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Different sets of numbers have different properties. For example,The set of counting numbers is closed under addition but not under subtraction.The set of integers is closed under addition, subtraction and multiplication but not under division.Rational numbers are closed under all four basic operations of arithmetic, but not for square roots.A set S is "closed" with respect to operation # if whenever x and y are any two elements of S, then x#y is also in S. y = 0 is excluded for division.So, the answer depends on what you mean by "number".
Because if X and Y are any two whole number, then X*Y is also a whole number. Always.
That the set of perfect squares is closed under multiplication. That is if x and y are any two perfect squares, then x*y is a perfect square.
The set of positive numbers, the set of negative numbers are two examples. Any subsets of these will also not be closed.
Yes. When you add any whole numbers you get another whole number. That is what closed means in this context. The answer is still a whole number.