Absolute maximum

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:

1. abs in terms of max
2. max in terms of abs