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Closure depends on the set as much as it depends on the operation.

For example, subtraction is closed for all integers but not for natural numbers. Division by a non-zero number is closed for the rational numbers but not integers.

The set {1, 2, 3} is not closed under addition.

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Q: What binary operations have closure?

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They are binary operations.

It gives closure to the set of real numbers with regard to the binary operation of addition. This makes the set a ring. The additive inverse is used, sometimes implicitly, in subtraction.

There are many. There are those that deal with the four basic binary operations, then there are rules governing exponents and logarithms.

I am not at all sure that there are any rules that apply to integers in isolation. Any rules that exist are in the context of binary operations like addition or multiplication of integers.

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Related questions

If a set has closure with regards to certain operations then any solution that is obtained using those operations must belong to that set.

There are a few rules to perform arithmetic operations in binary numbers. According to those rules you can add or subtract binary numbers. There are only two arithmetic operations used in binary numbers, they are addition and subtraction.

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They are binary operations.

It provides closure under the binary operation of addition.

Commutativity is a property of binary operations. A fact is not a binary operator.

Binary arithmetic operations.

Operations, or more precisely, binary mathematical operations

Binary counters are used in simple timing operations. They can generate clock signals among many other less than complex operations.

to implement operations on binary heap in c

The closure property is an attribute of a set with respect to a binary operation, not only a binary operation. A set S is closed with respect to multiplication if, for any two elements, x and y, belonging to S, x*y also belongs to S.

It already has; binary.

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