When you combine any two numbers in a set the result is also in that set.
e.g. The set of whole numbers is closed with respect to addition, subtraction and multiplication. i.e. when you add, subtract or multiply two numbers the answer will always be a whole number.
But the set of whole numbers is NOT closed with respect to division as the answer is not always a whole number e.g. 7÷5=1.4 The answer is not a whole number.
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The answer depends on the context. Sets (or intervals) can be open or closed, or semi-open. In a different context, sets can be closed (or not) with respect to some operation (addition, division, something else) defined on element of the set. Without that context, it is not possible to answer the question.
Examples of the purpose of closure in math
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The main difference between Kaleen closure and positive closure is; the positive closure does not contains the null, but Kaleen closure can contain the null.
it is the closure of the set
No. Closure is the property of a set with respect to an operation. You cannot have closure without a defined set and you cannot have closure without a defined operation.