Operation Closure Math Example 1

Follow the full solution, then compare it with the other examples linked below.

Example 1

easy
Are whole numbers closed under addition? Test with \(5 + 7\) and \(12 + 0\). Explain what closure means.

Solution

  1. 1
    Closure means: performing the operation on two members of the set always gives another member of the same set.
  2. 2
    Test: \(5 + 7 = 12\). Is 12 a whole number? Yes.
  3. 3
    Test: \(12 + 0 = 12\). Is 12 a whole number? Yes.
  4. 4
    Whole numbers are closed under addition: the sum of any two whole numbers is always a whole number.

Answer

Yes — whole numbers are closed under addition
A set is closed under an operation if applying the operation to any elements of the set always produces another element in the set.

About Operation Closure

A set is closed under an operation if performing that operation on members of the set always produces a result that is also in the set. For example, integers are closed under addition.

Learn more about Operation Closure →

More Operation Closure Examples

Example 2 medium

Are whole numbers closed under subtraction? Provide a counterexample if not.

Example 3 easy

Are integers closed under multiplication? Test with ((-3) times 4) and ((-2) times (-5)).

Example 4 medium

Are integers closed under division? Provide a counterexample if not.

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