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No. A number cannot be closed under addition: only a set can be closed. The set of rational numbers is closed under addition.

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Yes.

Q: Is a rational number closed under addition?

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Rational numbers are closed under addition, subtraction, multiplication. They are not closed under division, since you can't divide by zero. However, rational numbers excluding the zero are closed under division.

Yes.

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.

Yes, the set is closed.

Yes, it is.

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No. The set of rational numbers is closed under addition (and multiplication).

Rational numbers are closed under addition, subtraction, multiplication. They are not closed under division, since you can't divide by zero. However, rational numbers excluding the zero are closed under division.

Yes.

Yes, they can.

Yes.

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.

Yes, the set is closed.

Yes. They are closed under addition, subtraction, multiplication. The rational numbers WITHOUT ZERO are closed under division.

Yes, it is.

The set of rational numbers is closed under all 4 basic operations.

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.