Razlika između inačica stranice »Parcijalno uređeni skup«
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|definicija=A '''partially ordered set''' (or poset) is a set taken together with a [[parcijalni uređaj|partial order]] on it. Formally, a partially ordered set is defined as an [[uređeni par|ordered pair]] <math>P=(X,\leq)</math>, where <math>X</math> is called the ground set of <math>P</math> and <math>\leq</math> is the partial order of <math>P</math>. | |definicija=A '''partially ordered set''' (or poset) is a set taken together with a [[parcijalni uređaj|partial order]] on it. Formally, a partially ordered set is defined as an [[uređeni par|ordered pair]] <math>P=(X,\leq)</math>, where <math>X</math> is called the ground set of <math>P</math> and <math>\leq</math> is the partial order of <math>P</math>. | ||
|cite=Insall, Matt and Weisstein, Eric W. "Partially Ordered Set." From MathWorld--A Wolfram Web Resource. http://mathworld.wolfram.com/PartiallyOrderedSet.html | |cite=Insall, Matt and Weisstein, Eric W. "Partially Ordered Set." From MathWorld--A Wolfram Web Resource. http://mathworld.wolfram.com/PartiallyOrderedSet.html | ||
| − | |napomena=An element <math>u</math> in a partially ordered set <math>(X,\leq )</math> is said to be an [[gornja međa|upper bound]] for a [[podskup|subset]] <math>S</math> of <math>X | + | |napomena=An element <math>u</math> in a partially ordered set <math>(X,\leq )</math> is said to be an [[gornja međa|upper bound]] for a [[podskup|subset]] <math>S</math> of <math>X</math> if for every <math>s \in S</math>, we have <math>s\leq u</math>. Similarly, a [[donja međa|lower bound]] for a subset <math>S</math> is an element <math>l</math> such that for every <math>s \in S</math>, <math>l\leq s</math>. If there is an upper bound and a lower bound for <math>X</math>, then the poset <math>(X,\leq )</math> is said to be [[omeđeni skup|bounded]]. |
|see_also=Circle Order, Cover Relation, Dominance, Ground Set, Hasse Diagram, Interval Order, Isomorphic Posets, Lattice-Ordered Set, Order Isomorphic, Partial Order, Partially Ordered Multiset, Poset Dimension, Realizer, Relation}} | |see_also=Circle Order, Cover Relation, Dominance, Ground Set, Hasse Diagram, Interval Order, Isomorphic Posets, Lattice-Ordered Set, Order Isomorphic, Partial Order, Partially Ordered Multiset, Poset Dimension, Realizer, Relation}} | ||
Trenutačna izmjena od 17:36, 12. listopada 2016.
Skraćeni oblik: uređeni skup
Definicija: skup na kojemu je zadana relacija uređaja
Školska definicija: Uzmimo bilo koja dva prirodna broja \(a\) i \(b\). Tada za ta dva broja vrijedi samo jedna od triju mogućnosti:
1. \(a=b\) (\(a\) je jednako \(b\)) ili
2. \(a < b\) (\(a\) je manje od \(b\)) ili
3. \(a > b\) (\(a\) je veće od \(b\)).
Dopušteni nazivi: djelomično uređeni skup
Podređeni nazivi: potpuno uređeni skup
Engleske istovrijednice: uređeni skup=ordered set, parcijalno uređeni skup=partially ordered set, poset
Struna ID: 30111
Obrađivač: Zoran Škoda
Faza obrade: zaključaj naziv
Vrsta riječi: imenica Rod: muški Broj: jednina
Cilj projekta "Hrvatsko nazivlje u matematici" je na jednom mjestu prikupiti i obraditi sve hrvatske nazive koji na izravan ili neizravan način imaju veze s matematikom. Ako želite na bilo koji način doprinijeti ostvarenju ciljeva ovog projekta, molim javite se voditelju projekta na adresu goran.igaly@math.hr
WMW naziv: partially ordered set
WMW definicija: A partially ordered set (or poset) is a set taken together with a partial order on it. Formally, a partially ordered set is defined as an ordered pair \(P=(X,\leq)\), where \(X\) is called the ground set of \(P\) and \(\leq\) is the partial order of \(P\).
WMW napomena: An element \(u\) in a partially ordered set \((X,\leq )\) is said to be an upper bound for a subset \(S\) of \(X\) if for every \(s \in S\), we have \(s\leq u\). Similarly, a lower bound for a subset \(S\) is an element \(l\) such that for every \(s \in S\), \(l\leq s\). If there is an upper bound and a lower bound for \(X\), then the poset \((X,\leq )\) is said to be bounded.
WMW See also: Circle Order, Cover Relation, Dominance, Ground Set, Hasse Diagram, Interval Order, Isomorphic Posets, Lattice-Ordered Set, Order Isomorphic, Partial Order, Partially Ordered Multiset, Poset Dimension, Realizer, Relation
Izvor: Insall, Matt and Weisstein, Eric W. "Partially Ordered Set." From MathWorld--A Wolfram Web Resource. http://mathworld.wolfram.com/PartiallyOrderedSet.html
Struna ID: 30111