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What does the notation inf… mean?
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up vote
0
down vote
favorite
I came across
$$infk : f in C^k$$
What does $infcdot$ mean? I have been looking, but haven't found anything.
notation supremum-and-infimum
edited Jul 21 at 11:26
Rodrigo de Azevedo
12.6k41751
asked Jul 21 at 11:15
Filip
336
add a comment |Â
up vote
0
down vote
favorite
I came across
$$infk : f in C^k$$
What does $infcdot$ mean? I have been looking, but haven't found anything.
notation supremum-and-infimum
edited Jul 21 at 11:26
Rodrigo de Azevedo
12.6k41751
asked Jul 21 at 11:15
Filip
336
3
It means infimum.
– Raskolnikov
Jul 21 at 11:16
2
It doesn't make a lot of sense in this particular context, since if $f$ is $mathcal C^k$ for any one $k$, then it is also $mathcal C^0$, so this infimum is either $0$ or (perhaps) $infty$.
– Henning Makholm
Jul 21 at 11:23
add a comment |Â
up vote
0
down vote
favorite
up vote
0
down vote
favorite
I came across
$$infk : f in C^k$$
What does $infcdot$ mean? I have been looking, but haven't found anything.
notation supremum-and-infimum
edited Jul 21 at 11:26
Rodrigo de Azevedo
12.6k41751
asked Jul 21 at 11:15
Filip
336
I came across
$$infk : f in C^k$$
What does $infcdot$ mean? I have been looking, but haven't found anything.
notation supremum-and-infimum
edited Jul 21 at 11:26
Rodrigo de Azevedo
12.6k41751
asked Jul 21 at 11:15
Filip
336
edited Jul 21 at 11:26
Rodrigo de Azevedo
12.6k41751
edited Jul 21 at 11:26
Rodrigo de Azevedo
12.6k41751
edited Jul 21 at 11:26
Rodrigo de Azevedo
12.6k41751
12.6k41751
asked Jul 21 at 11:15
Filip
336
asked Jul 21 at 11:15
Filip
336
asked Jul 21 at 11:15
Filip
336
336
3
It means infimum.
– Raskolnikov
Jul 21 at 11:16
2
It doesn't make a lot of sense in this particular context, since if $f$ is $mathcal C^k$ for any one $k$, then it is also $mathcal C^0$, so this infimum is either $0$ or (perhaps) $infty$.
– Henning Makholm
Jul 21 at 11:23
add a comment |Â
3
It means infimum.
– Raskolnikov
Jul 21 at 11:16
2
It doesn't make a lot of sense in this particular context, since if $f$ is $mathcal C^k$ for any one $k$, then it is also $mathcal C^0$, so this infimum is either $0$ or (perhaps) $infty$.
– Henning Makholm
Jul 21 at 11:23
3
3
It means infimum.
– Raskolnikov
Jul 21 at 11:16
It means infimum.
– Raskolnikov
Jul 21 at 11:16
2
2
It doesn't make a lot of sense in this particular context, since if $f$ is $mathcal C^k$ for any one $k$, then it is also $mathcal C^0$, so this infimum is either $0$ or (perhaps) $infty$.
– Henning Makholm
Jul 21 at 11:23
It doesn't make a lot of sense in this particular context, since if $f$ is $mathcal C^k$ for any one $k$, then it is also $mathcal C^0$, so this infimum is either $0$ or (perhaps) $infty$.
– Henning Makholm
Jul 21 at 11:23
add a comment |Â
3 Answers
3
active
oldest
votes
up vote
3
down vote
accepted
It means infimum. So, $infldots$ is the infimum of the set $ldots$ (assuming that it is a non-empty set of real numbers with a lower bound).
answered Jul 21 at 11:18
José Carlos Santos
114k1698177
To save a google search: en.m.wikipedia.org/wiki/Infimum_and_supremum
– Crosby
Jul 21 at 11:19
add a comment |Â
up vote
4
down vote
Suppose that you have a non-empty set of numbers,as an example $A = 1,10,pi,55, 11.2, sqrt2, 1over 2$ then the infimum of this set is the greatest lower bound of the set. In this simple case $$infA=1over 2$$
As an added bonus: what you gave us $$infk: fin C^k$$ means that, given a function $f$ differentiable $n$ times, the infimum is the lower possible $k$ such that the $k$-th derivative of this function is continuous. But I think that $k$ will be $0$ every time..
answered Jul 21 at 11:22
Davide Morgante
1,812220
1
"lower upper bound"??
– Henning Makholm
Jul 21 at 11:24
Oops, my bad, I'm correcting it
– Davide Morgante
Jul 21 at 11:24
2
Maybe you meant not "infinium" but "infimum" and not "lower bound" but "greatest lower bound"
– Ã®Ñ€Ñ–ù ïрþш
Jul 21 at 11:35
Thank you all, I wrote the answer quickly! Now it's all corrected
– Davide Morgante
Jul 21 at 11:37
1
And by axiom, every non empty down bounded set of real numbers has infimum...
– dmtri
Jul 21 at 12:17
add a comment |Â
up vote
3
down vote
Lower bound of some set of numbers is number which smaller or equal to any number of the set.
Greatest lower bound of some set of numbers is a number which is a lower bound of the set and is bigger or equal to any other lower bound of the set. $inf A$ means greatest lower bound of the set $A$. So e.g. $inf A = 5$ means greatest lower bound of the set $A$ is $5$.
Greatest lower bound is also called infimum.
answered Jul 21 at 11:30
îріù ïрþш
993513
add a comment |Â
3 Answers
3
active
oldest
votes
3 Answers
3
active
oldest
votes
active
oldest
votes
active
oldest
votes
up vote
3
down vote
accepted
It means infimum. So, $infldots$ is the infimum of the set $ldots$ (assuming that it is a non-empty set of real numbers with a lower bound).
answered Jul 21 at 11:18
José Carlos Santos
114k1698177
To save a google search: en.m.wikipedia.org/wiki/Infimum_and_supremum
– Crosby
Jul 21 at 11:19
add a comment |Â
up vote
3
down vote
accepted
It means infimum. So, $infldots$ is the infimum of the set $ldots$ (assuming that it is a non-empty set of real numbers with a lower bound).
answered Jul 21 at 11:18
José Carlos Santos
114k1698177
To save a google search: en.m.wikipedia.org/wiki/Infimum_and_supremum
– Crosby
Jul 21 at 11:19
add a comment |Â
up vote
3
down vote
accepted
up vote
3
down vote
accepted
It means infimum. So, $infldots$ is the infimum of the set $ldots$ (assuming that it is a non-empty set of real numbers with a lower bound).
answered Jul 21 at 11:18
José Carlos Santos
114k1698177
It means infimum. So, $infldots$ is the infimum of the set $ldots$ (assuming that it is a non-empty set of real numbers with a lower bound).
answered Jul 21 at 11:18
José Carlos Santos
114k1698177
answered Jul 21 at 11:18
José Carlos Santos
114k1698177
answered Jul 21 at 11:18
José Carlos Santos
114k1698177
answered Jul 21 at 11:18
José Carlos Santos
114k1698177
114k1698177
To save a google search: en.m.wikipedia.org/wiki/Infimum_and_supremum
– Crosby
Jul 21 at 11:19
add a comment |Â
To save a google search: en.m.wikipedia.org/wiki/Infimum_and_supremum
– Crosby
Jul 21 at 11:19
To save a google search: en.m.wikipedia.org/wiki/Infimum_and_supremum
– Crosby
Jul 21 at 11:19
To save a google search: en.m.wikipedia.org/wiki/Infimum_and_supremum
– Crosby
Jul 21 at 11:19
add a comment |Â
up vote
4
down vote
Suppose that you have a non-empty set of numbers,as an example $A = 1,10,pi,55, 11.2, sqrt2, 1over 2$ then the infimum of this set is the greatest lower bound of the set. In this simple case $$infA=1over 2$$
As an added bonus: what you gave us $$infk: fin C^k$$ means that, given a function $f$ differentiable $n$ times, the infimum is the lower possible $k$ such that the $k$-th derivative of this function is continuous. But I think that $k$ will be $0$ every time..
answered Jul 21 at 11:22
Davide Morgante
1,812220
1
"lower upper bound"??
– Henning Makholm
Jul 21 at 11:24
Oops, my bad, I'm correcting it
– Davide Morgante
Jul 21 at 11:24
2
Maybe you meant not "infinium" but "infimum" and not "lower bound" but "greatest lower bound"
– Ã®Ñ€Ñ–ù ïрþш
Jul 21 at 11:35
Thank you all, I wrote the answer quickly! Now it's all corrected
– Davide Morgante
Jul 21 at 11:37
1
And by axiom, every non empty down bounded set of real numbers has infimum...
– dmtri
Jul 21 at 12:17
add a comment |Â
up vote
4
down vote
Suppose that you have a non-empty set of numbers,as an example $A = 1,10,pi,55, 11.2, sqrt2, 1over 2$ then the infimum of this set is the greatest lower bound of the set. In this simple case $$infA=1over 2$$
As an added bonus: what you gave us $$infk: fin C^k$$ means that, given a function $f$ differentiable $n$ times, the infimum is the lower possible $k$ such that the $k$-th derivative of this function is continuous. But I think that $k$ will be $0$ every time..
answered Jul 21 at 11:22
Davide Morgante
1,812220
1
"lower upper bound"??
– Henning Makholm
Jul 21 at 11:24
Oops, my bad, I'm correcting it
– Davide Morgante
Jul 21 at 11:24
2
Maybe you meant not "infinium" but "infimum" and not "lower bound" but "greatest lower bound"
– Ã®Ñ€Ñ–ù ïрþш
Jul 21 at 11:35
Thank you all, I wrote the answer quickly! Now it's all corrected
– Davide Morgante
Jul 21 at 11:37
1
And by axiom, every non empty down bounded set of real numbers has infimum...
– dmtri
Jul 21 at 12:17
add a comment |Â
up vote
4
down vote
up vote
4
down vote
Suppose that you have a non-empty set of numbers,as an example $A = 1,10,pi,55, 11.2, sqrt2, 1over 2$ then the infimum of this set is the greatest lower bound of the set. In this simple case $$infA=1over 2$$
As an added bonus: what you gave us $$infk: fin C^k$$ means that, given a function $f$ differentiable $n$ times, the infimum is the lower possible $k$ such that the $k$-th derivative of this function is continuous. But I think that $k$ will be $0$ every time..
answered Jul 21 at 11:22
Davide Morgante
1,812220
Suppose that you have a non-empty set of numbers,as an example $A = 1,10,pi,55, 11.2, sqrt2, 1over 2$ then the infimum of this set is the greatest lower bound of the set. In this simple case $$infA=1over 2$$
As an added bonus: what you gave us $$infk: fin C^k$$ means that, given a function $f$ differentiable $n$ times, the infimum is the lower possible $k$ such that the $k$-th derivative of this function is continuous. But I think that $k$ will be $0$ every time..
answered Jul 21 at 11:22
Davide Morgante
1,812220
edited Jul 21 at 12:18
answered Jul 21 at 11:22
Davide Morgante
1,812220
answered Jul 21 at 11:22
Davide Morgante
1,812220
answered Jul 21 at 11:22
Davide Morgante
1,812220
1,812220
1
"lower upper bound"??
– Henning Makholm
Jul 21 at 11:24
Oops, my bad, I'm correcting it
– Davide Morgante
Jul 21 at 11:24
2
Maybe you meant not "infinium" but "infimum" and not "lower bound" but "greatest lower bound"
– Ã®Ñ€Ñ–ù ïрþш
Jul 21 at 11:35
Thank you all, I wrote the answer quickly! Now it's all corrected
– Davide Morgante
Jul 21 at 11:37
1
And by axiom, every non empty down bounded set of real numbers has infimum...
– dmtri
Jul 21 at 12:17
add a comment |Â
1
"lower upper bound"??
– Henning Makholm
Jul 21 at 11:24
Oops, my bad, I'm correcting it
– Davide Morgante
Jul 21 at 11:24
2
Maybe you meant not "infinium" but "infimum" and not "lower bound" but "greatest lower bound"
– Ã®Ñ€Ñ–ù ïрþш
Jul 21 at 11:35
Thank you all, I wrote the answer quickly! Now it's all corrected
– Davide Morgante
Jul 21 at 11:37
1
And by axiom, every non empty down bounded set of real numbers has infimum...
– dmtri
Jul 21 at 12:17
1
1
"lower upper bound"??
– Henning Makholm
Jul 21 at 11:24
"lower upper bound"??
– Henning Makholm
Jul 21 at 11:24
Oops, my bad, I'm correcting it
– Davide Morgante
Jul 21 at 11:24
Oops, my bad, I'm correcting it
– Davide Morgante
Jul 21 at 11:24
2
2
Maybe you meant not "infinium" but "infimum" and not "lower bound" but "greatest lower bound"
– Ã®Ñ€Ñ–ù ïрþш
Jul 21 at 11:35
Maybe you meant not "infinium" but "infimum" and not "lower bound" but "greatest lower bound"
– Ã®Ñ€Ñ–ù ïрþш
Jul 21 at 11:35
Thank you all, I wrote the answer quickly! Now it's all corrected
– Davide Morgante
Jul 21 at 11:37
Thank you all, I wrote the answer quickly! Now it's all corrected
– Davide Morgante
Jul 21 at 11:37
1
1
And by axiom, every non empty down bounded set of real numbers has infimum...
– dmtri
Jul 21 at 12:17
And by axiom, every non empty down bounded set of real numbers has infimum...
– dmtri
Jul 21 at 12:17
add a comment |Â
up vote
3
down vote
Lower bound of some set of numbers is number which smaller or equal to any number of the set.
Greatest lower bound of some set of numbers is a number which is a lower bound of the set and is bigger or equal to any other lower bound of the set. $inf A$ means greatest lower bound of the set $A$. So e.g. $inf A = 5$ means greatest lower bound of the set $A$ is $5$.
Greatest lower bound is also called infimum.
answered Jul 21 at 11:30
îріù ïрþш
993513
add a comment |Â
up vote
3
down vote
Lower bound of some set of numbers is number which smaller or equal to any number of the set.
Greatest lower bound of some set of numbers is a number which is a lower bound of the set and is bigger or equal to any other lower bound of the set. $inf A$ means greatest lower bound of the set $A$. So e.g. $inf A = 5$ means greatest lower bound of the set $A$ is $5$.
Greatest lower bound is also called infimum.
answered Jul 21 at 11:30
îріù ïрþш
993513
add a comment |Â
up vote
3
down vote
up vote
3
down vote
Lower bound of some set of numbers is number which smaller or equal to any number of the set.
Greatest lower bound of some set of numbers is a number which is a lower bound of the set and is bigger or equal to any other lower bound of the set. $inf A$ means greatest lower bound of the set $A$. So e.g. $inf A = 5$ means greatest lower bound of the set $A$ is $5$.
Greatest lower bound is also called infimum.
answered Jul 21 at 11:30
îріù ïрþш
993513
Lower bound of some set of numbers is number which smaller or equal to any number of the set.
Greatest lower bound of some set of numbers is a number which is a lower bound of the set and is bigger or equal to any other lower bound of the set. $inf A$ means greatest lower bound of the set $A$. So e.g. $inf A = 5$ means greatest lower bound of the set $A$ is $5$.
Greatest lower bound is also called infimum.
answered Jul 21 at 11:30
îріù ïрþш
993513
answered Jul 21 at 11:30
îріù ïрþш
993513
answered Jul 21 at 11:30
îріù ïрþш
993513
answered Jul 21 at 11:30
îріù ïрþш
993513
993513
add a comment |Â
add a comment |Â
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3
It means infimum.
– Raskolnikov
Jul 21 at 11:16
2
It doesn't make a lot of sense in this particular context, since if $f$ is $mathcal C^k$ for any one $k$, then it is also $mathcal C^0$, so this infimum is either $0$ or (perhaps) $infty$.
– Henning Makholm
Jul 21 at 11:23