uniqueness of inverse (for groups)
Lemma Suppose is a group. Then every element in has a unique inverse.
Proof. Suppose . By the group axioms we know that there is an such that
where is the identity element in . If there is also a satisfying
so , and has a unique inverse.
|Title||uniqueness of inverse (for groups)|
|Date of creation||2013-03-22 14:14:33|
|Last modified on||2013-03-22 14:14:33|
|Last modified by||waj (4416)|