Yes. The empty set is closed under the two operations.
If you mean the set of non-negative integers ("whole numbers" is a bit ambiguous in this sense), it is closed under addition and multiplication. If you mean "integers", the set is closed under addition, subtraction, multiplication.
Quite simply, they are closed under addition. No "when".
No. A number cannot be closed under addition: only a set can be closed. The set of rational numbers is closed under addition.
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.
Because when you add any negative numbers, the sum will also be a negative number.
Yes. The empty set is closed under the two operations.
The set of even numbers is closed under addition, the set of odd numbers is not.
If you mean the set of non-negative integers ("whole numbers" is a bit ambiguous in this sense), it is closed under addition and multiplication. If you mean "integers", the set is closed under addition, subtraction, multiplication.
The numbers are not closed under addition because whole numbers, even integers, and natural numbers are closed.
Quite simply, they are closed under addition. No "when".
No. A number cannot be closed under addition: only a set can be closed. The set of rational numbers is 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.
I know that whole numbers, integers, negative numbers, positive numbers, and even numbers are. Anyone feel free to correct me.
yes because real numbers are any number ever made and they can be closed under addition
No. For a set to be closed with respect to an operation, the result of applying the operation to any elements of the set also must be in the set. The set of negative numbers is not closed under multiplication because, for example (-1)*(-2)=2. In that example, we multiplied two numbers that were in the set (negative numbers) and the product was not in the set (it is a positive number). On the other hand, the set of all negative numbers is closed under the operation of addition because the sum of any two negative numbers is a negatoive number.
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.