Please clarify what set you are talking about. There are several sets of numbers. Also, "closed under..." should be followed by an operation; "natural" is not an operation.
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A set of real numbers is closed under subtraction when you take two real numbers and subtract , the answer is always a real number .
Yes. The set of real numbers is closed under addition, subtraction, multiplication. The set of real numbers without zero is closed under division.
It depends on your definition of whole numbers. The classic definition of whole numbers is the set of counting numbers and zero. In this case, the set of whole numbers is not closed under subtraction, because 3-6 = -3, and -3 is not a member of this set. However, if you use whole numbers as the set of all integers, then whole numbers would be closed under subtraction.
No, the natural numbers are not closed under division. For example, 2 and 3 are natural numbers, but 2/3 is not.
The set of rational numbers is closed under all 4 basic operations.