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Infimum of sum of three terms
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$begingroup$
Let $(X,d)$ be a metric space, $b in mathbb{R}$ a constant and $f,g : X rightarrow mathbb{R}$.
I found the following statement in some notes and I cannot understand how they conclude it :
begin{equation}
inf limits_{x in X} {f(x) + g(x) + b} = inf limits_{x in X} {f(x) + b} + inf limits_{x in X} {f(x) + g(x) }
end{equation}
Is this possible ?
Could someone give me some help ?
real-analysis calculus
edited yesterday
Thomas Shelby
3,7342625
asked yesterday
vl.athvl.ath
879
$endgroup$
add a comment |
$begingroup$
Let $(X,d)$ be a metric space, $b in mathbb{R}$ a constant and $f,g : X rightarrow mathbb{R}$.
I found the following statement in some notes and I cannot understand how they conclude it :
begin{equation}
inf limits_{x in X} {f(x) + g(x) + b} = inf limits_{x in X} {f(x) + b} + inf limits_{x in X} {f(x) + g(x) }
end{equation}
Is this possible ?
Could someone give me some help ?
real-analysis calculus
edited yesterday
Thomas Shelby
3,7342625
asked yesterday
vl.athvl.ath
879
$endgroup$
1
$begingroup$
"Some notes" could be wrong, but this statement is just so wrong that I suspect you're either misquoting or leaving out something very important.
$endgroup$
– Robert Israel
yesterday
$begingroup$
it must be the second one.. i will look for the thing i am missing
$endgroup$
– vl.ath
yesterday
add a comment |
$begingroup$
Let $(X,d)$ be a metric space, $b in mathbb{R}$ a constant and $f,g : X rightarrow mathbb{R}$.
I found the following statement in some notes and I cannot understand how they conclude it :
begin{equation}
inf limits_{x in X} {f(x) + g(x) + b} = inf limits_{x in X} {f(x) + b} + inf limits_{x in X} {f(x) + g(x) }
end{equation}
Is this possible ?
Could someone give me some help ?
real-analysis calculus
edited yesterday
Thomas Shelby
3,7342625
asked yesterday
vl.athvl.ath
879
$endgroup$
Let $(X,d)$ be a metric space, $b in mathbb{R}$ a constant and $f,g : X rightarrow mathbb{R}$.
I found the following statement in some notes and I cannot understand how they conclude it :
begin{equation}
inf limits_{x in X} {f(x) + g(x) + b} = inf limits_{x in X} {f(x) + b} + inf limits_{x in X} {f(x) + g(x) }
end{equation}
Is this possible ?
Could someone give me some help ?
real-analysis calculus
real-analysis calculus
edited yesterday
Thomas Shelby
3,7342625
asked yesterday
vl.athvl.ath
879
edited yesterday
Thomas Shelby
3,7342625
asked yesterday
vl.athvl.ath
879
edited yesterday
Thomas Shelby
3,7342625
edited yesterday
Thomas Shelby
3,7342625
edited yesterday
Thomas Shelby
3,7342625
3,7342625
asked yesterday
vl.athvl.ath
879
asked yesterday
vl.athvl.ath
879
asked yesterday
vl.athvl.ath
879
879
1
$begingroup$
"Some notes" could be wrong, but this statement is just so wrong that I suspect you're either misquoting or leaving out something very important.
$endgroup$
– Robert Israel
yesterday
$begingroup$
it must be the second one.. i will look for the thing i am missing
$endgroup$
– vl.ath
yesterday
add a comment |
1
$begingroup$
"Some notes" could be wrong, but this statement is just so wrong that I suspect you're either misquoting or leaving out something very important.
$endgroup$
– Robert Israel
yesterday
$begingroup$
it must be the second one.. i will look for the thing i am missing
$endgroup$
– vl.ath
yesterday
1
1
$begingroup$
"Some notes" could be wrong, but this statement is just so wrong that I suspect you're either misquoting or leaving out something very important.
$endgroup$
– Robert Israel
yesterday
$begingroup$
"Some notes" could be wrong, but this statement is just so wrong that I suspect you're either misquoting or leaving out something very important.
$endgroup$
– Robert Israel
yesterday
$begingroup$
it must be the second one.. i will look for the thing i am missing
$endgroup$
– vl.ath
yesterday
$begingroup$
it must be the second one.. i will look for the thing i am missing
$endgroup$
– vl.ath
yesterday
add a comment |
1 Answer
1
active
oldest
votes
$begingroup$
No, it is not true in general. For example, take $f (x)=1$ and $g (x)=-1$.
answered yesterday
Thomas ShelbyThomas Shelby
3,7342625
$endgroup$
add a comment |
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$begingroup$
No, it is not true in general. For example, take $f (x)=1$ and $g (x)=-1$.
answered yesterday
Thomas ShelbyThomas Shelby
3,7342625
$endgroup$
add a comment |
$begingroup$
No, it is not true in general. For example, take $f (x)=1$ and $g (x)=-1$.
answered yesterday
Thomas ShelbyThomas Shelby
3,7342625
$endgroup$
add a comment |
$begingroup$
No, it is not true in general. For example, take $f (x)=1$ and $g (x)=-1$.
answered yesterday
Thomas ShelbyThomas Shelby
3,7342625
$endgroup$
No, it is not true in general. For example, take $f (x)=1$ and $g (x)=-1$.
answered yesterday
Thomas ShelbyThomas Shelby
3,7342625
answered yesterday
Thomas ShelbyThomas Shelby
3,7342625
answered yesterday
Thomas ShelbyThomas Shelby
3,7342625
answered yesterday
Thomas ShelbyThomas Shelby
3,7342625
3,7342625
add a comment |
add a comment |
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1
$begingroup$
"Some notes" could be wrong, but this statement is just so wrong that I suspect you're either misquoting or leaving out something very important.
$endgroup$
– Robert Israel
yesterday
$begingroup$
it must be the second one.. i will look for the thing i am missing
$endgroup$
– vl.ath
yesterday