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To be closed under an operation, when that operation is applied to two member of a set then the result must also be a member of the set.

Thus the sets ℂ (Complex numbers), ℝ (Real Numbers), ℚ (Rational Numbers) and ℤ (integers) are closed under subtraction.

ℤ+ (the positive integers), ℤ- (the negative integers) and ℕ (the natural numbers) are not closed under subtraction as subtraction can lead to a result which is not a member of the set.

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Q: Which sets of numbers are closed under subtraction?
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I know that whole numbers, integers, negative numbers, positive numbers, and even numbers are. Anyone feel free to correct me.


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Related questions

Is set of numbers closed under natural and subtraction?

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.


Which set is closed under the operation of subtraction?

The set of integers, rational numbers, real numbers, complex numbers are some of the sets. Also, many of their subsets: for example, all numbers divisible by 3.


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Subtraction and addition are not properties of numbers themselves: they are operators that can be defined on sets of numbers.


What are the properties of number?

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".


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I know that whole numbers, integers, negative numbers, positive numbers, and even numbers are. Anyone feel free to correct me.


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