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 
March 5th, 2013, 02:27 AM  #2  
Senior Member Joined: Feb 2013 Posts: 281 Thanks: 0  Re: Inequality proof!! Quote: Quote:
 
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.) 
March 5th, 2013, 01:12 PM  #4  
Global Moderator Joined: May 2007 Posts: 6,806 Thanks: 716  Re: Inequality proof!! Quote:
(x+y)  (a+b) = (xa) + (yb) (xa) + (yb) ? xa + yb < r  
March 5th, 2013, 05:19 PM  #5  
Member Joined: Sep 2012 Posts: 69 Thanks: 0  Re: Inequality proof!! Quote:
Quote:
I used the definition of the absolute value.  
March 5th, 2013, 08:31 PM  #6  
Math Team Joined: Mar 2012 From: India, West Bengal Posts: 3,871 Thanks: 86 Math Focus: Number Theory  Re: Inequality proof!! Quote:
 
March 5th, 2013, 09:29 PM  #7  
Member Joined: Sep 2012 Posts: 69 Thanks: 0  Re: Inequality proof!! Quote:
I copied the definition of absolute value exactly from my text book.  
March 5th, 2013, 09:54 PM  #8  
Math Team Joined: Mar 2012 From: India, West Bengal Posts: 3,871 Thanks: 86 Math Focus: Number Theory  Re: Inequality proof!! Quote:
 
March 6th, 2013, 06:39 AM  #9  
Member Joined: Sep 2012 Posts: 69 Thanks: 0  Re: Inequality proof!! Quote:
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??  
March 6th, 2013, 08:59 AM  #10  
Math Team Joined: Mar 2012 From: India, West Bengal Posts: 3,871 Thanks: 86 Math Focus: Number Theory  Re: Inequality proof!! Quote:
 

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