True or False The set of whole numbers is closed under subtraction Why
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True or False The set of whole numbers is closed under subtraction Why
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True
Yes, the set of integers is closed under subtraction.
A set is closed under a particular operation (like division, addition, subtraction, etc) if whenever two elements of the set are combined by the operation, the answer is always an element of the original set. Examples: I) The positive integers are closed under addition, because adding any two positive integers gives another positive integer. II) The integers are notclosed under division, because it is not true that an integer divided by an integer is an integer (as in the case of 1 divided by 5, for example). In this case, the answer depends on the definition of “whole numbers”. If this term is taken to mean positive whole numbers (1, 2, 3, …), then the answer is no, they are not closed under subtraction, because it is possible to subtract two positive whole numbers and get an answer that is not a positive whole number (as in the case of 1 – 10 = -9, which is not a positive whole number)