Mixing
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An ordering on a set A
$begingroup$
Let $A= {2,3,4,5,6,7,8,9,10}$.
An ordering on A is defined $xleq y $ $Leftrightarrow$ $y ; text{is multiple of}
;x$.
Find the maximal and minimal elements of A.
$2$ is the minimum or not ?
$5$ is a maximal element ?
I don't have any idea for this question.
Thanks your helping.
order-theory
asked Feb 1 at 19:03
mathsstudentmathsstudent
536
$endgroup$
add a comment |
$begingroup$
Let $A= {2,3,4,5,6,7,8,9,10}$.
An ordering on A is defined $xleq y $ $Leftrightarrow$ $y ; text{is multiple of}
;x$.
Find the maximal and minimal elements of A.
$2$ is the minimum or not ?
$5$ is a maximal element ?
I don't have any idea for this question.
Thanks your helping.
order-theory
asked Feb 1 at 19:03
mathsstudentmathsstudent
536
$endgroup$
1
$begingroup$
What is the question?
$endgroup$
– Garmekain
Feb 1 at 19:06
$begingroup$
What is the question? That is a fine partial order.
$endgroup$
– Ross Millikan
Feb 1 at 19:07
$begingroup$
Find the maximal and minimum elements of A. 2 is the minimum or not ? And 5 is maximal ?
$endgroup$
– mathsstudent
Feb 1 at 19:24
$begingroup$
Please edit that into your question
$endgroup$
– Ross Millikan
Feb 1 at 19:28
add a comment |
$begingroup$
Let $A= {2,3,4,5,6,7,8,9,10}$.
An ordering on A is defined $xleq y $ $Leftrightarrow$ $y ; text{is multiple of}
;x$.
Find the maximal and minimal elements of A.
$2$ is the minimum or not ?
$5$ is a maximal element ?
I don't have any idea for this question.
Thanks your helping.
order-theory
asked Feb 1 at 19:03
mathsstudentmathsstudent
536
$endgroup$
Let $A= {2,3,4,5,6,7,8,9,10}$.
An ordering on A is defined $xleq y $ $Leftrightarrow$ $y ; text{is multiple of}
;x$.
Find the maximal and minimal elements of A.
$2$ is the minimum or not ?
$5$ is a maximal element ?
I don't have any idea for this question.
Thanks your helping.
order-theory
order-theory
asked Feb 1 at 19:03
mathsstudentmathsstudent
536
asked Feb 1 at 19:03
mathsstudentmathsstudent
536
edited Feb 1 at 19:36
mathsstudent
asked Feb 1 at 19:03
mathsstudentmathsstudent
536
asked Feb 1 at 19:03
mathsstudentmathsstudent
536
asked Feb 1 at 19:03
mathsstudentmathsstudent
536
536
1
$begingroup$
What is the question?
$endgroup$
– Garmekain
Feb 1 at 19:06
$begingroup$
What is the question? That is a fine partial order.
$endgroup$
– Ross Millikan
Feb 1 at 19:07
$begingroup$
Find the maximal and minimum elements of A. 2 is the minimum or not ? And 5 is maximal ?
$endgroup$
– mathsstudent
Feb 1 at 19:24
$begingroup$
Please edit that into your question
$endgroup$
– Ross Millikan
Feb 1 at 19:28
add a comment |
1
$begingroup$
What is the question?
$endgroup$
– Garmekain
Feb 1 at 19:06
$begingroup$
What is the question? That is a fine partial order.
$endgroup$
– Ross Millikan
Feb 1 at 19:07
$begingroup$
Find the maximal and minimum elements of A. 2 is the minimum or not ? And 5 is maximal ?
$endgroup$
– mathsstudent
Feb 1 at 19:24
$begingroup$
Please edit that into your question
$endgroup$
– Ross Millikan
Feb 1 at 19:28
1
1
$begingroup$
What is the question?
$endgroup$
– Garmekain
Feb 1 at 19:06
$begingroup$
What is the question?
$endgroup$
– Garmekain
Feb 1 at 19:06
$begingroup$
What is the question? That is a fine partial order.
$endgroup$
– Ross Millikan
Feb 1 at 19:07
$begingroup$
What is the question? That is a fine partial order.
$endgroup$
– Ross Millikan
Feb 1 at 19:07
$begingroup$
Find the maximal and minimum elements of A. 2 is the minimum or not ? And 5 is maximal ?
$endgroup$
– mathsstudent
Feb 1 at 19:24
$begingroup$
Find the maximal and minimum elements of A. 2 is the minimum or not ? And 5 is maximal ?
$endgroup$
– mathsstudent
Feb 1 at 19:24
$begingroup$
Please edit that into your question
$endgroup$
– Ross Millikan
Feb 1 at 19:28
$begingroup$
Please edit that into your question
$endgroup$
– Ross Millikan
Feb 1 at 19:28
add a comment |
1 Answer
1
active
oldest
votes
$begingroup$
The minimal elements of $A$ are those which do not have any divisors in $A$: by inspection these are $2,3,5,$ and $7$.
The maximal elements of $A$ are those which do not divide any other elements of $A$: by inspection these are $7,8,9,$ and $10$.
answered Feb 1 at 19:27
pwerthpwerth
3,340417
$endgroup$
$begingroup$
I do not understand the part of maximal. A number is both maximal and minimal in the same time. Is it possible ?
$endgroup$
– mathsstudent
Feb 1 at 19:35
$begingroup$
What is your definition of maximal/minimal? I used the one found on wikipedia: en.wikipedia.org/wiki/Maximal_and_minimal_elements
$endgroup$
– pwerth
Feb 1 at 22:05
$begingroup$
But $5$ divides $10$.
$endgroup$
– amrsa
Feb 2 at 14:35
add a comment |
Your Answer
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1 Answer
1
active
oldest
votes
1 Answer
1
active
oldest
votes
active
oldest
votes
active
oldest
votes
$begingroup$
The minimal elements of $A$ are those which do not have any divisors in $A$: by inspection these are $2,3,5,$ and $7$.
The maximal elements of $A$ are those which do not divide any other elements of $A$: by inspection these are $7,8,9,$ and $10$.
answered Feb 1 at 19:27
pwerthpwerth
3,340417
$endgroup$
$begingroup$
I do not understand the part of maximal. A number is both maximal and minimal in the same time. Is it possible ?
$endgroup$
– mathsstudent
Feb 1 at 19:35
$begingroup$
What is your definition of maximal/minimal? I used the one found on wikipedia: en.wikipedia.org/wiki/Maximal_and_minimal_elements
$endgroup$
– pwerth
Feb 1 at 22:05
$begingroup$
But $5$ divides $10$.
$endgroup$
– amrsa
Feb 2 at 14:35
add a comment |
$begingroup$
The minimal elements of $A$ are those which do not have any divisors in $A$: by inspection these are $2,3,5,$ and $7$.
The maximal elements of $A$ are those which do not divide any other elements of $A$: by inspection these are $7,8,9,$ and $10$.
answered Feb 1 at 19:27
pwerthpwerth
3,340417
$endgroup$
$begingroup$
I do not understand the part of maximal. A number is both maximal and minimal in the same time. Is it possible ?
$endgroup$
– mathsstudent
Feb 1 at 19:35
$begingroup$
What is your definition of maximal/minimal? I used the one found on wikipedia: en.wikipedia.org/wiki/Maximal_and_minimal_elements
$endgroup$
– pwerth
Feb 1 at 22:05
$begingroup$
But $5$ divides $10$.
$endgroup$
– amrsa
Feb 2 at 14:35
add a comment |
$begingroup$
The minimal elements of $A$ are those which do not have any divisors in $A$: by inspection these are $2,3,5,$ and $7$.
The maximal elements of $A$ are those which do not divide any other elements of $A$: by inspection these are $7,8,9,$ and $10$.
answered Feb 1 at 19:27
pwerthpwerth
3,340417
$endgroup$
The minimal elements of $A$ are those which do not have any divisors in $A$: by inspection these are $2,3,5,$ and $7$.
The maximal elements of $A$ are those which do not divide any other elements of $A$: by inspection these are $7,8,9,$ and $10$.
answered Feb 1 at 19:27
pwerthpwerth
3,340417
edited Feb 4 at 19:28
answered Feb 1 at 19:27
pwerthpwerth
3,340417
answered Feb 1 at 19:27
pwerthpwerth
3,340417
answered Feb 1 at 19:27
pwerthpwerth
3,340417
3,340417
$begingroup$
I do not understand the part of maximal. A number is both maximal and minimal in the same time. Is it possible ?
$endgroup$
– mathsstudent
Feb 1 at 19:35
$begingroup$
What is your definition of maximal/minimal? I used the one found on wikipedia: en.wikipedia.org/wiki/Maximal_and_minimal_elements
$endgroup$
– pwerth
Feb 1 at 22:05
$begingroup$
But $5$ divides $10$.
$endgroup$
– amrsa
Feb 2 at 14:35
add a comment |
$begingroup$
I do not understand the part of maximal. A number is both maximal and minimal in the same time. Is it possible ?
$endgroup$
– mathsstudent
Feb 1 at 19:35
$begingroup$
What is your definition of maximal/minimal? I used the one found on wikipedia: en.wikipedia.org/wiki/Maximal_and_minimal_elements
$endgroup$
– pwerth
Feb 1 at 22:05
$begingroup$
But $5$ divides $10$.
$endgroup$
– amrsa
Feb 2 at 14:35
$begingroup$
I do not understand the part of maximal. A number is both maximal and minimal in the same time. Is it possible ?
$endgroup$
– mathsstudent
Feb 1 at 19:35
$begingroup$
I do not understand the part of maximal. A number is both maximal and minimal in the same time. Is it possible ?
$endgroup$
– mathsstudent
Feb 1 at 19:35
$begingroup$
What is your definition of maximal/minimal? I used the one found on wikipedia: en.wikipedia.org/wiki/Maximal_and_minimal_elements
$endgroup$
– pwerth
Feb 1 at 22:05
$begingroup$
What is your definition of maximal/minimal? I used the one found on wikipedia: en.wikipedia.org/wiki/Maximal_and_minimal_elements
$endgroup$
– pwerth
Feb 1 at 22:05
$begingroup$
But $5$ divides $10$.
$endgroup$
– amrsa
Feb 2 at 14:35
$begingroup$
But $5$ divides $10$.
$endgroup$
– amrsa
Feb 2 at 14:35
add a comment |
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1
$begingroup$
What is the question?
$endgroup$
– Garmekain
Feb 1 at 19:06
$begingroup$
What is the question? That is a fine partial order.
$endgroup$
– Ross Millikan
Feb 1 at 19:07
$begingroup$
Find the maximal and minimum elements of A. 2 is the minimum or not ? And 5 is maximal ?
$endgroup$
– mathsstudent
Feb 1 at 19:24
$begingroup$
Please edit that into your question
$endgroup$
– Ross Millikan
Feb 1 at 19:28