Q: Are polynomial expressions closed under subtraction?

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Yes.

No.

Yes.

Rational numbers are closed under addition, subtraction, multiplication. They are not closed under division, since you can't divide by zero. However, rational numbers excluding the zero are closed under division.

Real numbers are closed under addition and subtraction. To get a number outside the real number system you would have to use square root.

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Yes.

Yes, because there is no way of multiplying two polynomials to get something that isn't a polynomial.

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.

Yes. They are closed under addition, subtraction, multiplication. The rational numbers WITHOUT ZERO are closed under division.

Yes.

No.

Rational numbers are closed under addition, subtraction, multiplication. They are not closed under division, since you can't divide by zero. However, rational numbers excluding the zero are closed under division.

A set of real numbers is closed under subtraction when you take two real numbers and subtract , the answer is always a real number .

Yes, the set of integers is closed under subtraction.

Yes, they are.

Real numbers are closed under addition and subtraction. To get a number outside the real number system you would have to use square root.

To be closed under an operation, when that operation is applied to two member of a set then the result must also be a member of the set. Thus the sets ℂ (Complex numbers), ℝ (Real Numbers), ℚ (Rational Numbers) and ℤ (integers) are closed under subtraction. ℤ+ (the positive integers), ℤ- (the negative integers) and ℕ (the natural numbers) are not closed under subtraction as subtraction can lead to a result which is not a member of the set.