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What operations is not closed for polynomials?

division


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.


What operations are irrational numbers closed under?

None.


Are polynomial expressions closed under multiplication?

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


Are decidable languages closed under any operations?

Yes, decidable languages are closed under operations such as union, intersection, concatenation, and complementation. This means that if a language is decidable, performing these operations on it will result in another decidable language.


Are whole numbers closed under the operations of multiplication?

Yes.


Is this set of negative numbers closed under multiplication or addition?

Yes. The empty set is closed under the two operations.


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

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


What is the significance of closed under concatenation in the context of string operations?

In the context of string operations, being closed under concatenation means that when you combine two strings together, the result is still a valid string. This property is important because it ensures that string operations can be performed without creating invalid or unexpected results.


How the polynomials and non polynomials alike?

In my opinion the question is poorly defined, since "non-polynomial" could be just about anything.


When factoring polynomials under what circumstances do you change the operation?

you dont


Are whole numbers closed under the operations of addition?

Yes. When you add any whole numbers you get another whole number. That is what closed means in this context. The answer is still a whole number.