Razlika između inačica stranice »Relacija potpunog uređaja«
| Redak 26: | Redak 26: | ||
{{WMW | {{WMW | ||
|Struna_ID=13069 | |Struna_ID=13069 | ||
| − | |naziv= | + | |naziv=total order |
|klasifikacija= | |klasifikacija= | ||
|definicija=A [[:en:relation|relation]] $\leq$ is a total order on a set $S$ ("$\leq$ totally orders $S$") if the following properties hold.<br /> | |definicija=A [[:en:relation|relation]] $\leq$ is a total order on a set $S$ ("$\leq$ totally orders $S$") if the following properties hold.<br /> | ||
| Redak 34: | Redak 34: | ||
4. Comparability ([[:en:trichotomy law|trichotomy law]]): For any $a,b \in S$, either $a\leq b$ or $b\leq a$. | 4. Comparability ([[:en:trichotomy law|trichotomy law]]): For any $a,b \in S$, either $a\leq b$ or $b\leq a$. | ||
|cite=Weisstein, Eric W. "Totally Ordered Set." From MathWorld--A Wolfram Web Resource. http://mathworld.wolfram.com/TotallyOrderedSet.html | |cite=Weisstein, Eric W. "Totally Ordered Set." From MathWorld--A Wolfram Web Resource. http://mathworld.wolfram.com/TotallyOrderedSet.html | ||
| − | |napomena=The first three are the axioms of a partial order, while addition of the trichotomy law defines a total order. | + | |napomena=The first three are the axioms of a [[:en:partial order|partial order]], while addition of the [[:en:trichotomy law|trichotomy law]] defines a total order. |
|see_also=Order Isomorphic, Order Type, Partial Order, Relation, Total Order, Trichotomy Law, Well Ordered Set | |see_also=Order Isomorphic, Order Type, Partial Order, Relation, Total Order, Trichotomy Law, Well Ordered Set | ||
|primjeri=}} | |primjeri=}} | ||
Inačica od 08:04, 8. prosinca 2015.
Skraćeni oblik: potpuni uređaj
Definicija: Relacija parcijalnog uređaja "\(\leq\)" je relacija potpunog uređaja ako za svaki \(x,y\in S\) vrijedi \(x\leq y\) ili \(y\leq x\)
Dopušteni nazivi: totalni uređaj, relacija totalnog uređaja
Engleske istovrijednice: total order
Struna "light" ID: 13069
Obrađivač: Goran Igaly
Vrsta riječi: imenica Rod: ženski 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: total order
WMW definicija: A relation \(\leq\) is a total order on a set \(S\) ("\(\leq\) totally orders \(S\)") if the following properties hold.
1. Reflexivity\[a\leq a\] for all \(a \in S\).
2. Antisymmetry\[a\leq b\] and \(b\leq a\) implies \(a=b\).
3. Transitivity\[a\leq b\] and \(b\leq c\) implies \(a\leq c\).
4. Comparability (trichotomy law): For any \(a,b \in S\), either \(a\leq b\) or \(b\leq a\).
WMW napomena: The first three are the axioms of a partial order, while addition of the trichotomy law defines a total order.
WMW See also: Order Isomorphic, Order Type, Partial Order, Relation, Total Order, Trichotomy Law, Well Ordered Set
Izvor: Weisstein, Eric W. "Totally Ordered Set." From MathWorld--A Wolfram Web Resource. http://mathworld.wolfram.com/TotallyOrderedSet.html
Struna ID: 13069