Why is this relation not complete? [closed]Reflexive but not Transitive relationBinary relation, reflexive,...
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Why is this relation not complete? [closed]
Reflexive but not Transitive relationBinary relation, reflexive, symmetric and transitiveProving an equivalence relation(specifically transitivity)why this is not transitive yet a reflexive relation?Why is one relation transitive but the other is not?Why is the Relation R3 Transitive?Why is this not transitive R = {(1,1),(1,3),(2,2),(3,1)}?I don't know why this relation is NOT antisymmetricWhy is this relation not transitive?Why is this relation not reflexive?
$begingroup$
Why this relation bellow is not complete?
$A=mathbb{R^{2}}$, $x,y in A$ we define: $xgeq y iff x_{1} geq y_{1}$ and $x_{2} geq y_{2}$
I understand that this relation is transitive, reflexive and antissimetric. But after knowing that it is not complete I got confused a bit.
If I choose $x=(1,3)$ and $y=(frac{1}{2},4)$ it is an example that R is not complete?
relations
asked Mar 13 at 22:58
LinkmanLinkman
1396
$endgroup$
closed as unclear what you're asking by Peter, Lord Shark the Unknown, Lee David Chung Lin, Cesareo, Riccardo.Alestra Mar 14 at 10:41
Please clarify your specific problem or add additional details to highlight exactly what you need. As it's currently written, it’s hard to tell exactly what you're asking. See the How to Ask page for help clarifying this question. If this question can be reworded to fit the rules in the help center, please edit the question.
|
show 3 more comments
$begingroup$
Why this relation bellow is not complete?
$A=mathbb{R^{2}}$, $x,y in A$ we define: $xgeq y iff x_{1} geq y_{1}$ and $x_{2} geq y_{2}$
I understand that this relation is transitive, reflexive and antissimetric. But after knowing that it is not complete I got confused a bit.
If I choose $x=(1,3)$ and $y=(frac{1}{2},4)$ it is an example that R is not complete?
relations
asked Mar 13 at 22:58
LinkmanLinkman
1396
$endgroup$
closed as unclear what you're asking by Peter, Lord Shark the Unknown, Lee David Chung Lin, Cesareo, Riccardo.Alestra Mar 14 at 10:41
Please clarify your specific problem or add additional details to highlight exactly what you need. As it's currently written, it’s hard to tell exactly what you're asking. See the How to Ask page for help clarifying this question. If this question can be reworded to fit the rules in the help center, please edit the question.
1
$begingroup$
What is a complete relation?
$endgroup$
– saulspatz
Mar 13 at 23:04
$begingroup$
@saulspatz If it is possible to compare is complete. My example of x and y does not fit on the complete requiement. Right?
$endgroup$
– Linkman
Mar 13 at 23:20
1
$begingroup$
I don't know the definition of a "complete relation." That is not standard terminology, so far as I know. Please tell us what definition you are using.
$endgroup$
– saulspatz
Mar 13 at 23:22
$begingroup$
Im sorry @saulspatz. For all$x,y$ , $xRy$ OR $yRx$ it is a complete. relation. I believe it is known as Total Relation
$endgroup$
– Linkman
Mar 13 at 23:29
2
$begingroup$
Thanks. A partial order, that is, a relation which is reflexive, antisymmetric, and transitive, in which the condition you mention holds is known as a "total order" or a "linear order." I've never seen the term "total relation," so far as I can recall. You should add the clarification to the body of your question, since others will share my confusion. And yes your example shows that $A$ is not complete.
$endgroup$
– saulspatz
Mar 13 at 23:34
|
show 3 more comments
$begingroup$
Why this relation bellow is not complete?
$A=mathbb{R^{2}}$, $x,y in A$ we define: $xgeq y iff x_{1} geq y_{1}$ and $x_{2} geq y_{2}$
I understand that this relation is transitive, reflexive and antissimetric. But after knowing that it is not complete I got confused a bit.
If I choose $x=(1,3)$ and $y=(frac{1}{2},4)$ it is an example that R is not complete?
relations
asked Mar 13 at 22:58
LinkmanLinkman
1396
$endgroup$
Why this relation bellow is not complete?
$A=mathbb{R^{2}}$, $x,y in A$ we define: $xgeq y iff x_{1} geq y_{1}$ and $x_{2} geq y_{2}$
I understand that this relation is transitive, reflexive and antissimetric. But after knowing that it is not complete I got confused a bit.
If I choose $x=(1,3)$ and $y=(frac{1}{2},4)$ it is an example that R is not complete?
relations
relations
asked Mar 13 at 22:58
LinkmanLinkman
1396
asked Mar 13 at 22:58
LinkmanLinkman
1396
asked Mar 13 at 22:58
LinkmanLinkman
1396
asked Mar 13 at 22:58
LinkmanLinkman
1396
asked Mar 13 at 22:58
LinkmanLinkman
1396
1396
closed as unclear what you're asking by Peter, Lord Shark the Unknown, Lee David Chung Lin, Cesareo, Riccardo.Alestra Mar 14 at 10:41
Please clarify your specific problem or add additional details to highlight exactly what you need. As it's currently written, it’s hard to tell exactly what you're asking. See the How to Ask page for help clarifying this question. If this question can be reworded to fit the rules in the help center, please edit the question.
closed as unclear what you're asking by Peter, Lord Shark the Unknown, Lee David Chung Lin, Cesareo, Riccardo.Alestra Mar 14 at 10:41
Please clarify your specific problem or add additional details to highlight exactly what you need. As it's currently written, it’s hard to tell exactly what you're asking. See the How to Ask page for help clarifying this question. If this question can be reworded to fit the rules in the help center, please edit the question.
1
$begingroup$
What is a complete relation?
$endgroup$
– saulspatz
Mar 13 at 23:04
$begingroup$
@saulspatz If it is possible to compare is complete. My example of x and y does not fit on the complete requiement. Right?
$endgroup$
– Linkman
Mar 13 at 23:20
1
$begingroup$
I don't know the definition of a "complete relation." That is not standard terminology, so far as I know. Please tell us what definition you are using.
$endgroup$
– saulspatz
Mar 13 at 23:22
$begingroup$
Im sorry @saulspatz. For all$x,y$ , $xRy$ OR $yRx$ it is a complete. relation. I believe it is known as Total Relation
$endgroup$
– Linkman
Mar 13 at 23:29
2
$begingroup$
Thanks. A partial order, that is, a relation which is reflexive, antisymmetric, and transitive, in which the condition you mention holds is known as a "total order" or a "linear order." I've never seen the term "total relation," so far as I can recall. You should add the clarification to the body of your question, since others will share my confusion. And yes your example shows that $A$ is not complete.
$endgroup$
– saulspatz
Mar 13 at 23:34
|
show 3 more comments
1
$begingroup$
What is a complete relation?
$endgroup$
– saulspatz
Mar 13 at 23:04
$begingroup$
@saulspatz If it is possible to compare is complete. My example of x and y does not fit on the complete requiement. Right?
$endgroup$
– Linkman
Mar 13 at 23:20
1
$begingroup$
I don't know the definition of a "complete relation." That is not standard terminology, so far as I know. Please tell us what definition you are using.
$endgroup$
– saulspatz
Mar 13 at 23:22
$begingroup$
Im sorry @saulspatz. For all$x,y$ , $xRy$ OR $yRx$ it is a complete. relation. I believe it is known as Total Relation
$endgroup$
– Linkman
Mar 13 at 23:29
2
$begingroup$
Thanks. A partial order, that is, a relation which is reflexive, antisymmetric, and transitive, in which the condition you mention holds is known as a "total order" or a "linear order." I've never seen the term "total relation," so far as I can recall. You should add the clarification to the body of your question, since others will share my confusion. And yes your example shows that $A$ is not complete.
$endgroup$
– saulspatz
Mar 13 at 23:34
1
1
$begingroup$
What is a complete relation?
$endgroup$
– saulspatz
Mar 13 at 23:04
$begingroup$
What is a complete relation?
$endgroup$
– saulspatz
Mar 13 at 23:04
$begingroup$
@saulspatz If it is possible to compare is complete. My example of x and y does not fit on the complete requiement. Right?
$endgroup$
– Linkman
Mar 13 at 23:20
$begingroup$
@saulspatz If it is possible to compare is complete. My example of x and y does not fit on the complete requiement. Right?
$endgroup$
– Linkman
Mar 13 at 23:20
1
1
$begingroup$
I don't know the definition of a "complete relation." That is not standard terminology, so far as I know. Please tell us what definition you are using.
$endgroup$
– saulspatz
Mar 13 at 23:22
$begingroup$
I don't know the definition of a "complete relation." That is not standard terminology, so far as I know. Please tell us what definition you are using.
$endgroup$
– saulspatz
Mar 13 at 23:22
$begingroup$
Im sorry @saulspatz. For all$x,y$ , $xRy$ OR $yRx$ it is a complete. relation. I believe it is known as Total Relation
$endgroup$
– Linkman
Mar 13 at 23:29
$begingroup$
Im sorry @saulspatz. For all$x,y$ , $xRy$ OR $yRx$ it is a complete. relation. I believe it is known as Total Relation
$endgroup$
– Linkman
Mar 13 at 23:29
2
2
$begingroup$
Thanks. A partial order, that is, a relation which is reflexive, antisymmetric, and transitive, in which the condition you mention holds is known as a "total order" or a "linear order." I've never seen the term "total relation," so far as I can recall. You should add the clarification to the body of your question, since others will share my confusion. And yes your example shows that $A$ is not complete.
$endgroup$
– saulspatz
Mar 13 at 23:34
$begingroup$
Thanks. A partial order, that is, a relation which is reflexive, antisymmetric, and transitive, in which the condition you mention holds is known as a "total order" or a "linear order." I've never seen the term "total relation," so far as I can recall. You should add the clarification to the body of your question, since others will share my confusion. And yes your example shows that $A$ is not complete.
$endgroup$
– saulspatz
Mar 13 at 23:34
|
show 3 more comments
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$begingroup$
What is a complete relation?
$endgroup$
– saulspatz
Mar 13 at 23:04
$begingroup$
@saulspatz If it is possible to compare is complete. My example of x and y does not fit on the complete requiement. Right?
$endgroup$
– Linkman
Mar 13 at 23:20
1
$begingroup$
I don't know the definition of a "complete relation." That is not standard terminology, so far as I know. Please tell us what definition you are using.
$endgroup$
– saulspatz
Mar 13 at 23:22
$begingroup$
Im sorry @saulspatz. For all$x,y$ , $xRy$ OR $yRx$ it is a complete. relation. I believe it is known as Total Relation
$endgroup$
– Linkman
Mar 13 at 23:29
2
$begingroup$
Thanks. A partial order, that is, a relation which is reflexive, antisymmetric, and transitive, in which the condition you mention holds is known as a "total order" or a "linear order." I've never seen the term "total relation," so far as I can recall. You should add the clarification to the body of your question, since others will share my confusion. And yes your example shows that $A$ is not complete.
$endgroup$
– saulspatz
Mar 13 at 23:34