Consider the set of natural numbers. when you add two natural numbers, you will always get
a natural number. for example, 3+4 = 7. so, the set of natural numbers is said to be closed
under the operation of addition.
similarly, adding two integers or two rational numbers or two real numbers always produces
an integer, or rational number, or a real number, respectively. so, all the systems of numbers
are closed under the operation of addition,
a. think of polynomials as a system. for each of the following operations, determine whether
the system is closed under the operation. in each case, explain why it is closed or provide
an example showing that it isn't.
1. addition
type your response here:
2. subtraction
type your response here:
3. multiplication
type your response here:
4. division