Q: Are polynomials a closed set under addition?

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

Yes, the set is closed.

Yes. The empty set is closed under the two operations.

Yes it is.

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.

Related questions

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.

Yes. The set of real numbers is closed under addition, subtraction, multiplication. The set of real numbers without zero is closed under division.

Yes, the set is closed.

That is correct, the set is not closed.

Yes. The empty set is closed under the two operations.

no

no it is not

Yes it is.

It means that you can do any of those operations, and again get a number from the set - in this case, a polynomial. Note that if you divide a polynomial by another polynomial, you will NOT always get a polynomial, so the set of polynomials is not closed under division.

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