No.
Quite simply, they are closed under addition. No "when".
Natural (ℕ), integer (ℤ), rational (ℚ), real (ℝ) and complex (ℂ) numbers are all closed under addition.
of course!
The set of even numbers is closed under addition, the set of odd numbers is not.
The numbers are not closed under addition because whole numbers, even integers, and natural numbers are closed.
yes because real numbers are any number ever made and they can be closed under addition
Yes. The set of real numbers is closed under addition, subtraction, multiplication. The set of real numbers without zero is closed under division.
No. A number cannot be closed under addition: only a set can be closed. The set of rational numbers is closed under addition.
No.
Yes. The entire set of natural numbers is closed under addition (but not subtraction). So are the even numbers (but not the odd numbers), the multiples of 3, of 4, etc.
Yes, the set is closed.
Yes.