The relevant property is the closure of the set of rational numbers under the operation of addition.
The way in which the binary functions, addition and multiplication, are defined on the set of rational numbers ensures that the set is closed under these two operations.
Since the set of rational numbers is closed under addition, any rational number added to 0.5 will total another rational number.
is under root 8 is a rational number
No. A number cannot be closed under addition: only a set can be closed. The set of rational numbers is closed under addition.
7 is a rational number because whole numbers, integers, and natural numbers fit under rational and 7 is a natural number:)Yes.
No.
If a set is closed under an operation. then the answer will be a part of that set. If you add, subtract or multiply any two rational numbers you get another national number. But when it comes to division, it is closed except for one number and that is ZERO. eg 3.56 (rational number) ÷ 0 = no answer. Since no answer is not a rational number, that rational numbers are not closed under the operation of division.
Rational numbers are closed under multiplication, because if you multiply any rational number you will get a pattern. Rational numbers also have a pattern or terminatge, which is good to keep in mind.
No. Zero is a rational number, but division by zero is not defined.
No Q is not cyclic under addition.
No. The set of rational numbers is closed under addition (and multiplication).