Identity element facts for kids

The identity element (also called the neutral element) is a very special part of a set in mathematics. Think of it like a secret ingredient that, when combined with another element from the same set, doesn't change the other element at all! It leaves the other element exactly as it was.

For example, when you are doing addition, the identity element is the number 0. This is because adding 0 to any number doesn't change that number. If you have 7 apples and add 0 more apples, you still have 7 apples! So, 7 + 0 = 7.

When you are doing multiplication, the identity element is the number 1. This is because multiplying any number by 1 doesn't change that number. If you have 5 groups of 1 item, you still have 5 items in total! So, 5 × 1 = 5.

Sometimes, in more advanced math like group theory, the identity element is shown using the symbol .

Understanding Identity Elements with Examples

Let's look at some common ways identity elements work:

Addition: The Power of Zero

In the world of real numbers (which are all the numbers you usually use, like 1, 2.5, -3, etc.), the number 0 is the identity element for addition.

• If you take any real number, say 15, and add 0 to it, you still get 15.
• 15 + 0 = 15
• This works for all real numbers.

Multiplication: The Role of One

For real numbers, the number 1 is the identity element for multiplication.

• If you take any real number, like 20, and multiply it by 1, you still get 20.
• 20 × 1 = 20
• This also works for all real numbers.

Special Cases: When Identity Elements Only Work One Way

Sometimes, an identity element might only work from one side. For example, with exponentiation (like 2³), the number 1 can be a "right identity."

• If you have a number a and raise it to the power of 1 (a¹), the number stays the same. For example, 5¹ = 5.
• However, if you raise 1 to the power of a (1^a), it's always 1, not necessarily a. So, 1⁵ = 1, not 5. This means 1 is only a "right identity" for exponentiation.

Related pages

• Identity (mathematics)
• Null vector
• One
• Zero

See also

In Spanish: Elemento neutro para niños