0
Still curious? Ask our experts.
Chat with our AI personalities
Jordan
Ross
ViviAdd your answer:
Earn +20 pts
Are rational numbers closed under subtraction?
Yes. They are closed under addition, subtraction, multiplication. The rational numbers WITHOUT ZERO are closed under division.
Are integers closed under division?
No. Integers are not closed under division because they consist of negative and positive whole numbers. NO FRACTIONS!No.For a set to be closed under an operation, the result of the operation on any members of the set must be a member of the set.When the integer one (1) is divided by the integer four (4) the result is not an integer (1/4 = 0.25) and so not member of the set; thus integers are not closed under division.
Is the sum of rational numbers always rational?
Yes. In general, the set of rational numbers is closed under addition, subtraction, and multiplication; and the set of rational numbers without zero is closed under division.
Under which operation is the set of odd integers closed?
addition
Is the set of irrational numbers closed under subtraction?
No; here's a counterexample to show that the set of irrational numbers is NOT closed under subtraction: pi - pi = 0. pi is an irrational number. If you subtract it from itself, you get zero, which is a rational number. Closure would require that the difference(answer) be an irrational number as well, which it isn't. Therefore the set of irrational numbers is NOT closed under subtraction.
