Let $a,b,c,dinBbb{R}$ such that $|c|ne|d|$. Prove that $frac{a+b}{c+d}lefrac{|a|+|b|}{||c|-|d||}$ [closed]
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I can figure that $a+ble|a+b|le|a|+|b|$ but I do not know how to deal with $||c|-|d||$
real-analysis inequality real-numbers absolute-value
asked Dec 3 '18 at 2:06
Albert DiazAlbert Diaz
975
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closed as off-topic by Carl Mummert, RRL, Cesareo, rtybase, Rebellos Dec 3 '18 at 14:02
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0
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I can figure that $a+ble|a+b|le|a|+|b|$ but I do not know how to deal with $||c|-|d||$
real-analysis inequality real-numbers absolute-value
asked Dec 3 '18 at 2:06
Albert DiazAlbert Diaz
975
$endgroup$
closed as off-topic by Carl Mummert, RRL, Cesareo, rtybase, Rebellos Dec 3 '18 at 14:02
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." – Carl Mummert, RRL, Cesareo, rtybase, Rebellos
If this question can be reworded to fit the rules in the help center, please edit the question.
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This question is missing context or other details: Please improve the question by providing additional context, which ideally includes the source and motivation of the problem, 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.
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– Carl Mummert
Dec 3 '18 at 2:24
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$begingroup$
I can figure that $a+ble|a+b|le|a|+|b|$ but I do not know how to deal with $||c|-|d||$
real-analysis inequality real-numbers absolute-value
asked Dec 3 '18 at 2:06
Albert DiazAlbert Diaz
975
$endgroup$
I can figure that $a+ble|a+b|le|a|+|b|$ but I do not know how to deal with $||c|-|d||$
real-analysis inequality real-numbers absolute-value
real-analysis inequality real-numbers absolute-value
asked Dec 3 '18 at 2:06
Albert DiazAlbert Diaz
975
asked Dec 3 '18 at 2:06
Albert DiazAlbert Diaz
975
edited Dec 3 '18 at 2:20
Albert Diaz
asked Dec 3 '18 at 2:06
Albert DiazAlbert Diaz
975
asked Dec 3 '18 at 2:06
Albert DiazAlbert Diaz
975
asked Dec 3 '18 at 2:06
Albert DiazAlbert Diaz
975
975
closed as off-topic by Carl Mummert, RRL, Cesareo, rtybase, Rebellos Dec 3 '18 at 14:02
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." – Carl Mummert, RRL, Cesareo, rtybase, Rebellos
If this question can be reworded to fit the rules in the help center, please edit the question.
closed as off-topic by Carl Mummert, RRL, Cesareo, rtybase, Rebellos Dec 3 '18 at 14:02
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." – Carl Mummert, RRL, Cesareo, rtybase, Rebellos
If this question can be reworded to fit the rules in the help center, please edit the question.
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This question is missing context or other details: Please improve the question by providing additional context, which ideally includes the source and motivation of the problem, 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.
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– Carl Mummert
Dec 3 '18 at 2:24
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This question is missing context or other details: Please improve the question by providing additional context, which ideally includes the source and motivation of the problem, 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.
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– Carl Mummert
Dec 3 '18 at 2:24
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This question is missing context or other details: Please improve the question by providing additional context, which ideally includes the source and motivation of the problem, 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.
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– Carl Mummert
Dec 3 '18 at 2:24
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This question is missing context or other details: Please improve the question by providing additional context, which ideally includes the source and motivation of the problem, 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.
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– Carl Mummert
Dec 3 '18 at 2:24
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1 Answer
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It is the reversed triangle inequality. For $x,y in mathbb{R}$, we have that $||x| -|y|| leq |x - y|$.
See this post:
Reverse Triangle Inequality Proof
answered Dec 3 '18 at 2:09
riri92riri92
2118
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add a comment |
1 Answer
1
active
oldest
votes
1 Answer
1
active
oldest
votes
active
oldest
votes
active
oldest
votes
2
$begingroup$
It is the reversed triangle inequality. For $x,y in mathbb{R}$, we have that $||x| -|y|| leq |x - y|$.
See this post:
Reverse Triangle Inequality Proof
answered Dec 3 '18 at 2:09
riri92riri92
2118
$endgroup$
add a comment |
2
$begingroup$
It is the reversed triangle inequality. For $x,y in mathbb{R}$, we have that $||x| -|y|| leq |x - y|$.
See this post:
Reverse Triangle Inequality Proof
answered Dec 3 '18 at 2:09
riri92riri92
2118
$endgroup$
add a comment |
2
2
2
$begingroup$
It is the reversed triangle inequality. For $x,y in mathbb{R}$, we have that $||x| -|y|| leq |x - y|$.
See this post:
Reverse Triangle Inequality Proof
answered Dec 3 '18 at 2:09
riri92riri92
2118
$endgroup$
It is the reversed triangle inequality. For $x,y in mathbb{R}$, we have that $||x| -|y|| leq |x - y|$.
See this post:
Reverse Triangle Inequality Proof
answered Dec 3 '18 at 2:09
riri92riri92
2118
answered Dec 3 '18 at 2:09
riri92riri92
2118
answered Dec 3 '18 at 2:09
riri92riri92
2118
answered Dec 3 '18 at 2:09
riri92riri92
2118
2118
add a comment |
add a comment |
$begingroup$
This question is missing context or other details: Please improve the question by providing additional context, which ideally includes the source and motivation of the problem, 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.
$endgroup$
– Carl Mummert
Dec 3 '18 at 2:24