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What does it mean for a polynomial to be closed under addition subtraction and multiplication?
Wiki User
∙ 8y ago
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.
Wiki User
∙ 8y ago
Wiki User
∙ 8y agoIf you perform any of those operations on a polynomial, the result will be a polynomial.
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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 are odd integers closed under multiplication but not under addition?
The numbers are not closed under addition because whole numbers, even integers, and natural numbers are closed.
When is a set of negative irrational numbers closed?
It cannot be closed under the four basic operations (addition, subtraction, multiplication, division) because it is indeed possible to come up with two negative irrational numbers such that their sum/difference/product/quotient is a rational number, indicating that the set is not closed. You will have to think of a different operation.
What are the characteristics of integers?
Integers are the natural numbers (counting numbers: 1,2,3,etc.), and their negative counterparts, and zero. The set of Integers is closed for addition, subtraction, and multiplication, but not division. Closed means that the answer will be a part of the set. Example: 1/3 (1 divided by 3 equals one third) is not an integer, even though both 1 and 3 are integers.
What is the principle of closure math?
When you combine any two numbers in a set the result is also in that set. e.g. The set of whole numbers is closed with respect to addition, subtraction and multiplication. i.e. when you add, subtract or multiply two numbers the answer will always be a whole number. But the set of whole numbers is NOT closed with respect to division as the answer is not always a whole number e.g. 7÷5=1.4 The answer is not a whole number.
Are polynomial expressions closed under subtraction?
Yes they are closed under multiplication, addition, and subtraction.
What operations are closed for integers?
Addition, subtraction and multiplication.
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 rational numbers closed under subtraction?
Yes. They are closed under addition, subtraction, multiplication. The rational numbers WITHOUT ZERO are closed under division.
What operations is the set -1 0 1 closed to A Addition B Division C Multiplication D Subtraction?
Multiplication.
What is always true about whole numbers?
They form a closed set under addition, subtraction or multiplication.
What is the set of whole numbers closed by?
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.
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.
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.
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.
