Definition
Closure property
A set has closure under an operation when every allowed calculation stays in that set.
What it means
Picture a fence around a set of numbers. Choose any allowed numbers inside and use the named operation. Closure means the result never lands outside the fence. You must name both the set and the operation.
Remember it
Start inside, finish inside—every time.
Example
Whole numbers are closed under addition: 18 and 7 are whole numbers, and 18 + 7 = 25 is also a whole number. Whole numbers are not closed under subtraction, because 7 − 18 = −11, which is outside the whole numbers.
Watch for
Checking one successful calculation does not prove closure. The rule must work for every allowed pair; one counterexample is enough to show that closure fails.
Common mix-up
Closure is not a property of an operation by itself. The same operation can be closed on one set and not closed on another.
Exact meaning
A set is closed under an operation when applying that operation to any allowed members of the set always produces a result that is also a member of the same set.