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December 16th, 2018, 10:41 AM   #1
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Homogeneous Functions

I've been working on a few inequality proofs over the last few months, and some of the solutions I've looked at mentioned that since the inequality is homogeneous, you can make extra condtions like $abc=1$ or $a+b+c=1$ or others.

What I don't get is how can you tell if an inequality is homogeneous? The book never mentioned how they got that.

BTW, I found a few definitions online, but I don't for sure if that's what they are using. So, I was just wondering if someone could confirm or set me on the right track to getting it.

Last edited by ProofOfALifetime; December 16th, 2018 at 11:03 AM.
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December 16th, 2018, 03:43 PM   #2
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Nevermind, I got it!
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December 16th, 2018, 06:38 PM   #3
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Do you mean inequalities which involve homogeneous functions?
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December 17th, 2018, 11:18 AM   #4
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Quote:
Originally Posted by Joppy View Post
Do you mean inequalities which involve homogeneous functions?
I don't really know. I just know that some of the solutions to inequalities I've looked at (I'm attaching some) mention it.

It says, "By the homogeneity of the inequality.."
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December 17th, 2018, 11:18 AM   #5
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Here is another example. That part, "hence in homogeneous form.."
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Last edited by ProofOfALifetime; December 17th, 2018 at 11:46 AM.
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December 29th, 2018, 04:52 PM   #6
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I found a book that explains it clearly! So I am posting the page so this thread will be more useful.
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