My Math Forum Homogeneous Functions

 Real Analysis Real Analysis Math Forum

 December 16th, 2018, 10:41 AM #1 Senior Member     Joined: Oct 2016 From: Arizona Posts: 207 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 11:03 AM.
 December 16th, 2018, 03:43 PM #2 Senior Member     Joined: Oct 2016 From: Arizona Posts: 207 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, 06:38 PM #3 Senior Member   Joined: Feb 2016 From: Australia Posts: 1,801 Thanks: 636 Math Focus: Yet to find out. Do you mean inequalities which involve homogeneous functions?
December 17th, 2018, 11:18 AM   #4
Senior Member

Joined: Oct 2016
From: Arizona

Posts: 207
Thanks: 37

Math Focus: I'm still deciding, but my recent focus has been olympiad problems and math journal problems.
Quote:
 Originally Posted by Joppy 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.."
Attached Images
 48372136_730283900680187_5026679403678007296_n.jpg (35.4 KB, 7 views)

Last edited by ProofOfALifetime; December 17th, 2018 at 11:46 AM.

December 17th, 2018, 11:18 AM   #5
Senior Member

Joined: Oct 2016
From: Arizona

Posts: 207
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.."
Attached Images
 48426105_730283904013520_3707896338092916736_n.jpg (42.7 KB, 7 views)

Last edited by ProofOfALifetime; December 17th, 2018 at 11:46 AM.

December 29th, 2018, 04:52 PM   #6
Senior Member

Joined: Oct 2016
From: Arizona

Posts: 207
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.
Attached Images
 49348598_737369413304969_8279041215320555520_n.jpg (79.4 KB, 5 views)

 Tags functions, homogeneous

 Thread Tools Display Modes Linear Mode

 Similar Threads Thread Thread Starter Forum Replies Last Post r-soy Calculus 4 February 17th, 2013 05:54 PM r-soy Calculus 7 February 17th, 2013 01:36 PM Epimetheus Calculus 1 January 19th, 2013 06:26 AM LouArnold Algebra 0 September 24th, 2012 10:37 PM azer Real Analysis 1 December 31st, 2011 04:07 AM

 Contact - Home - Forums - Cryptocurrency Forum - Top