My Math Forum Problem involving analytic expressions

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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) $\max(x,y,z)=x+y+z-\min(x,y,z)-\phi(x,y,z)$. Thanks from topsquark, tahirimanov19, romsek and 2 others 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. Thanks from idontknow 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 non-standard (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
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Quote:
 Originally Posted by idontknow the correct answers are given in post#2.
It's not since max is not an analytic function.

 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
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Quote:
 Originally Posted by skipjack The problem didn't require each function used to be analytic.
The title in the question obviously required that.

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