My Math Forum A homogeneous variable equation, not so easy!!!

 Algebra Pre-Algebra and Basic Algebra Math Forum

 April 11th, 2012, 11:15 AM #1 Math Team     Joined: Mar 2012 From: India, West Bengal Posts: 3,871 Thanks: 86 Math Focus: Number Theory A homogeneous variable equation, not so easy!!! Prove that if F(x+y)=F(x)+F(y) then F(z)=a*z . (Do not involve any types of iteration please, ) Thank you
April 11th, 2012, 01:13 PM   #2
Global Moderator

Joined: May 2007

Posts: 6,806
Thanks: 716

Re: A homogeneous variable equation, not so easy!!!

Quote:
 Originally Posted by mathbalarka Prove that if F(x+y)=F(x)+F(y) then F(z)=a*z . (Do not involve any types of iteration please, ) Thank you
It is not easy, particularly since you need to assume continuity for it to hold.
The general idea is to first prove it for y as an integer multiple of x, using mathematical induction. This can then be extended to fractions. To have it hold for reals, you need continuity.

 Tags easy, equation, homogeneous, variable

 Thread Tools Display Modes Linear Mode

 Similar Threads Thread Thread Starter Forum Replies Last Post fantexihong Calculus 4 September 20th, 2012 10:55 AM arron1990 Calculus 5 February 21st, 2012 07:22 AM ebende Applied Math 0 July 20th, 2011 06:34 AM yiorgos Applied Math 7 July 12th, 2010 03:08 AM Machete Applied Math 0 November 2nd, 2008 03:43 PM

 Contact - Home - Forums - Cryptocurrency Forum - Top