Word completion (996 bytes)
1: '''Word completion''' is a common feature in web browsers and simil...
5: ...tion''', as in some software such as [[Bash]] the completion of a string is invoked by hitting the tab key.
7: The [[Pocket PC]] comes with word completion, because tapping away at 5 to 10 wpm is frustrati...
9: In Microsoft's Visual Basic IDE, word completion is triggered with the Control-spacebar key combin...

Tab completion (2186 bytes)
1: '''Tab completion''' is a function of many [[command shell]]s, espe...
13: *More characters can then be filled in, and tab completion invoked in order to get the desired file's name. ...
14: ...e above list. If the list of possible options for completion is great, the shell will ask the user whether or ...
16: ==Completion in Microsoft operating systems==
18: ...DOS such as [[4DOS]] would feature Unix-style tab completion.

Completion rate (767 bytes)
1: '''Completion rates''' measure the useful transmission of compl...
6: ...ews network. They often suffer from resulting low completion rates.

Degree completion (635 bytes)
1: ...g which they picked up in a haphazard way. Degree completion programs, unlike [[diploma mill]]s, work within t...
3: ...ogical Seminary]], for example, provides a degree completion program for missionaries and others who for one r...

The Completion Backward Principle (289 bytes)
1: '''''The Completion Backward Principle''''' (1981) is the first album...

Knuth-Bendix completion algorithm (4305 bytes)
1: ... cannot turn into a rewrite rule). The enhanced [[completion without failure]] will not fail on unorientable e...

Dedekind sum (906 bytes)
1: ...m to express the [[functional equation]] of the [[Dedekind eta function]]. They have subsequently been much ...

Dedekind infinite (806 bytes)
1: ...s consistent that a set could be infinite but not Dedekind-infinite. This can be taken as an argument in fav...
3: Named after the German mathematician [[Richard Dedekind]].

Dedekind cut (3450 bytes)
2: ... ''B''. The original and most important cases are Dedekind cuts for [[rational number]]s and [[real number]]...
4: ==Handling Dedekind cuts==
6: ...t ''a''. For example it is shown that the typical Dedekind cut in the real numbers is either a pair with ''A...
8: ==Ordering Dedekind cuts==
14: ...und|least-upper-bound]] property, then the set of Dedekind cuts will be strictly bigger than ''S''.

Richard Dedekind (7519 bytes)
1: [[image:Dedekind.jpg|right]]
2: '''Julius Wilhelm Richard Dedekind''' ([[October 6]], [[1831]] - [[February 12]], [[...
4: ... youngest of four children of Julius Levin Ulrich Dedekind. He later rejected his first names Julius Wilhelm...
6: ...tainly have seen Dedekind's gift for mathematics. Dedekind received his doctorate in [[1852]] and he was Gau...
8: ...as the same time as [[Bernhard Riemann|Riemann]]. Dedekind began teaching as ''Privatdozent'' in Göttingen a...

Dedekind domain (3298 bytes)
3: ...hich has [[Krull dimension]] 1. In other words, a Dedekind domain is a [[commutative]] [[ring (algebra)|ring...
5: ...ind domains is that an integral domain ''R'' is a Dedekind domain if and only if the [[localization of a rin...
7: ...ntegral closure]] of '''Z''' in ''F''). This is a Dedekind domain, and ''F'' is its fraction field. A concre...
9: The study of Dedekind domains began when [[Dedekind]] introduced the notion of ideal in a ring in the...
10: ...f [[prime ideal|prime ideals]]. This explains why Dedekind thought of ideals as "idealized numbers".

Dedekind eta function (1829 bytes)
1: The '''Dedekind eta function''' is a function defined on the [[up...

Dedekind zeta function (2485 bytes)
1: In [[mathematics]], the '''Dedekind zeta function''' is a [[Dirichlet series]] define...
25: ...uation (L-function)|functional equation]] for the Dedekind zeta function, relating its values at ''s'' and 1...
27: ...h ''K'' is an [[abelian extension]] of ''Q'', its Dedekind zeta function can be written as a product of [[Di...
37: ...nsion]] of ''Q'' with [[Galois group]] ''G'', its Dedekind zeta function has a comparable factorization in t...

Principal ideal domain (2337 bytes)
17: ...in]], and hence every principal ideal domain is a Dedekind domain.
19: ...ath>PID, but then this shows equality and hence, Dedekind <math>\cap</math> UFD = PID.

Discrete valuation ring (2115 bytes)
7: # ''R'' is a [[local ring|local]] [[Dedekind domain]].
10: # There is some [[valuation (mathematics)|Dedekind valuation]] &nu; on the field of fractions ''K'' ...
16: ...al]] generated by 2. Any [[localization]] of a [[Dedekind domain]] is a discrete valuation ring; in practic...

Fractional ideal (2843 bytes)
1: ...tional ideal''' is introduced in the context of [[Dedekind domain]]s. In general commutative rings there is ...
3: ...le]] and [[field of quotients]]. Let ''R'' be a [[Dedekind domain]]. It is an [[integral domain]], and so it...
5: ...n a natural manner, and it can be shown that in a Dedekind domain, the fractional ideals form an abelian mul...
11: An alternative characterization of Dedekind domain is that every fractional ideal of ''R'' be...

Vorlesungen über Zahlentheorie (3764 bytes)
1: ...jeune Dirichlet| P.G.L. Dirichlet]] and [[Richard Dedekind]], and published in [[1863]].
3: ...y Dedekind and published after Dirichlet's death. Dedekind added several appendices to the ''Vorlesungen'', ...
26: This translation does not include Dedekind's Supplements X and XI in which he begins to deve...
28: ...Gauss']] ''[[Disquisitiones Arithmeticae]]'', and Dedekind added footnotes which specifically cross-referenc...
35: ...ch Gauss|Gauss]], and the modern number theory of Dedekind, [[Riemann]] and [[Hilbert]]. Dirichlet does not ...

Global field (1464 bytes)
6: ... can be realized as the [[quotient field]] of a [[Dedekind domain]] in which every non-zero [[Ideal (ring th...

Complete measure (1110 bytes)
3: ...ete. The smallest such extension is called the '''completion''' of the measure.
6: The completion of &mu; can be constructed as follows.
10: Then &mu;' is a complete measure, and is the completion of &mu;.

Eta function (160 bytes)
4: * The [[Dedekind eta function]]

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