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April 27, 2024, 11:33:25 pm
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Author Topic: Inequalities by Induction  (Read 871 times)  Share 

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aadharmg

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Inequalities by Induction
« on: November 01, 2017, 04:10:10 pm »
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Let's say I have a question where I have to prove an inequality by induction but the actual inequality has terms on either side. Can I collect all terms on one side, prove that whole thing to be less than or greater than 0, and then after proving say that because this is true then the rearrangement, which would be the original inequality, is also true?
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Zainbow

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Re: Inequalities by Induction
« Reply #1 on: November 01, 2017, 04:18:12 pm »
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I'm pretty sure you can, don't quote me on it though
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RuiAce

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Re: Inequalities by Induction
« Reply #2 on: November 01, 2017, 04:42:10 pm »
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Yes. Proving LHS ≥ RHS is equivalent to proving LHS - RHS ≥ 0.
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