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October 10th, 2019, 12:57 PM  #1 
Senior Member Joined: Dec 2015 From: Earth Posts: 826 Thanks: 113 Math Focus: Elementary Math  Problem involving analytic expressions
Given 3 random numbers $\displaystyle x,y,z \in \mathbb{R}\;$: (a) Find the number that is bounded by the two other numbers. Express it in terms of a function like $\displaystyle \phi (x,y,z)$. (b) Express the largest number in terms of $\displaystyle \phi(x,y,z)$. Last edited by skipjack; October 11th, 2019 at 05:36 AM. 
October 10th, 2019, 01:24 PM  #2 
Global Moderator Joined: May 2007 Posts: 6,852 Thanks: 743 
a) $\phi(x,y,z)=x+y+z\max(x,y,z)\min(x,y,z)$. b) $\max(x,y,z)=x+y+z\min(x,y,z)\phi(x,y,z)$. Last edited by skipjack; October 10th, 2019 at 02:42 PM. 
October 10th, 2019, 10:16 PM  #3 
Senior Member Joined: Sep 2016 From: USA Posts: 684 Thanks: 457 Math Focus: Dynamical systems, analytic function theory, numerics 
The word "analytic" has a specific meaning in math and I don't think it's what you are intending here.
Last edited by skipjack; October 11th, 2019 at 05:32 AM. 
October 11th, 2019, 03:45 AM  #4 
Senior Member Joined: Dec 2015 From: Earth Posts: 826 Thanks: 113 Math Focus: Elementary Math 
add: I forgot to write x,y,z are positive real numbers! I mean nonstandard (elementary) expression. For example about (b) with simple math: $\displaystyle \max(x,y,z)=(1)^{\displaystyle \lfloor (x+y+z)/3 \rfloor }+2\lfloor (x+y+z)/3 \rfloor \; $, x,y,z >0 , holds true only for positive integers. I'm just trying to say that the equality above is analytic since it involves integer parts and the negative base 1 ... etc. (The correct answers are given in post#2. Last edited by skipjack; October 11th, 2019 at 12:58 PM. 
October 11th, 2019, 04:09 AM  #5 
Senior Member Joined: Oct 2009 Posts: 906 Thanks: 354  
October 11th, 2019, 05:36 AM  #6 
Global Moderator Joined: Dec 2006 Posts: 21,110 Thanks: 2326 
The problem didn't require each function used to be analytic.

October 11th, 2019, 07:44 AM  #7 
Senior Member Joined: Oct 2009 Posts: 906 Thanks: 354  

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