Mixing
What is the meaning of $|f-g|_infty$? [closed]
Clash Royale CLAN TAG#URR8PPP
up vote
0
down vote
favorite
Let $I subseteq mathbbR$ be a bounded interval and let $f;g in C[I]$.
Is $|f-g|_infty:=rho (f;g):=undersetx in Imathrmmax |(f-g)(x)|$, the maximum distance between $f$ and $g$ on $I$?
real-analysis functions
edited Jul 16 at 20:14
Xander Henderson
13.1k83150
asked Jul 16 at 20:10
Mario 04
6013
closed as off-topic by Xander Henderson, José Carlos Santos, Adrian Keister, Trần Thúc Minh TrÃ, Parcly Taxel Jul 17 at 3:11
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 improve the question by providing additional context, which ideally includes your thoughts on the problem and any attempts you have made to solve it. This information helps others identify where you have difficulties and helps them write answers appropriate to your experience level." – Xander Henderson, José Carlos Santos, Adrian Keister, Trần Thúc Minh TrÃÂ, Parcly Taxel
add a comment |Â
up vote
0
down vote
favorite
Let $I subseteq mathbbR$ be a bounded interval and let $f;g in C[I]$.
Is $|f-g|_infty:=rho (f;g):=undersetx in Imathrmmax |(f-g)(x)|$, the maximum distance between $f$ and $g$ on $I$?
real-analysis functions
edited Jul 16 at 20:14
Xander Henderson
13.1k83150
asked Jul 16 at 20:10
Mario 04
6013
closed as off-topic by Xander Henderson, José Carlos Santos, Adrian Keister, Trần Thúc Minh TrÃ, Parcly Taxel Jul 17 at 3:11
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 improve the question by providing additional context, which ideally includes your thoughts on the problem and any attempts you have made to solve it. This information helps others identify where you have difficulties and helps them write answers appropriate to your experience level." – Xander Henderson, José Carlos Santos, Adrian Keister, Trần Thúc Minh TrÃÂ, Parcly Taxel
3
en.wikipedia.org/wiki/Function_space#Norm
– Holo
Jul 16 at 20:13
Is $I$ a closed interval? If not, then $maxxin I |(f-g)(x)|$ may not exist.
– Xander Henderson
Jul 16 at 20:16
add a comment |Â
up vote
0
down vote
favorite
up vote
0
down vote
favorite
Let $I subseteq mathbbR$ be a bounded interval and let $f;g in C[I]$.
Is $|f-g|_infty:=rho (f;g):=undersetx in Imathrmmax |(f-g)(x)|$, the maximum distance between $f$ and $g$ on $I$?
real-analysis functions
edited Jul 16 at 20:14
Xander Henderson
13.1k83150
asked Jul 16 at 20:10
Mario 04
6013
Let $I subseteq mathbbR$ be a bounded interval and let $f;g in C[I]$.
Is $|f-g|_infty:=rho (f;g):=undersetx in Imathrmmax |(f-g)(x)|$, the maximum distance between $f$ and $g$ on $I$?
real-analysis functions
edited Jul 16 at 20:14
Xander Henderson
13.1k83150
asked Jul 16 at 20:10
Mario 04
6013
edited Jul 16 at 20:14
Xander Henderson
13.1k83150
edited Jul 16 at 20:14
Xander Henderson
13.1k83150
edited Jul 16 at 20:14
Xander Henderson
13.1k83150
13.1k83150
asked Jul 16 at 20:10
Mario 04
6013
asked Jul 16 at 20:10
Mario 04
6013
asked Jul 16 at 20:10
Mario 04
6013
6013
closed as off-topic by Xander Henderson, José Carlos Santos, Adrian Keister, Trần Thúc Minh TrÃ, Parcly Taxel Jul 17 at 3:11
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 improve the question by providing additional context, which ideally includes your thoughts on the problem and any attempts you have made to solve it. This information helps others identify where you have difficulties and helps them write answers appropriate to your experience level." – Xander Henderson, José Carlos Santos, Adrian Keister, Trần Thúc Minh TrÃÂ, Parcly Taxel
closed as off-topic by Xander Henderson, José Carlos Santos, Adrian Keister, Trần Thúc Minh TrÃ, Parcly Taxel Jul 17 at 3:11
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 improve the question by providing additional context, which ideally includes your thoughts on the problem and any attempts you have made to solve it. This information helps others identify where you have difficulties and helps them write answers appropriate to your experience level." – Xander Henderson, José Carlos Santos, Adrian Keister, Trần Thúc Minh TrÃÂ, Parcly Taxel
3
en.wikipedia.org/wiki/Function_space#Norm
– Holo
Jul 16 at 20:13
Is $I$ a closed interval? If not, then $maxxin I |(f-g)(x)|$ may not exist.
– Xander Henderson
Jul 16 at 20:16
add a comment |Â
3
en.wikipedia.org/wiki/Function_space#Norm
– Holo
Jul 16 at 20:13
Is $I$ a closed interval? If not, then $maxxin I |(f-g)(x)|$ may not exist.
– Xander Henderson
Jul 16 at 20:16
3
3
en.wikipedia.org/wiki/Function_space#Norm
– Holo
Jul 16 at 20:13
en.wikipedia.org/wiki/Function_space#Norm
– Holo
Jul 16 at 20:13
Is $I$ a closed interval? If not, then $maxxin I |(f-g)(x)|$ may not exist.
– Xander Henderson
Jul 16 at 20:16
Is $I$ a closed interval? If not, then $maxxin I |(f-g)(x)|$ may not exist.
– Xander Henderson
Jul 16 at 20:16
add a comment |Â
1 Answer
1
active
oldest
votes
up vote
2
down vote
accepted
It would be
$$
sup_xin I|f(x)-g(x)|
$$
Note that we take the $sup $ since we have no guarantee that the max will exist ($I$ may not be closed).
answered Jul 16 at 20:14
Foobaz John
18.1k41245
While this is a correct statement, I don't see how this answers the question, which asks about the meaning of $|f-g|_infty$.
– Xander Henderson
Jul 16 at 20:18
By "meaning" I meant the definition.
– Mario 04
Jul 16 at 20:44
add a comment |Â
1 Answer
1
active
oldest
votes
1 Answer
1
active
oldest
votes
active
oldest
votes
active
oldest
votes
up vote
2
down vote
accepted
It would be
$$
sup_xin I|f(x)-g(x)|
$$
Note that we take the $sup $ since we have no guarantee that the max will exist ($I$ may not be closed).
answered Jul 16 at 20:14
Foobaz John
18.1k41245
While this is a correct statement, I don't see how this answers the question, which asks about the meaning of $|f-g|_infty$.
– Xander Henderson
Jul 16 at 20:18
By "meaning" I meant the definition.
– Mario 04
Jul 16 at 20:44
add a comment |Â
up vote
2
down vote
accepted
It would be
$$
sup_xin I|f(x)-g(x)|
$$
Note that we take the $sup $ since we have no guarantee that the max will exist ($I$ may not be closed).
answered Jul 16 at 20:14
Foobaz John
18.1k41245
While this is a correct statement, I don't see how this answers the question, which asks about the meaning of $|f-g|_infty$.
– Xander Henderson
Jul 16 at 20:18
By "meaning" I meant the definition.
– Mario 04
Jul 16 at 20:44
add a comment |Â
up vote
2
down vote
accepted
up vote
2
down vote
accepted
It would be
$$
sup_xin I|f(x)-g(x)|
$$
Note that we take the $sup $ since we have no guarantee that the max will exist ($I$ may not be closed).
answered Jul 16 at 20:14
Foobaz John
18.1k41245
It would be
$$
sup_xin I|f(x)-g(x)|
$$
Note that we take the $sup $ since we have no guarantee that the max will exist ($I$ may not be closed).
answered Jul 16 at 20:14
Foobaz John
18.1k41245
answered Jul 16 at 20:14
Foobaz John
18.1k41245
answered Jul 16 at 20:14
Foobaz John
18.1k41245
answered Jul 16 at 20:14
Foobaz John
18.1k41245
18.1k41245
While this is a correct statement, I don't see how this answers the question, which asks about the meaning of $|f-g|_infty$.
– Xander Henderson
Jul 16 at 20:18
By "meaning" I meant the definition.
– Mario 04
Jul 16 at 20:44
add a comment |Â
While this is a correct statement, I don't see how this answers the question, which asks about the meaning of $|f-g|_infty$.
– Xander Henderson
Jul 16 at 20:18
By "meaning" I meant the definition.
– Mario 04
Jul 16 at 20:44
While this is a correct statement, I don't see how this answers the question, which asks about the meaning of $|f-g|_infty$.
– Xander Henderson
Jul 16 at 20:18
While this is a correct statement, I don't see how this answers the question, which asks about the meaning of $|f-g|_infty$.
– Xander Henderson
Jul 16 at 20:18
By "meaning" I meant the definition.
– Mario 04
Jul 16 at 20:44
By "meaning" I meant the definition.
– Mario 04
Jul 16 at 20:44
add a comment |Â
3
en.wikipedia.org/wiki/Function_space#Norm
– Holo
Jul 16 at 20:13
Is $I$ a closed interval? If not, then $maxxin I |(f-g)(x)|$ may not exist.
– Xander Henderson
Jul 16 at 20:16