

52 relations: Abelian group, Addition, American Journal of Physics, American Mathematical Monthly, Binary number, Character (mathematics), Complex number, Conlon Nancarrow, Cyclic group, Dense set, Direct limit, Division (mathematics), Equidistributed sequence, Fixed-point arithmetic, Floating-point arithmetic, Fraction (mathematics), Gallon, Group (mathematics), Group homomorphism, Half-integer, IEEE 754, Inch, Indecomposable continuum, Integer, Inverse limit, Irrational number, Localization of a ring, Mathematics, Multiplication, Musical notation, Natural number, Overring, P-adic number, Permutation, Pint, Pontryagin duality, Power of two, Prüfer group, Protorus, Quart, Rational number, Real line, Solenoid (mathematics), Subgroup, Subring, Subtraction, Surreal number, Time signature, Topological group, Unit circle, ..., Urysohn's lemma, Van der Corput sequence. Expand index (2 more) »

Abelian group

In abstract algebra, an abelian group, also called a commutative group, is a group in which the result of applying the group operation to two group elements does not depend on the order in which they are written.

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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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American Journal of Physics

The American Journal of Physics is a monthly, peer-reviewed scientific journal published by the American Association of Physics Teachers and the American Institute of Physics.

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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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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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Character (mathematics)

In mathematics, a character is (most commonly) a special kind of function from a group to a field (such as the complex numbers).

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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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Conlon Nancarrow

Conlon Nancarrow (October 27, 1912 – August 10, 1997) was an American-born composer who lived and worked in Mexico for most of his life.

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Cyclic group

In algebra, a cyclic group or monogenous group is a group that is generated by a single element.

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Dense set

In topology and related areas of mathematics, a subset A of a topological space X is called dense (in X) if every point x in X either belongs to A or is a limit point of A, that is the closure of A is constituting the whole set X. Informally, for every point in X, the point is either in A or arbitrarily "close" to a member of A — for instance, every real number either is a rational number or has a rational number arbitrarily close to it (see Diophantine approximation).

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Direct limit

In mathematics, a direct limit is a way to construct a (typically large) object from many (typically smaller) objects that are put together in a specific way.

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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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Equidistributed sequence

In mathematics, a sequence of real numbers is said to be equidistributed, or uniformly distributed, if the proportion of terms falling in a subinterval is proportional to the length of that interval.

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Fixed-point arithmetic

In computing, a fixed-point number representation is a real data type for a number that has a fixed number of digits after (and sometimes also before) the radix point (after the decimal point '.' in English decimal notation).

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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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Fraction (mathematics)

A fraction (from Latin fractus, "broken") represents a part of a whole or, more generally, any number of equal parts.

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Gallon

The gallon is a unit of measurement for fluid capacity in both the US customary units and the British imperial systems of measurement.

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Group (mathematics)

In mathematics, a group is an algebraic structure consisting of a set of elements equipped with an operation that combines any two elements to form a third element and that satisfies four conditions called the group axioms, namely closure, associativity, identity and invertibility.

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Group homomorphism

In mathematics, given two groups, (G, ∗) and (H, ·), a group homomorphism from (G, ∗) to (H, ·) is a function h: G → H such that for all u and v in G it holds that where the group operation on the left hand side of the equation is that of G and on the right hand side that of H. From this property, one can deduce that h maps the identity element eG of G to the identity element eH of H, and it also maps inverses to inverses in the sense that Hence one can say that h "is compatible with the group structure".

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Half-integer

In mathematics, a half-integer is a number of the form where n is an integer.

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IEEE 754

The IEEE Standard for Floating-Point Arithmetic (IEEE 754) is a technical standard for floating-point computation established in 1985 by the Institute of Electrical and Electronics Engineers (IEEE).

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Inch

The inch (abbreviation: in or &Prime) is a unit of length in the (British) imperial and United States customary systems of measurement now formally equal to yard but usually understood as of a foot.

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Indecomposable continuum

In point-set topology, an indecomposable continuum is a continuum that is indecomposable, i.e. that cannot be expressed as the union of any two of its proper subcontinua.

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Integer

An integer (from the Latin ''integer'' meaning "whole")Integer 's first literal meaning in Latin is "untouched", from in ("not") plus tangere ("to touch").

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Inverse limit

In mathematics, the inverse limit (also called the projective limit or limit) is a construction that allows one to "glue together" several related objects, the precise manner of the gluing process being specified by morphisms between the objects.

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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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Localization of a ring

In commutative algebra, localization is a systematic method of adding multiplicative inverses to a ring.

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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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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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Musical notation

Music notation or musical notation is any system used to visually represent aurally perceived music played with instruments or sung by the human voice through the use of written, printed, or otherwise-produced symbols.

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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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Overring

In mathematics, an overring B of an integral domain A is a subring of the field of fractions K of A that contains A: i.e., A \subseteq B \subseteq K. For instance, an overring of the integers is a ring in which all elements are rational numbers, such as the ring of dyadic rationals.

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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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Permutation

In mathematics, the notion of permutation relates to the act of arranging all the members of a set into some sequence or order, or if the set is already ordered, rearranging (reordering) its elements, a process called permuting.

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Pint

The pint (symbol pt, sometimes abbreviated as "p") is a unit of volume or capacity in both the imperial and United States customary measurement systems.

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Pontryagin duality

In mathematics, specifically in harmonic analysis and the theory of topological groups, Pontryagin duality explains the general properties of the Fourier transform on locally compact abelian groups, such as \R, the circle, or finite cyclic groups.

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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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Prüfer group

In mathematics, specifically in group theory, the Prüfer p-group or the p-quasicyclic group or p∞-group, Z(p∞), for a prime number p is the unique ''p''-group in which every element has p different p-th roots.

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Protorus

In mathematics, a protorus is a compact connected topological abelian group.

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Quart

The quart (abbreviation qt.) is an English unit of volume equal to a quarter gallon.

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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 line

In mathematics, the real line, or real number line is the line whose points are the real numbers.

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Solenoid (mathematics)

In mathematics, a solenoid is a compact connected topological space (i.e. a continuum) that may be obtained as the inverse limit of an inverse system of topological groups and continuous homomorphisms where each Si is a circle and fi is the map that uniformly wraps the circle Si+1 ni times (ni ≥ 2) around the circle Si.

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Subgroup

In group theory, a branch of mathematics, given a group G under a binary operation ∗, a subset H of G is called a subgroup of G if H also forms a group under the operation ∗.

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Subring

In mathematics, a subring of R is a subset of a ring that is itself a ring when binary operations of addition and multiplication on R are restricted to the subset, and which shares the same multiplicative identity as R. For those who define rings without requiring the existence of a multiplicative identity, a subring of R is just a subset of R that is a ring for the operations of R (this does imply it contains the additive identity of R).

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Subtraction

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

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Surreal number

In mathematics, the surreal number system is a totally ordered proper class containing the real numbers as well as infinite and infinitesimal numbers, respectively larger or smaller in absolute value than any positive real number.

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Time signature

The time signature (also known as meter signature, metre signature, or measure signature) is a notational convention used in Western musical notation to specify how many beats (pulses) are to be contained in each measure (bar) and which note value is equivalent to one beat.

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Topological group

In mathematics, a topological group is a group G together with a topology on G such that the group's binary operation and the group's inverse function are continuous functions with respect to the topology.

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Unit circle

In mathematics, a unit circle is a circle with a radius of one.

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Urysohn's lemma

In topology, Urysohn's lemma is a lemma that states that a topological space is normal if and only if any two disjoint closed subsets can be separated by a continuous function.

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Van der Corput sequence

A van der Corput sequence is an example of the simplest one-dimensional low-discrepancy sequence over the unit interval; it was first described in 1935 by the Dutch mathematician J. G. van der Corput.

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Dyadic fraction, Dyadic numbers, Dyadic rational number, Dyadic rationals, Dyadic solenoid.

References

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

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