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Are polynomial expressions closed under subtraction?
Yes they are closed under multiplication, addition, and subtraction.
Is a rational number closed under addition?
No. A number cannot be closed under addition: only a set can be closed. The set of rational numbers is closed under addition.
When are complex numbers closed under addition?
Quite simply, they are closed under addition. No "when".
Are integers closed under addition?
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 polynomial expressions closed under subtraction?
Yes they are closed under multiplication, addition, and subtraction.
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.
Is a rational number closed under addition?
No. A number cannot be closed under addition: only a set can be closed. The set of rational numbers is closed under addition.
When are complex numbers closed under addition?
Quite simply, they are closed under addition. No "when".
What is closed and not-closed under addition?
The set of even numbers is closed under addition, the set of odd numbers is not.
Is the set of non-deterministic polynomial time (NP) problems closed under the operation of union?
Yes, the set of non-deterministic polynomial time (NP) problems is closed under the operation of union.
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.
What operations are polynomials closed under?
+,-,X only
Are real numbers closed under addition?
yes because real numbers are any number ever made and they can be closed under addition
ARe odd integers not closed under addition?
That is correct, the set is not closed.
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.
