A
cute name for an elementary result in
group theory.
We let a
-1 denote the
inverse of an
element a in a
group, ie the the element such that a
-1*a = a*a
-1 = e, where e is the
identity element. Then (using the
associative property of the
operation in a group)
(a*b)*(b-1*a-1) = a*(b*b-1)*a-1 = a*a-1 = e
Thus the inverse of a*b is b-1*a-1.
This result is sometimes called the shoes-and-socks theorem because of the following analogy: if you want to undo the act of putting your socks and then your shoes on, you first have to remove your shoes and then take off your socks.