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It means that given a set, if x and y are any members of the set then x+y is also a member of the set.

For example, positive integers are closed under addition, but they are not closed under subtraction, since 5 and 8 are members of the set of positive integers but 5 - 8 = -3 is not a positive integer.

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Q: What does the word closure property for addition mean?
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