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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.

Q: How a kaleen closure is different from positive closure?

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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.

Examples of the purpose of closure in math

The sign of the sum is positive when the absolute value of the positive addend is greater than that of the negative addend.

A king closure is a brick cut to bond in a corner of brickwork, a brick with a corner cut off.

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Add two positive integers and you ALWAYS have a positive integers. The positive integers are closed under addition.

it is the closure of the set

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Closure is a noun.

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.

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Examples of the purpose of closure in math

Yes.Suppose a and b are two positive rational numbers. Then a can be expressed in the form p/q where p and q are positive integers, and b can be expressed in the form r/s where r and s are positive integers.Then b - a = r/s - p/q = (qr - ps)/qs.Now, since p, q, r and s are integers, thenby the closure of the set of integers under multiplications, qr, ps and qs are integers;q and s are positive => qs is positive, andby the closure of the set of integers under addition (and subtraction), qr - ps is an integer.That is, b - a = (qr - ps)/qs is a ratio of two integers, where the denominator of the ratio is positive.

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