The Reflexive Property of Equality: Definition & Examples Video

An error occurred trying to load this video.

Try refreshing the page, or contact customer support.

Coming up next: X Variable: Definition & Concept

You're on a roll. Keep up the good work!

Take Quiz Watch Next Lesson
Your next lesson will play in 10 seconds
  • 0:01 Reflexive Property of Equality
  • 1:01 Importance
  • 1:38 Examples
  • 2:22 Symmetric Property of Equality
  • 2:54 Lesson Summary
Save Save Save

Want to watch this again later?

Log in or sign up to add this lesson to a Custom Course.

Log in or Sign up

Speed Speed

Recommended Lessons and Courses for You

Lesson Transcript
Instructor: Karin Gonzalez

Karin has taught middle and high school Health and has a master's degree in social work.

In this lesson, we will review the definition of the reflexive property of equality. We will also look at why this property is important. Following the lesson will be a brief quiz to test your knowledge on the reflexive property of equality.

Defining the Reflexive Property of Equality

If you look in a mirror, what do you see? Your reflection! You are seeing an image of yourself. You could look at the reflexive property of equality as when a number looks across an equal sign and sees a mirror image of itself! Reflexive pretty much means something relating to itself.

The reflexive property of equality simply states that a value is equal to itself. Further, this property states that for all real numbers, x = x. What is a real number, though?

Real numbers include all the numbers on a number line. They include rational numbers and irrational numbers. A rational number is any number that can be written as a fraction. An irrational number, on the other hand, is a real number that cannot be written as a simple fraction. Square roots would be in this category. In fact, real numbers pretty much entail every number possible except for negative square roots because they are imaginary numbers.

Therefore, the reflexive property of equality pretty much covers most values and numbers. Again, it states simply that any value or number is equal to itself.

Importance of the Reflexive Property of Equality

Why is the reflexive property of equality important or even necessary to state? After all, it seems so obvious! The reason is that if we don't clearly make a statement of something in mathematics, how do we know that we all agree that it is true? Even for something so simple as the reflexive property of equality, we need to have a property so that we know that we all agree that x = x.

Also, if we did not have the reflexive property of equality, how would we explain that x < x or x > x is not true? Because of this property of equality, we can affirm that statements like x < x are false.


Here are some examples of the reflexive property of equality:

x = x

y = y

x + y = x + y

1 = 1

1/2 = 1/2

432 = 432

46 + 56 = 46 + 56

2x + y = 2x + y

4.789 = 4.789

6^2 = 6^2

To unlock this lesson you must be a Member.
Create your account

Register to view this lesson

Are you a student or a teacher?

Unlock Your Education

See for yourself why 30 million people use

Become a member and start learning now.
Become a Member  Back
What teachers are saying about
Try it risk-free for 30 days

Earning College Credit

Did you know… We have over 200 college courses that prepare you to earn credit by exam that is accepted by over 1,500 colleges and universities. You can test out of the first two years of college and save thousands off your degree. Anyone can earn credit-by-exam regardless of age or education level.

To learn more, visit our Earning Credit Page

Transferring credit to the school of your choice

Not sure what college you want to attend yet? has thousands of articles about every imaginable degree, area of study and career path that can help you find the school that's right for you.

Create an account to start this course today
Try it risk-free for 30 days!
Create an account