Yes they are closed under multiplication, addition, and subtraction.
No. A number cannot be closed under addition: only a set can be closed. The set of rational numbers is closed under addition.
Quite simply, they are closed under addition. No "when".
yes
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 they are closed under multiplication, addition, and subtraction.
Yes, because there is no way of multiplying two polynomials to get something that isn't a polynomial.
It means that you can do any of those operations, and again get a number from the set - in this case, a polynomial. Note that if you divide a polynomial by another polynomial, you will NOT always get a polynomial, so the set of polynomials is not 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.
Quite simply, they are closed under addition. No "when".
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.
That is correct, the set is not closed.
yes
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.