nincompoop
  • nincompoop
Prove for fun -
Mathematics
  • Stacey Warren - Expert brainly.com
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SOLVED
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schrodinger
  • schrodinger
I got my questions answered at brainly.com in under 10 minutes. Go to brainly.com now for free help!
anonymous
  • anonymous
and what should we prove?
nincompoop
  • nincompoop
The maximum of two numbers x and y is denoted by max (x,y). The max (-1, 3) = max (3,3) = 3 and max (-1, -3) = max(-3, -1) = -1. The minimum of x and y is denoted b min (x,y). Prove that: \[\max(x,y) = \frac{ x+y+|y-x| }{ 2 },\] \[mix (x,y) = \frac{ x+y-|y-x| }{ 2 }.\]
nincompoop
  • nincompoop
typo, it's min not mix LOL

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More answers

anonymous
  • anonymous
if y>x then |y-x| =(y-x) so max(x,y)=y you can easily prove that if x>y then |y-x|=(x-y) max(x,y) = x you can prove that This Sucks!
anonymous
  • anonymous
@nincompoop min is also same.
nincompoop
  • nincompoop
are you sure that's the way to prove it?
anonymous
  • anonymous
Is there a problem with this proof?
sirm3d
  • sirm3d
\[\frac{x+y+|y-x|}{2}=\cases{\frac{x+y+(y-x)}{2}\qquad, y>x\\\frac{x+y+(x-y)}{2}\qquad ,x>y}\\=\cases{y\qquad ,y>x\\x\qquad ,x>y}\]
nincompoop
  • nincompoop
max(x,y) = (x+y +|y| - |x|)/2 -> (x+y +y-x)/2 =x and (x+y-y+x)/2 = y
nincompoop
  • nincompoop
max x if x>y and max y if y>x
nincompoop
  • nincompoop
thanks guys
anonymous
  • anonymous
@nin I think |y-x| is not eual to |y|-|x|
nincompoop
  • nincompoop
it's the same. I read that recently LOL
nincompoop
  • nincompoop
spivak calculus 4th edition
anonymous
  • anonymous
|5-(-3)| is not |5|-|-3|
nincompoop
  • nincompoop
|5 -(-3)| = |5+3| = |5| + |3|
anonymous
  • anonymous
|dw:1378730644761:dw|
nincompoop
  • nincompoop
no no no
nincompoop
  • nincompoop
for all nubers a and b, we have |a + b | ≤ |a| + |b| 1) a ≥ 0, b ≥ 0 a + b ≥ 0 -> |a + b | = a + b = |a| + |b| 2) a≤0, b≤0 |a+b| = -(a+b) = -a + (-b) = |a| + |b| 3) a ≥ 0, b ≤ 0 |a+b| ≤ a - b i) if a + b ≥ 0 a+b ≥ a-b b≤-b ii) if a+b ≤ 0 -a - b ≤ a - b -a ≤ a
nincompoop
  • nincompoop
|dw:1378732211686:dw|
nincompoop
  • nincompoop
|dw:1378732505412:dw|

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