## What set of numbers is closed under multiplication?

In mathematics, a set is closed under an operation **if performing that operation on members of the set always produces a member of that set**. For example, the natural numbers are closed under addition, but not under subtraction: 1 − 2 is not a natural number even though both 1 and 2 are naturals.

## What set of numbers is closed under Division?

- A.
**Rational numbers**are closed under division. If you divide a rational number, it will remain a rational number. If you divide an integer or a whole number, there is a chance that the new resulting number will not be an integer or a whole number.

## Are real numbers closed under addition?

- For example, the set of all
**real****numbers**is**closed****under****addition**, because when you add any two**real****numbers**you always get a**real**number. As another example, the set of all odd integers is NOT**closed****under****addition**, because when you add two odd**numbers**you get an EVEN number, something not in that set.

## What are whole numbers closed under?

- Remember that the exponents in polynomials are whole numbers. The whole numbers are closed under
**addition**, which guarantees that the new exponents will be whole numbers. Consequently, polynomials are closed under**multiplication**.

## What set of numbers is closed under multiplication?What set of numbers is closed under multiplication?

The sets of numbers that are closed under multiplication are the following: **Whole numbers, and Integers**. The answers would be options A and D. Whole numbers are closed only under addition and multiplication. Integers are closed under addition, subtraction, multiplication, and division (with the exception of division by 0). Hope this answer helps.

## What set of numbers is closed under Division?What set of numbers is closed under Division?

A. **Rational numbers** are closed under division. If you divide a rational number, it will remain a rational number. If you divide an integer or a whole number, there is a chance that the new resulting number will not be an integer or a whole number.

## Are real numbers closed under addition?Are real numbers closed under addition?

For example, the set of all **real** **numbers** is **closed** **under** **addition**, because when you add any two **real** **numbers** you always get a **real** number. As another example, the set of all odd integers is NOT **closed** **under** **addition**, because when you add two odd **numbers** you get an EVEN number, something not in that set.

## What are whole numbers closed under?What are whole numbers closed under?

Remember that the exponents in __polynomials__ are whole numbers. The whole numbers are closed under **addition**, which guarantees that the new exponents will be whole numbers. Consequently, polynomials are closed under **multiplication**.