Natural (ℕ), integer (ℤ), rational (ℚ), real (ℝ) and complex (ℂ) numbers are all closed under addition.
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 is closed.
Yes, it is.
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.
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.
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.
Yes, the set is closed.
no
no it is not
Yes, it is.
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.
Yes. The empty set is closed under the two operations.
Let + (addition) be a binary operation on the set of odd numbers S. The set S is closed under + if for all a, b ϵ S, we also have a + b ϵ S. Let 3, 5 ϵ the set of odd numbers 3 + 5 = 8 (8 is not an odd number) Since 3 + 5 = 8 is not an element of the set of the odd numbers, the set of the odd numbers is not closed under addition.
Hennd
The set of all odd numbers. 1+1=2