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Are polynomial expressions closed under addition?
Yes.
Is a counting number closed under subtraction?
No.
Are integers closed under subtraction?
Yes.
Are rational numbers closed under division multiplication addition or subtraction?
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.
Are real numbers closed under addition and subtraction?
Real numbers are closed under addition and subtraction. To get a number outside the real number system you would have to use square root.
Are polynomial expressions closed under addition?
Yes.
Are polynomial expressions closed under multiplication?
Yes, because there is no way of multiplying two polynomials to get something that isn't a polynomial.
What does it mean for a polynomial to be closed under addition subtraction and multiplication?
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.
Are rational numbers closed under subtraction?
Yes. They are closed under addition, subtraction, multiplication. The rational numbers WITHOUT ZERO are closed under division.
Is a counting number closed under subtraction?
No.
Are integers closed under subtraction?
Yes.
Are rational numbers closed under division multiplication addition or subtraction?
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.
Which set of numbers is closed under subtraction?
A set of real numbers is closed under subtraction when you take two real numbers and subtract , the answer is always a real number .
Is the collection of integers closed under subraction?
Yes, the set of integers is closed under subtraction.
Are rational numbers closed under subtraction operation?
Yes, they are.
Are real numbers closed under addition and subtraction?
Real numbers are closed under addition and subtraction. To get a number outside the real number system you would have to use square root.
Which sets of numbers are closed under subtraction?
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.
