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# Maximum absolute or absolute maxima

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## Question

The absolute value of a real number is defined as its numerical value without regard for sign. So, for example, abs(2) = abs(−2) = 2.
The maximum of two real numbers is defined as the numerically bigger of the two. For example, max(2, −3) = max(2, 2) = 2.
Express:
abs in terms of max
max in terms of abs

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• Solution

abs (x) = max(x,-x)

max(x,y) = 1/2(x+y+abs(x-y))

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abs (x) = max(x,-x)

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max(x,y) = 1/2(x+y+abs(x-y))

Edited by Rainman

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