How can we call the quantity $sup{|a-b|: ain A text{ and } bin B}$ where $A$ and $B$ are sets
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How can we call the quantity $sup{|a-b|: ain A, bin B}$ where $A$ and $B$ are sets
analysis
edited Dec 8 '18 at 20:47
Bernard
119k740113
asked Dec 8 '18 at 20:26
J.B.J.B.
1
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add a comment |
$begingroup$
How can we call the quantity $sup{|a-b|: ain A, bin B}$ where $A$ and $B$ are sets
analysis
edited Dec 8 '18 at 20:47
Bernard
119k740113
asked Dec 8 '18 at 20:26
J.B.J.B.
1
$endgroup$
$begingroup$
Perhaps it's maximum distance between sets $A$ and $B$?
$endgroup$
– user3342072
Dec 8 '18 at 20:28
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We could call it Bill. As $|a-b|$ is often referred to as the distance between point this is the supremum of distances between points of the set. Is there any reason we need to call it anything else.
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– fleablood
Dec 8 '18 at 21:09
add a comment |
$begingroup$
How can we call the quantity $sup{|a-b|: ain A, bin B}$ where $A$ and $B$ are sets
analysis
edited Dec 8 '18 at 20:47
Bernard
119k740113
asked Dec 8 '18 at 20:26
J.B.J.B.
1
$endgroup$
How can we call the quantity $sup{|a-b|: ain A, bin B}$ where $A$ and $B$ are sets
analysis
analysis
edited Dec 8 '18 at 20:47
Bernard
119k740113
asked Dec 8 '18 at 20:26
J.B.J.B.
1
edited Dec 8 '18 at 20:47
Bernard
119k740113
asked Dec 8 '18 at 20:26
J.B.J.B.
1
edited Dec 8 '18 at 20:47
Bernard
119k740113
edited Dec 8 '18 at 20:47
Bernard
119k740113
edited Dec 8 '18 at 20:47
Bernard
119k740113
119k740113
asked Dec 8 '18 at 20:26
J.B.J.B.
1
asked Dec 8 '18 at 20:26
J.B.J.B.
1
asked Dec 8 '18 at 20:26
J.B.J.B.
1
1
$begingroup$
Perhaps it's maximum distance between sets $A$ and $B$?
$endgroup$
– user3342072
Dec 8 '18 at 20:28
$begingroup$
We could call it Bill. As $|a-b|$ is often referred to as the distance between point this is the supremum of distances between points of the set. Is there any reason we need to call it anything else.
$endgroup$
– fleablood
Dec 8 '18 at 21:09
add a comment |
$begingroup$
Perhaps it's maximum distance between sets $A$ and $B$?
$endgroup$
– user3342072
Dec 8 '18 at 20:28
$begingroup$
We could call it Bill. As $|a-b|$ is often referred to as the distance between point this is the supremum of distances between points of the set. Is there any reason we need to call it anything else.
$endgroup$
– fleablood
Dec 8 '18 at 21:09
$begingroup$
Perhaps it's maximum distance between sets $A$ and $B$?
$endgroup$
– user3342072
Dec 8 '18 at 20:28
$begingroup$
Perhaps it's maximum distance between sets $A$ and $B$?
$endgroup$
– user3342072
Dec 8 '18 at 20:28
$begingroup$
We could call it Bill. As $|a-b|$ is often referred to as the distance between point this is the supremum of distances between points of the set. Is there any reason we need to call it anything else.
$endgroup$
– fleablood
Dec 8 '18 at 21:09
$begingroup$
We could call it Bill. As $|a-b|$ is often referred to as the distance between point this is the supremum of distances between points of the set. Is there any reason we need to call it anything else.
$endgroup$
– fleablood
Dec 8 '18 at 21:09
add a comment |
1 Answer
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I would call this the lenticular diameter of the two sets, by appealing to the geometric case of compact sets belonging to $mathbb{R}^2$.
It should be noted that this is very closely realted to, but not quite the same as, the diameter of the union of the two sets.
answered Dec 8 '18 at 20:33
RandomMathGuyRandomMathGuy
462
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1 Answer
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1 Answer
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$begingroup$
I would call this the lenticular diameter of the two sets, by appealing to the geometric case of compact sets belonging to $mathbb{R}^2$.
It should be noted that this is very closely realted to, but not quite the same as, the diameter of the union of the two sets.
answered Dec 8 '18 at 20:33
RandomMathGuyRandomMathGuy
462
$endgroup$
add a comment |
$begingroup$
I would call this the lenticular diameter of the two sets, by appealing to the geometric case of compact sets belonging to $mathbb{R}^2$.
It should be noted that this is very closely realted to, but not quite the same as, the diameter of the union of the two sets.
answered Dec 8 '18 at 20:33
RandomMathGuyRandomMathGuy
462
$endgroup$
add a comment |
$begingroup$
I would call this the lenticular diameter of the two sets, by appealing to the geometric case of compact sets belonging to $mathbb{R}^2$.
It should be noted that this is very closely realted to, but not quite the same as, the diameter of the union of the two sets.
answered Dec 8 '18 at 20:33
RandomMathGuyRandomMathGuy
462
$endgroup$
I would call this the lenticular diameter of the two sets, by appealing to the geometric case of compact sets belonging to $mathbb{R}^2$.
It should be noted that this is very closely realted to, but not quite the same as, the diameter of the union of the two sets.
answered Dec 8 '18 at 20:33
RandomMathGuyRandomMathGuy
462
edited Dec 8 '18 at 20:46
answered Dec 8 '18 at 20:33
RandomMathGuyRandomMathGuy
462
answered Dec 8 '18 at 20:33
RandomMathGuyRandomMathGuy
462
answered Dec 8 '18 at 20:33
RandomMathGuyRandomMathGuy
462
462
add a comment |
add a comment |
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$begingroup$
Perhaps it's maximum distance between sets $A$ and $B$?
$endgroup$
– user3342072
Dec 8 '18 at 20:28
$begingroup$
We could call it Bill. As $|a-b|$ is often referred to as the distance between point this is the supremum of distances between points of the set. Is there any reason we need to call it anything else.
$endgroup$
– fleablood
Dec 8 '18 at 21:09