A set is called closed under an operation if performing that operation between any two elements of that set will result in another

Question

A set is called closed under an operation if performing that operation between any two elements of that set will result in another element of the set. For example, natural numbers are closed under addition because adding two natural numbers will always result in a natural number. It is not closed under subtraction, though, because 4-5 will not equal a natural number. Using this definition, are integers closed under division? Explain.

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1 month 2022-12-31T00:52:21+00:00 1 Answer 0 views 0

Answer ( 1 )

1. The explanation for closure property of sets is as explained below.

How to interpret the closure property operation in sets?

A set is closed under addition if you can add any two numbers in the set and still have a number in the set as a result. A set is closed under (scalar) multiplication if you can multiply any two elements, and the result is still a number in the set.
For example, the set {1,−1} is closed under multiplication but not addition.
A set is closed under an operation if performance of that operation on members of the set always produces a member of that set. For example, the positive integers are closed under addition, but not under subtraction: is not a positive integer even though both 1 and 2 are positive integers.
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