December 16th, 2018, 11:41 AM  #1 
Senior Member Joined: Oct 2016 From: Arizona Posts: 209 Thanks: 37 Math Focus: I'm still deciding, but my recent focus has been olympiad problems and math journal problems.  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 12:03 PM. 
December 16th, 2018, 04:43 PM  #2 
Senior Member Joined: Oct 2016 From: Arizona Posts: 209 Thanks: 37 Math Focus: I'm still deciding, but my recent focus has been olympiad problems and math journal problems. 
Nevermind, I got it!

December 16th, 2018, 07:38 PM  #3 
Senior Member Joined: Feb 2016 From: Australia Posts: 1,847 Thanks: 661 Math Focus: Yet to find out. 
Do you mean inequalities which involve homogeneous functions?

December 17th, 2018, 12:18 PM  #4  
Senior Member Joined: Oct 2016 From: Arizona Posts: 209 Thanks: 37 Math Focus: I'm still deciding, but my recent focus has been olympiad problems and math journal problems.  Quote:
It says, "By the homogeneity of the inequality.." Last edited by ProofOfALifetime; December 17th, 2018 at 12:46 PM.  
December 17th, 2018, 12:18 PM  #5 
Senior Member Joined: Oct 2016 From: Arizona Posts: 209 Thanks: 37 Math Focus: I'm still deciding, but my recent focus has been olympiad problems and math journal problems. 
Here is another example. That part, "hence in homogeneous form.."
Last edited by ProofOfALifetime; December 17th, 2018 at 12:46 PM. 
December 29th, 2018, 05:52 PM  #6 
Senior Member Joined: Oct 2016 From: Arizona Posts: 209 Thanks: 37 Math Focus: I'm still deciding, but my recent focus has been olympiad problems and math journal problems. 
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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