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October 10th, 2019, 12:57 PM   #1
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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.
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October 10th, 2019, 01:24 PM   #2
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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.
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October 10th, 2019, 10:16 PM   #3
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The word "analytic" has a specific meaning in math and I don't think it's what you are intending here.
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Last edited by skipjack; October 11th, 2019 at 05:32 AM.
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October 11th, 2019, 03:45 AM   #4
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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.
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October 11th, 2019, 04:09 AM   #5
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Quote:
Originally Posted by idontknow View Post
the correct answers are given in post#2.
It's not since max is not an analytic function.
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October 11th, 2019, 05:36 AM   #6
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The problem didn't require each function used to be analytic.
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October 11th, 2019, 07:44 AM   #7
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Quote:
Originally Posted by skipjack View Post
The problem didn't require each function used to be analytic.
The title in the question obviously required that.
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