Compute $operatorname{diam}(A)$ of the set $A ={(0,0),(1,1),(1,2),(2,2)}$ in metric space$ (mathbb R^2,d),$...
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Compute the diameter of $A,;$ i.e. compute $operatorname{diam}(A)$ of the set $A ={(0,0),(1,1),(1,2),(2,2)}$ in metric space $(mathbb R^2, d),$ where $d$ is defined by the formula:
$$dbig((x_1,y_1),(x_2,y_2)big)=begin{cases} |y_1-y_2|, & x_1 = x_2\ \ |x_1-x_2|+|y_1|+|y_2|, & x_1neq x_2 end{cases}.$$
Can anyone explain this clearly?
Thanks .
real-analysis metric-spaces
edited Jan 2 at 21:38
Chris Custer
11.6k3824
asked Jan 2 at 17:38
Arda Batuhan DemirArda Batuhan Demir
11
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closed as off-topic by José Carlos Santos, amWhy, Davide Giraudo, Cesareo, Leucippus Jan 3 at 0:34
This question appears to be off-topic. The users who voted to close gave this specific reason:
- "This question is missing context or other details: Please provide additional context, which ideally explains why the question is relevant to you and our community. Some forms of context include: background and motivation, relevant definitions, source, possible strategies, your current progress, why the question is interesting or important, etc." – José Carlos Santos, amWhy, Davide Giraudo, Cesareo, Leucippus
If this question can be reworded to fit the rules in the help center, please edit the question.
add a comment |
$begingroup$
Compute the diameter of $A,;$ i.e. compute $operatorname{diam}(A)$ of the set $A ={(0,0),(1,1),(1,2),(2,2)}$ in metric space $(mathbb R^2, d),$ where $d$ is defined by the formula:
$$dbig((x_1,y_1),(x_2,y_2)big)=begin{cases} |y_1-y_2|, & x_1 = x_2\ \ |x_1-x_2|+|y_1|+|y_2|, & x_1neq x_2 end{cases}.$$
Can anyone explain this clearly?
Thanks .
real-analysis metric-spaces
edited Jan 2 at 21:38
Chris Custer
11.6k3824
asked Jan 2 at 17:38
Arda Batuhan DemirArda Batuhan Demir
11
$endgroup$
closed as off-topic by José Carlos Santos, amWhy, Davide Giraudo, Cesareo, Leucippus Jan 3 at 0:34
This question appears to be off-topic. The users who voted to close gave this specific reason:
- "This question is missing context or other details: Please provide additional context, which ideally explains why the question is relevant to you and our community. Some forms of context include: background and motivation, relevant definitions, source, possible strategies, your current progress, why the question is interesting or important, etc." – José Carlos Santos, amWhy, Davide Giraudo, Cesareo, Leucippus
If this question can be reworded to fit the rules in the help center, please edit the question.
$begingroup$
Just substitute in the formula and calculate the diameter.
$endgroup$
– Michael Rozenberg
Jan 2 at 17:46
add a comment |
$begingroup$
Compute the diameter of $A,;$ i.e. compute $operatorname{diam}(A)$ of the set $A ={(0,0),(1,1),(1,2),(2,2)}$ in metric space $(mathbb R^2, d),$ where $d$ is defined by the formula:
$$dbig((x_1,y_1),(x_2,y_2)big)=begin{cases} |y_1-y_2|, & x_1 = x_2\ \ |x_1-x_2|+|y_1|+|y_2|, & x_1neq x_2 end{cases}.$$
Can anyone explain this clearly?
Thanks .
real-analysis metric-spaces
edited Jan 2 at 21:38
Chris Custer
11.6k3824
asked Jan 2 at 17:38
Arda Batuhan DemirArda Batuhan Demir
11
$endgroup$
Compute the diameter of $A,;$ i.e. compute $operatorname{diam}(A)$ of the set $A ={(0,0),(1,1),(1,2),(2,2)}$ in metric space $(mathbb R^2, d),$ where $d$ is defined by the formula:
$$dbig((x_1,y_1),(x_2,y_2)big)=begin{cases} |y_1-y_2|, & x_1 = x_2\ \ |x_1-x_2|+|y_1|+|y_2|, & x_1neq x_2 end{cases}.$$
Can anyone explain this clearly?
Thanks .
real-analysis metric-spaces
real-analysis metric-spaces
edited Jan 2 at 21:38
Chris Custer
11.6k3824
asked Jan 2 at 17:38
Arda Batuhan DemirArda Batuhan Demir
11
edited Jan 2 at 21:38
Chris Custer
11.6k3824
asked Jan 2 at 17:38
Arda Batuhan DemirArda Batuhan Demir
11
edited Jan 2 at 21:38
Chris Custer
11.6k3824
edited Jan 2 at 21:38
Chris Custer
11.6k3824
edited Jan 2 at 21:38
Chris Custer
11.6k3824
11.6k3824
asked Jan 2 at 17:38
Arda Batuhan DemirArda Batuhan Demir
11
asked Jan 2 at 17:38
Arda Batuhan DemirArda Batuhan Demir
11
asked Jan 2 at 17:38
Arda Batuhan DemirArda Batuhan Demir
11
11
closed as off-topic by José Carlos Santos, amWhy, Davide Giraudo, Cesareo, Leucippus Jan 3 at 0:34
This question appears to be off-topic. The users who voted to close gave this specific reason:
- "This question is missing context or other details: Please provide additional context, which ideally explains why the question is relevant to you and our community. Some forms of context include: background and motivation, relevant definitions, source, possible strategies, your current progress, why the question is interesting or important, etc." – José Carlos Santos, amWhy, Davide Giraudo, Cesareo, Leucippus
If this question can be reworded to fit the rules in the help center, please edit the question.
closed as off-topic by José Carlos Santos, amWhy, Davide Giraudo, Cesareo, Leucippus Jan 3 at 0:34
This question appears to be off-topic. The users who voted to close gave this specific reason:
- "This question is missing context or other details: Please provide additional context, which ideally explains why the question is relevant to you and our community. Some forms of context include: background and motivation, relevant definitions, source, possible strategies, your current progress, why the question is interesting or important, etc." – José Carlos Santos, amWhy, Davide Giraudo, Cesareo, Leucippus
If this question can be reworded to fit the rules in the help center, please edit the question.
$begingroup$
Just substitute in the formula and calculate the diameter.
$endgroup$
– Michael Rozenberg
Jan 2 at 17:46
add a comment |
$begingroup$
Just substitute in the formula and calculate the diameter.
$endgroup$
– Michael Rozenberg
Jan 2 at 17:46
$begingroup$
Just substitute in the formula and calculate the diameter.
$endgroup$
– Michael Rozenberg
Jan 2 at 17:46
$begingroup$
Just substitute in the formula and calculate the diameter.
$endgroup$
– Michael Rozenberg
Jan 2 at 17:46
add a comment |
2 Answers
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Compute all $binom{4}{2}=6$ distances between distinct points and see what the maximum is. I don't see the problem (but yes, it's work, do it!)
E.g. $d((0,0), (1,1)) = 2$ and $d((1,1), (1,2))=1$ etc.
answered Jan 2 at 17:45
Henno BrandsmaHenno Brandsma
107k347114
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The diameter is $operatorname{max}{d((x_1,y_1),(x_2,y_2))mid (x_1,y_1),(x_2,y_2)in A}$.
It looks like it's $5$. As pointed out by @Henno Brandsma, there are $6$ distances to check.
answered Jan 2 at 18:48
Chris CusterChris Custer
11.6k3824
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2 Answers
2
active
oldest
votes
2 Answers
2
active
oldest
votes
active
oldest
votes
active
oldest
votes
$begingroup$
Compute all $binom{4}{2}=6$ distances between distinct points and see what the maximum is. I don't see the problem (but yes, it's work, do it!)
E.g. $d((0,0), (1,1)) = 2$ and $d((1,1), (1,2))=1$ etc.
answered Jan 2 at 17:45
Henno BrandsmaHenno Brandsma
107k347114
$endgroup$
add a comment |
$begingroup$
Compute all $binom{4}{2}=6$ distances between distinct points and see what the maximum is. I don't see the problem (but yes, it's work, do it!)
E.g. $d((0,0), (1,1)) = 2$ and $d((1,1), (1,2))=1$ etc.
answered Jan 2 at 17:45
Henno BrandsmaHenno Brandsma
107k347114
$endgroup$
add a comment |
$begingroup$
Compute all $binom{4}{2}=6$ distances between distinct points and see what the maximum is. I don't see the problem (but yes, it's work, do it!)
E.g. $d((0,0), (1,1)) = 2$ and $d((1,1), (1,2))=1$ etc.
answered Jan 2 at 17:45
Henno BrandsmaHenno Brandsma
107k347114
$endgroup$
Compute all $binom{4}{2}=6$ distances between distinct points and see what the maximum is. I don't see the problem (but yes, it's work, do it!)
E.g. $d((0,0), (1,1)) = 2$ and $d((1,1), (1,2))=1$ etc.
answered Jan 2 at 17:45
Henno BrandsmaHenno Brandsma
107k347114
answered Jan 2 at 17:45
Henno BrandsmaHenno Brandsma
107k347114
answered Jan 2 at 17:45
Henno BrandsmaHenno Brandsma
107k347114
answered Jan 2 at 17:45
Henno BrandsmaHenno Brandsma
107k347114
107k347114
add a comment |
add a comment |
$begingroup$
The diameter is $operatorname{max}{d((x_1,y_1),(x_2,y_2))mid (x_1,y_1),(x_2,y_2)in A}$.
It looks like it's $5$. As pointed out by @Henno Brandsma, there are $6$ distances to check.
answered Jan 2 at 18:48
Chris CusterChris Custer
11.6k3824
$endgroup$
add a comment |
$begingroup$
The diameter is $operatorname{max}{d((x_1,y_1),(x_2,y_2))mid (x_1,y_1),(x_2,y_2)in A}$.
It looks like it's $5$. As pointed out by @Henno Brandsma, there are $6$ distances to check.
answered Jan 2 at 18:48
Chris CusterChris Custer
11.6k3824
$endgroup$
add a comment |
$begingroup$
The diameter is $operatorname{max}{d((x_1,y_1),(x_2,y_2))mid (x_1,y_1),(x_2,y_2)in A}$.
It looks like it's $5$. As pointed out by @Henno Brandsma, there are $6$ distances to check.
answered Jan 2 at 18:48
Chris CusterChris Custer
11.6k3824
$endgroup$
The diameter is $operatorname{max}{d((x_1,y_1),(x_2,y_2))mid (x_1,y_1),(x_2,y_2)in A}$.
It looks like it's $5$. As pointed out by @Henno Brandsma, there are $6$ distances to check.
answered Jan 2 at 18:48
Chris CusterChris Custer
11.6k3824
answered Jan 2 at 18:48
Chris CusterChris Custer
11.6k3824
answered Jan 2 at 18:48
Chris CusterChris Custer
11.6k3824
answered Jan 2 at 18:48
Chris CusterChris Custer
11.6k3824
11.6k3824
add a comment |
add a comment |
$begingroup$
Just substitute in the formula and calculate the diameter.
$endgroup$
– Michael Rozenberg
Jan 2 at 17:46