Oct 4, 2006 18:01
17 yrs ago
1 viewer *
Serbian term
Greece
Montenegrin & Serbian language services
Native in: Montenegrin 
Works in: English to Montenegrin, Montenegrin to English, English to Serbian, and 2 more.
uredjenost (prirodnih brojeva)
Serbian to English
Social Sciences
Education / Pedagogy
Regulation of natural numbers, arrangement of natural numbers ili nesto trece?
Proposed translations
(English)
| 5 +2 | ordering, well-order relation, well-ordering |
Ulvija Tanovic (X)
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| 4 +2 | ordering set |
Maida Berbic
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| 4 | total order on the natural numbers |
V&M Stanković
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Proposed translations
+2
1 hr
Selected
ordering, well-order relation, well-ordering
well-order
In mathematics, a well-order relation (or well-ordering) on a set S is a linear order relation on S with the property that every non-empty subset of S has a least element in this ordering. Equivalently, a well-ordering is a well-founded linear ordering. The set S together with the well-order relation is then called a well-ordered set.
Roughly speaking, a well-ordered set is ordered in such a way that its elements can be considered one at a time, in order, and any time you haven't examined all of the elements, there's always a unique next element to consider.
Spelling note: The hyphen is frequently omitted in contemporary papers, yielding the spellings wellorder, wellordered, and wellordering.
Examples
* The standard ordering ≤ of the natural numbers is a well-ordering.
* The standard ordering ≤ of the integers is not a well-ordering, since, for example, the set of negative integers does not contain a least element.
In mathematics, a well-order relation (or well-ordering) on a set S is a linear order relation on S with the property that every non-empty subset of S has a least element in this ordering. Equivalently, a well-ordering is a well-founded linear ordering. The set S together with the well-order relation is then called a well-ordered set.
Roughly speaking, a well-ordered set is ordered in such a way that its elements can be considered one at a time, in order, and any time you haven't examined all of the elements, there's always a unique next element to consider.
Spelling note: The hyphen is frequently omitted in contemporary papers, yielding the spellings wellorder, wellordered, and wellordering.
Examples
* The standard ordering ≤ of the natural numbers is a well-ordering.
* The standard ordering ≤ of the integers is not a well-ordering, since, for example, the set of negative integers does not contain a least element.
Reference:
4 KudoZ points awarded for this answer.
Comment: "Hvala Ulvija, a hvala i svim ostalim kolegama koji su pomogli. Zao mi je sto poeni ne mogu da se podijele jer ste ti i Majda dale vrlo slicne odgovore. Stavila sam `ordering of the natural numbers`.
"
+2
32 mins
Maida Berbic
Native in Serbian
Accuracy, Timeliness and Responsiveness
Native in: Bosnian , Serbian
Works in: English to Bosnian, English to Serbian, Bosnian to English, and 6 more.
Related KudoZ points
:
8
ordering set
U principu bi bukvalan prevod bio "orderliness", medjutim nisam naisla na bas tako nesto u engleskom, a nisam ga uspjela naci ni na Google-u. Postoji tzv. "orderliness" and structure of the mathematics", ali ne kaze se isto u kontextu prirodnih brojeva (iako postoji njihovo uredjivanje).
Dakle, prevod bi bio ordering set/s of natural numbers.
Dakle, prevod bi bio ordering set/s of natural numbers.
Reference:
Peer comment(s):
| agree |
A.Đapo
48 mins
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Hvala ti Amra!
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| agree |
Pavle Perencevic
: Stavio bih samo "set of n.n.". Pošto se, pretpostavljam, radi o nižim razredima o.š., mislim da ne treba tražiti nekakav visokostručni termin - učenici treba da nauče koji broj dolazi pre ili posle nekog drugog broja i t. sl. Možda "sequence of n.n.?"
56 mins
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Hvala vam Pavle!
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| neutral |
PoveyTrans (X)
: Slazem se s Pavlem - "set of n.n." ali se ne moze reci tacno bez cijele rijecenice...You could also use "the ordering/order of natural numbers".
5 hrs
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Hvla Vam Simone!
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1 hr
V&M Stanković
Serbia
Serbia
Native in Serbian
Serbia
Sci/tech/leg. translators & Court transl
Native in: Serbian , Serbo-Croat
Works in: English to Serbian, Serbian to English, English to Serbo-Croat, and 5 more.
Related KudoZ points
:
44
total order on the natural numbers
Wikipedia:
Natural number
…
Properties
…
Furthermore, one defines a total order on the natural numbers by writing a ≤ b if and only if there exists another natural number c with a + c = b. This order is compatible with the arithmetical operations in the following sense: if a, b and c are natural numbers and a ≤ b, then a + c ≤ b + c and ac ≤ bc. An important property of the natural numbers is that they are well-ordered: every non-empty set of natural numbers has a least element.
(http://en.wikipedia.org/wiki/Natural_number)
“Viša elektrotehnička škola, Beograd
INŽENJERSKA MATEMATIKA
…
1) Uređenost skupa prirodnih brojeva pomoću binarnih relacija poretka " " i strogog poretka " " koja ima sledeća svojstva:
• za proizvoljna dva prirodna broja važi samo jedan od odnosa:
- svojstvo trihotomije
• ako su , i proizvoljni prirodni brojevi, tada u slučaju da je i - svojstvo tranzitivnosti.”
(http://www.vets.edu.yu/im/HTML/1.3.html)
“School of Mathematics, Georgia Institute of Technology, Atlanta
NUMBER SYSTEMS AND RELATIONS
…
5. A Total Order on Natural Numbers
Let m, n 2 N0. Define a binary relation _ on N0 by setting m _ n if and only if there exists a natural number p so that m + p = n…”
(http://www.math.gatech.edu/~trotter/chapter-2.pdf#search=""o...
Natural number
…
Properties
…
Furthermore, one defines a total order on the natural numbers by writing a ≤ b if and only if there exists another natural number c with a + c = b. This order is compatible with the arithmetical operations in the following sense: if a, b and c are natural numbers and a ≤ b, then a + c ≤ b + c and ac ≤ bc. An important property of the natural numbers is that they are well-ordered: every non-empty set of natural numbers has a least element.
(http://en.wikipedia.org/wiki/Natural_number)
“Viša elektrotehnička škola, Beograd
INŽENJERSKA MATEMATIKA
…
1) Uređenost skupa prirodnih brojeva pomoću binarnih relacija poretka " " i strogog poretka " " koja ima sledeća svojstva:
• za proizvoljna dva prirodna broja važi samo jedan od odnosa:
- svojstvo trihotomije
• ako su , i proizvoljni prirodni brojevi, tada u slučaju da je i - svojstvo tranzitivnosti.”
(http://www.vets.edu.yu/im/HTML/1.3.html)
“School of Mathematics, Georgia Institute of Technology, Atlanta
NUMBER SYSTEMS AND RELATIONS
…
5. A Total Order on Natural Numbers
Let m, n 2 N0. Define a binary relation _ on N0 by setting m _ n if and only if there exists a natural number p so that m + p = n…”
(http://www.math.gatech.edu/~trotter/chapter-2.pdf#search=""o...
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