# What is closed under addition examples?

## What is closed under addition examples?

So a set is closed under addition if the sum of any two elements in the set is also in the set. For example, the real numbers R have a standard binary operation called addition (the familiar one). Then the set of integers Z is closed under addition because the sum of any two integers is an integer.

## What type of numbers are closed under addition?

a) The set of integers is closed under the operation of addition because the sum of any two integers is always another integer and is therefore in the set of integers.

Is the set of real numbers closed under addition examples?

Real numbers are closed under addition, subtraction, and multiplication. That means if a and b are real numbers, then a + b is a unique real number, and a ⋅ b is a unique real number. For example: Any time you add, subtract, or multiply two real numbers, the result will be a real number.

### What does it mean if something is closed under addition?

Being closed under addition means that if we took any vectors x1 and x2 and added them together, their sum would also be in that vector space. Being closed under scalar multiplication means that vectors in a vector space, when multiplied by a scalar (any real number), it still belongs to the same vector space.

### When you add two whole numbers you always get a whole number?

Whole numbers (positive integers and zero) are said to be a closed set under addition: if you add two whole numbers, you always get a whole number. Whole numbers are not a closed set under subtraction: if you subtract two whole numbers, you do not always get a whole number.

How do you know if a set is closed under addition?

A set is closed under addition if you can add any two numbers in the set and still have a number in the set as a result. A set is closed under (scalar) multiplication if you can multiply any two elements, and the result is still a number in the set.

#### What is the best definition of closure?

1 : an act of closing : the condition of being closed closure of the eyelids business closures the closure of the factory. 2 : an often comforting or satisfying sense of finality victims needing closure also : something (such as a satisfying ending) that provides such a sense.