My Math Forum  

Go Back   My Math Forum > College Math Forum > Applied Math

Applied Math Applied Math Forum


Reply
 
LinkBack Thread Tools Display Modes
March 4th, 2013, 09:01 PM   #1
Member
 
Joined: Sep 2012

Posts: 69
Thanks: 0

Inequality proof!!

Today I was told that my proof was wrong!!
The question was this!
Let and . Prove that if and , then .
My proof was this!!
.
Since and r is positive real number, .
.
Can anyone comment on this?? Thanks
eChung00 is offline  
 
March 5th, 2013, 02:27 AM   #2
Senior Member
 
Joined: Feb 2013

Posts: 281
Thanks: 0

Re: Inequality proof!!

Quote:
What is it? It is just not true.

Quote:
latex]|x-a| + |y - b| = -(x-a) - (y-b)[/latex]
Why did you replace the absolute value with negative value? It is not a correct step.
csak is offline  
March 5th, 2013, 04:38 AM   #3
Math Team
 
Joined: Apr 2010

Posts: 2,780
Thanks: 361

Re: Inequality proof!!

Let , what do you know about relation in ?
(You might generally have seen using R for relations, but it would be slightly ambigious now I think.)
Hoempa is offline  
March 5th, 2013, 01:12 PM   #4
Global Moderator
 
Joined: May 2007

Posts: 6,806
Thanks: 716

Re: Inequality proof!!

Quote:
Originally Posted by eChung00
Today I was told that my proof was wrong!!
The question was this!
Let and . Prove that if and , then .
My proof was this!!
.
Since and r is positive real number, .
.
Can anyone comment on this?? Thanks
Basic proof:
(x+y) - (a+b) = (x-a) + (y-b)
|(x-a) + (y-b)| ? |x-a| + |y-b| < r
mathman is offline  
March 5th, 2013, 05:19 PM   #5
Member
 
Joined: Sep 2012

Posts: 69
Thanks: 0

Re: Inequality proof!!

Quote:
Originally Posted by csak
Quote:
What is it? It is just not true.

[quote:3nbm04il]latex]|x-a| + |y - b| = -(x-a) - (y-b)[/latex]
Why did you replace the absolute value with negative value? It is not a correct step.[/quote:3nbm04il]

Quote:
[quote:3nbm04il]latex]|x-a| + |y - b| = -(x-a) - (y-b)[/latex]
Why did you replace the absolute value with negative value? It is not a correct step.[/quote:3nbm04il][/quote]
I used the definition of the absolute value.
eChung00 is offline  
March 5th, 2013, 08:31 PM   #6
Math Team
 
mathbalarka's Avatar
 
Joined: Mar 2012
From: India, West Bengal

Posts: 3,871
Thanks: 86

Math Focus: Number Theory
Re: Inequality proof!!

Quote:
Originally Posted by eChung00
I used the definition of the absolute value.
This is not true in the way you used it. By the definition of absolute value, . You'll see that you are simply defining the function if you look at your application in the OP
mathbalarka is offline  
March 5th, 2013, 09:29 PM   #7
Member
 
Joined: Sep 2012

Posts: 69
Thanks: 0

Re: Inequality proof!!

Quote:
Originally Posted by mathbalarka
Quote:
Originally Posted by eChung00
I used the definition of the absolute value.
This is not true. By the definition of absolute value, . You are simply defining the function
I don't get it!! Can you explain it in more detail??
I copied the definition of absolute value exactly from my text book.
eChung00 is offline  
March 5th, 2013, 09:54 PM   #8
Math Team
 
mathbalarka's Avatar
 
Joined: Mar 2012
From: India, West Bengal

Posts: 3,871
Thanks: 86

Math Focus: Number Theory
Re: Inequality proof!!

Quote:
Originally Posted by eChung00
I don't get it!! Can you explain it in more detail??
I copied the definition of absolute value exactly from my text book.
You copied it exactly but didn't understood it. The definition is correct, for x<0 but that doesn't mean that but it's . You used this in the other way without changing the sign by multiplying -1 on the RHS.
mathbalarka is offline  
March 6th, 2013, 06:39 AM   #9
Member
 
Joined: Sep 2012

Posts: 69
Thanks: 0

Re: Inequality proof!!

Quote:
Originally Posted by mathbalarka
Quote:
Originally Posted by eChung00
I don't get it!! Can you explain it in more detail??
I copied the definition of absolute value exactly from my text book.
You copied it exactly but didn't understood it. The definition is correct, for x<0 but that doesn't mean that but it's . You used this in the other way without changing the sign by multiplying -1 on the RHS.
Thank you for the reply.. now I get what I did wrong...!
Can I ask you one more question??
The question I posted, my professor proved it by using triangle inequality like mathman did.
In the question, the promises are and and the conclusion we have to prove is . I thought if we have to prove something, we must start from the promises and end up with conclusion. But what my professor did and mathman did is they started from the part of the conclusion which is and end up with the sum of the two promises. is it possible to do it??
eChung00 is offline  
March 6th, 2013, 08:59 AM   #10
Math Team
 
mathbalarka's Avatar
 
Joined: Mar 2012
From: India, West Bengal

Posts: 3,871
Thanks: 86

Math Focus: Number Theory
Re: Inequality proof!!

Quote:
Originally Posted by eChung00
I thought if we have to prove something, we must start from the promises and end up with conclusion.
You can also start with the RHS (or LHS, that depends however) of the statement of conclusion and then end up with the equivalence by the promises.
mathbalarka is offline  
Reply

  My Math Forum > College Math Forum > Applied Math

Tags
inequality, proof



Thread Tools
Display Modes


Similar Threads
Thread Thread Starter Forum Replies Last Post
inequality: proof me if you can isymbol Algebra 8 October 20th, 2013 03:48 AM
Inequality proof KyVanchhay Math Events 0 July 27th, 2013 01:24 AM
inequality proof Jakarta Number Theory 5 March 4th, 2013 04:56 AM
Inequality proof shalikadm Algebra 5 November 19th, 2012 02:40 AM
Inequality Proof chaolun Real Analysis 2 April 22nd, 2011 12:10 AM





Copyright © 2019 My Math Forum. All rights reserved.