Q: Is the set of integers closed under addition?

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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.

Yes.

No. A number cannot be closed under addition: only a set can be closed. The set of rational numbers is closed under addition.

The set of integers is not closed under multiplication and so is not a field.

Yes, it is.

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That is correct, the set is not closed.

addition

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.

Yes.

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).

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.

The set of even numbers is closed under addition, the set of odd numbers is not.

No. A number cannot be closed under addition: only a set can be closed. The set of rational numbers is closed under addition.

The set of integers is not closed under multiplication and so is not a field.

It means that given a set, if x and y are any members of the set then x+y is also a member of the set. For example, positive integers are closed under addition, but they are not closed under subtraction, since 5 and 8 are members of the set of positive integers but 5 - 8 = -3 is not a positive integer.

yes