Nested absolute operations

Asked Aug 13 '14 at 23:33

Active Aug 14 '14 at 02:18

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The question is: are the following two functions equivalent? And if yes, what properties of the absolute value should I use to prove it?

$f_1(x,y,z)$ = $|\, x + |y+z| \,|$

$f_2(x,y,z)$ = $| \,|x+y| + z \,|$

edited Aug 14 '14 at 02:18

user137481

asked Aug 13 '14 at 23:33

ata6502

2

Consider $f_1(1,0,-1)$ and $f_2(1,0,-1)$. – qaphla Aug 13 '14 at 23:35
Great! It means the functions are not equivalent:
f1(1,0,−1) = 2; f2(1,0,−1) = 0

Is there any way to proof it using properties of the absolute value?
– ata6502 Aug 14 '14 at 01:08
Try x = -z and y = 0. – user137481 Aug 14 '14 at 02:28

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