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Yes they are closed under multiplication, addition, and subtraction.

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โˆ™ 2013-05-22 01:23:32
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Q: Are polynomial expressions closed under subtraction?
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Related questions

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.


Are integers closed under subtraction?

Yes.


Is a counting number closed under subtraction?

No.


Is the collection of integers closed under subraction?

Yes, the set of integers is closed under subtraction.


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 subtraction closed under the set of whole number?

Why, yes, it is.


Is the set of whole number closed under subtraction?

Yes, it is.


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.


Under what operation is the set of positive rational numbers not closed?

Subtraction.


Is the set of integers that are multiple of 4 is closed under subtraction?

Yes.


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.


Is the set of irrational numbers closed under subtraction?

No; here's a counterexample to show that the set of irrational numbers is NOT closed under subtraction: pi - pi = 0. pi is an irrational number. If you subtract it from itself, you get zero, which is a rational number. Closure would require that the difference(answer) be an irrational number as well, which it isn't. Therefore the set of irrational numbers is NOT closed under subtraction.


What does this mean Which set of these numbers is closed under subtraction?

It means whatever members of the set you subtract, the answer will still be a member of the set. For example, the set of positive integers is not closed under subtraction, since 3 - 8 = -5


Are rational numbers are closed under addition subtraction division or multiplication?

The set of rational numbers is closed under all 4 basic operations.


Are rational numbers are closed under addition subtraction multiplication and division?

They are closed under all except that division by zero is not defined.


Why has death rates decreased?

I Think is natural number a closed set under subtraction.


Is the set of real numbers 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.


What do interger's allow you to do that whole numbers do not?

Integers are closed under subtraction, meaning that any subtraction problem with integers has a solution in the set of integers.


What is always true about whole numbers?

They form a closed set under addition, subtraction or multiplication.


Is the set of whole numbers closed under subtraction?

It depends on your definition of whole numbers. The classic definition of whole numbers is the set of counting numbers and zero. In this case, the set of whole numbers is not closed under subtraction, because 3-6 = -3, and -3 is not a member of this set. However, if you use whole numbers as the set of all integers, then whole numbers would be closed under subtraction.