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 Abstract Algebra Abstract Algebra Math Forum

 December 6th, 2016, 12:43 PM #1 Newbie   Joined: Dec 2016 From: Vietnam Posts: 2 Thanks: 0 Condition of inequation I have two sets of numbers satisfying: x1+x2+...+xn>=y1+y2+...+yn Whether it is the case: x1^2+x2^2+...+xn^2>=y1^2+y2^2+...+yn^2 (xi^2 presents the square of xi). xi,yi here are not negative numbers. December 6th, 2016, 02:40 PM #2 Global Moderator   Joined: May 2007 Posts: 6,823 Thanks: 723 Proof by mathematical induction. Assuming you want to prove it for all n. x1>y1 implies x1^2>y1^2 x2>y2 implies x2^2>y2^2 Add together and get x1+x2>y1+y2 implies x1^2+x2^2>y1^2+y2^2 December 7th, 2016, 01:45 AM #3 Newbie   Joined: Dec 2016 From: Vietnam Posts: 2 Thanks: 0 What do you think about: 3+1>=2+2 3^2+1^2>=2^2+2^2 December 7th, 2016, 01:45 PM #4 Global Moderator   Joined: May 2007 Posts: 6,823 Thanks: 723 2+2>3+0 4+4<9+0 Tags condition, inequation Thread Tools Show Printable Version Email this Page Display Modes Linear Mode Switch to Hybrid Mode Switch to Threaded Mode Similar Threads Thread Thread Starter Forum Replies Last Post Dang Elementary Math 5 December 30th, 2013 03:58 PM metalari Algebra 1 December 2nd, 2012 02:47 AM msambinelli Applied Math 5 April 1st, 2012 07:48 AM kapital Elementary Math 6 December 29th, 2010 10:39 PM Alvy Calculus 3 March 27th, 2010 07:32 AM

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