Q: Are integers closed under addition

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negetive integers are not closed under addition but positive integers are.

Yes it is.

Yes.

If you mean the set of non-negative integers ("whole numbers" is a bit ambiguous in this sense), it is closed under addition and multiplication. If you mean "integers", the set is closed under addition, subtraction, multiplication.

Addition, subtraction and multiplication.

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negetive integers are not closed under addition but positive integers are.

The numbers are not closed under addition because whole numbers, even integers, and natural numbers are closed.

That is correct, the set is not closed.

Yes it is.

addition

Yes.

If you mean the set of non-negative integers ("whole numbers" is a bit ambiguous in this sense), it is closed under addition and multiplication. If you mean "integers", the set is closed under addition, subtraction, multiplication.

You don't say that "an integer is closed". It is the SET of integers which is closed UNDER A SPECIFIC OPERATION. For example, the SET of integers is closed under the operations of addition and multiplication. That means that an addition of two members of the set (two integers in this case) will again give you a member of the set (an integer in this case).

Any time you add integers, the sum will be another integer.

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

Because the set is not closed under addition. If x and y are odd, then x + y is not odd.

Yes, the set of integers is closed under subtraction.