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How do I show that $ ||x| - |y||leq|x - y| $ [duplicate]
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Reverse Triangle Inequality Proof
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How do I show that $$ ||x| - |y||leq|x - y| $$
I can see obviously that $ ||x| - |y||le |x|-|y|.$ I just can't figure this one out.
linear-algebra inequality
asked Jul 20 at 1:02
Red
1,747733
marked as duplicate by Math Lover, Community♦ Jul 20 at 2:52
This question has been asked before and already has an answer. If those answers do not fully address your question, please ask a new question.
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show 2 more comments
up vote
0
down vote
favorite
This question already has an answer here:
Reverse Triangle Inequality Proof
3 answers
How do I show that $$ ||x| - |y||leq|x - y| $$
I can see obviously that $ ||x| - |y||le |x|-|y|.$ I just can't figure this one out.
linear-algebra inequality
asked Jul 20 at 1:02
Red
1,747733
marked as duplicate by Math Lover, Community♦ Jul 20 at 2:52
This question has been asked before and already has an answer. If those answers do not fully address your question, please ask a new question.
Is your inequality correct? What if $x=-1$ and $y=2$?
– RayDansh
Jul 20 at 1:04
$x=1,y=-1$ obviously is not true
– rlartiga
Jul 20 at 1:04
Something's wrong: your claim is false... For example, $|1+|(-1)||$ is not less-than-or-equal $|1+(-1)|=|0|=0$
– paul garrett
Jul 20 at 1:05
2
Lookup the reverse triangle inequality. Btw, bothobviouslyclaims are false.
– dxiv
Jul 20 at 1:06
2
In response to your edit, the inequality $|x-y| leq |x|-|y|$ now fails, for instance with $x=1$ and $y=-1$.
– B. Mehta
Jul 20 at 1:06
 |Â
show 2 more comments
up vote
0
down vote
favorite
up vote
0
down vote
favorite
This question already has an answer here:
Reverse Triangle Inequality Proof
3 answers
How do I show that $$ ||x| - |y||leq|x - y| $$
I can see obviously that $ ||x| - |y||le |x|-|y|.$ I just can't figure this one out.
linear-algebra inequality
asked Jul 20 at 1:02
Red
1,747733
This question already has an answer here:
Reverse Triangle Inequality Proof
3 answers
How do I show that $$ ||x| - |y||leq|x - y| $$
I can see obviously that $ ||x| - |y||le |x|-|y|.$ I just can't figure this one out.
This question already has an answer here:
Reverse Triangle Inequality Proof
3 answers
linear-algebra inequality
asked Jul 20 at 1:02
Red
1,747733
edited Jul 20 at 1:10
asked Jul 20 at 1:02
Red
1,747733
asked Jul 20 at 1:02
Red
1,747733
asked Jul 20 at 1:02
Red
1,747733
1,747733
marked as duplicate by Math Lover, Community♦ Jul 20 at 2:52
This question has been asked before and already has an answer. If those answers do not fully address your question, please ask a new question.
marked as duplicate by Math Lover, Community♦ Jul 20 at 2:52
This question has been asked before and already has an answer. If those answers do not fully address your question, please ask a new question.
Is your inequality correct? What if $x=-1$ and $y=2$?
– RayDansh
Jul 20 at 1:04
$x=1,y=-1$ obviously is not true
– rlartiga
Jul 20 at 1:04
Something's wrong: your claim is false... For example, $|1+|(-1)||$ is not less-than-or-equal $|1+(-1)|=|0|=0$
– paul garrett
Jul 20 at 1:05
2
Lookup the reverse triangle inequality. Btw, bothobviouslyclaims are false.
– dxiv
Jul 20 at 1:06
2
In response to your edit, the inequality $|x-y| leq |x|-|y|$ now fails, for instance with $x=1$ and $y=-1$.
– B. Mehta
Jul 20 at 1:06
 |Â
show 2 more comments
Is your inequality correct? What if $x=-1$ and $y=2$?
– RayDansh
Jul 20 at 1:04
$x=1,y=-1$ obviously is not true
– rlartiga
Jul 20 at 1:04
Something's wrong: your claim is false... For example, $|1+|(-1)||$ is not less-than-or-equal $|1+(-1)|=|0|=0$
– paul garrett
Jul 20 at 1:05
2
Lookup the reverse triangle inequality. Btw, bothobviouslyclaims are false.
– dxiv
Jul 20 at 1:06
2
In response to your edit, the inequality $|x-y| leq |x|-|y|$ now fails, for instance with $x=1$ and $y=-1$.
– B. Mehta
Jul 20 at 1:06
Is your inequality correct? What if $x=-1$ and $y=2$?
– RayDansh
Jul 20 at 1:04
Is your inequality correct? What if $x=-1$ and $y=2$?
– RayDansh
Jul 20 at 1:04
$x=1,y=-1$ obviously is not true
– rlartiga
Jul 20 at 1:04
$x=1,y=-1$ obviously is not true
– rlartiga
Jul 20 at 1:04
Something's wrong: your claim is false... For example, $|1+|(-1)||$ is not less-than-or-equal $|1+(-1)|=|0|=0$
– paul garrett
Jul 20 at 1:05
Something's wrong: your claim is false... For example, $|1+|(-1)||$ is not less-than-or-equal $|1+(-1)|=|0|=0$
– paul garrett
Jul 20 at 1:05
2
2
Lookup the reverse triangle inequality. Btw, both
obviously claims are false.– dxiv
Jul 20 at 1:06
Lookup the reverse triangle inequality. Btw, both
obviously claims are false.– dxiv
Jul 20 at 1:06
2
2
In response to your edit, the inequality $|x-y| leq |x|-|y|$ now fails, for instance with $x=1$ and $y=-1$.
– B. Mehta
Jul 20 at 1:06
In response to your edit, the inequality $|x-y| leq |x|-|y|$ now fails, for instance with $x=1$ and $y=-1$.
– B. Mehta
Jul 20 at 1:06
 |Â
show 2 more comments
1 Answer
1
active
oldest
votes
up vote
3
down vote
accepted
Sketch: Notice first that if you can show $|x| - |y| leq |x-y|$ and $|y| - |x| leq |x-y|$, then you're done. Also observe that these two inequalities are ultimately the same, up to relabelling so it suffices to show $|x| - |y| leq |x-y|$. But now, rearrange this to $|x| leq |y| + |x-y|$ which should hopefully look familiar to you.
answered Jul 20 at 1:09
B. Mehta
11.7k21944
Possible duplicate of Reverse Triangle Inequality Proof
– Math Lover
Jul 20 at 1:43
add a comment |Â
1 Answer
1
active
oldest
votes
1 Answer
1
active
oldest
votes
active
oldest
votes
active
oldest
votes
up vote
3
down vote
accepted
Sketch: Notice first that if you can show $|x| - |y| leq |x-y|$ and $|y| - |x| leq |x-y|$, then you're done. Also observe that these two inequalities are ultimately the same, up to relabelling so it suffices to show $|x| - |y| leq |x-y|$. But now, rearrange this to $|x| leq |y| + |x-y|$ which should hopefully look familiar to you.
answered Jul 20 at 1:09
B. Mehta
11.7k21944
Possible duplicate of Reverse Triangle Inequality Proof
– Math Lover
Jul 20 at 1:43
add a comment |Â
up vote
3
down vote
accepted
Sketch: Notice first that if you can show $|x| - |y| leq |x-y|$ and $|y| - |x| leq |x-y|$, then you're done. Also observe that these two inequalities are ultimately the same, up to relabelling so it suffices to show $|x| - |y| leq |x-y|$. But now, rearrange this to $|x| leq |y| + |x-y|$ which should hopefully look familiar to you.
answered Jul 20 at 1:09
B. Mehta
11.7k21944
Possible duplicate of Reverse Triangle Inequality Proof
– Math Lover
Jul 20 at 1:43
add a comment |Â
up vote
3
down vote
accepted
up vote
3
down vote
accepted
Sketch: Notice first that if you can show $|x| - |y| leq |x-y|$ and $|y| - |x| leq |x-y|$, then you're done. Also observe that these two inequalities are ultimately the same, up to relabelling so it suffices to show $|x| - |y| leq |x-y|$. But now, rearrange this to $|x| leq |y| + |x-y|$ which should hopefully look familiar to you.
answered Jul 20 at 1:09
B. Mehta
11.7k21944
Sketch: Notice first that if you can show $|x| - |y| leq |x-y|$ and $|y| - |x| leq |x-y|$, then you're done. Also observe that these two inequalities are ultimately the same, up to relabelling so it suffices to show $|x| - |y| leq |x-y|$. But now, rearrange this to $|x| leq |y| + |x-y|$ which should hopefully look familiar to you.
answered Jul 20 at 1:09
B. Mehta
11.7k21944
answered Jul 20 at 1:09
B. Mehta
11.7k21944
answered Jul 20 at 1:09
B. Mehta
11.7k21944
answered Jul 20 at 1:09
B. Mehta
11.7k21944
11.7k21944
Possible duplicate of Reverse Triangle Inequality Proof
– Math Lover
Jul 20 at 1:43
add a comment |Â
Possible duplicate of Reverse Triangle Inequality Proof
– Math Lover
Jul 20 at 1:43
Possible duplicate of Reverse Triangle Inequality Proof
– Math Lover
Jul 20 at 1:43
Possible duplicate of Reverse Triangle Inequality Proof
– Math Lover
Jul 20 at 1:43
add a comment |Â
Is your inequality correct? What if $x=-1$ and $y=2$?
– RayDansh
Jul 20 at 1:04
$x=1,y=-1$ obviously is not true
– rlartiga
Jul 20 at 1:04
Something's wrong: your claim is false... For example, $|1+|(-1)||$ is not less-than-or-equal $|1+(-1)|=|0|=0$
– paul garrett
Jul 20 at 1:05
2
Lookup the reverse triangle inequality. Btw, both
obviouslyclaims are false.– dxiv
Jul 20 at 1:06
2
In response to your edit, the inequality $|x-y| leq |x|-|y|$ now fails, for instance with $x=1$ and $y=-1$.
– B. Mehta
Jul 20 at 1:06