Proof. If , we have nothing to prove. Make the induction hypothesis, that (1) is true for . Denote
where has been moved to the end by the induction hypothesis. But the product in the parenthesis, which exactly the factors in a certain , is also by the induction hypothesis equal to . Thus we obtain
whence (1) is true for .
Note. There is mentionned in the Remark of the entry “http://planetmath.org/node/2148commutativity” a more general notion of commutativity.
|Date of creation||2014-05-10 21:59:41|
|Last modified on||2014-05-10 21:59:41|
|Last modified by||pahio (2872)|