For every possible real #u#,
#absu = {(u, "if",u >= 0),(-u,"if",u < 0) :}#
So for any two numbers #a# and #b#,
#abs(a-b)# is either equal to #a-b# if that difference is positive or it is equal to #-(a-b)# if the difference #a-b# is negative.
#pi# is less than #11#, so #11-pi# is already positive and
#abs(11-pi) = 11-pi#
Bonus Example
#abs(2-pi)#
#pi# is greater than #2#, so #2-pi# is a negative number and the absolute value of a negative number is the opposite of that number:
#abs(2-pi) = -(2-pi)#
Now we can rewrites #-(2-pi) = -2 + pi = pi-2#
So
#abs(2-pi) = pi -2#
(It is worth trying to remember that #-(a-b)# is always equal to #b-a#. That means: if we reverse the order of subtraction, we change the sign of the answer.)
