Which of the following sets is closed under division?
natural numbers
non-zero integers
irrational numbers
non-zero rational numbers

Question

Which of the following sets is closed under division?
natural numbers
non-zero integers
irrational numbers
non-zero rational numbers

alekos · Answer

I reckon the last on

debbieg · Answer

"Closed" means that the result of the operation is part of the same set. So if you can think of a counter-example, then the set is not "closed". 

E.g., for natural numbers (1, 2, 3, 4, .... etc), if I divide 2 natural numbers, do I ALWAYS get a natural number? sometimes I do (6/3=2) but not always (5/4 is rational, but not natural).

Now think about each of the other 3 sets. Are they closed under division? If not, can you think of a counterexample?

anonymous · Answer

Only non zero rational numbers are closed under division

anonymous · Answer

thanks :)