Question 771748: is (1, 1/2, 1/3, 1/4, 1/5, ...) closed under multiplication?
Answer by DrBeeee(684)   (Show Source):
You can put this solution on YOUR website! CLosed under multiplication means that if you multiply any two elements (members) of the set together the answer (product) must be a member of the set. In the given set
(1) A = {1,1/2, 1/3...} we have the identity one, which by definition will yield a product that is a member of the set. All of the other members of the set are of the form
(2) 1/n or the inverse of a positive integer and when you multiply any two (or more) together you get
(3) (1/n)*(1/m) = 1/(n*m) and since n*m is just another positive integer, the prduct of any of the other members is also a member of the set.
Answer: Yes, the given set is closed under multiplication.
Can you show that it is NOT closed under addition? subtraction? or division?
|
|
|
