Back To Course

CAHSEE Math Exam: Tutoring Solution21 chapters | 211 lessons

Are you a student or a teacher?

Try Study.com, risk-free

As a member, you'll also get unlimited access to over 75,000 lessons in math, English, science, history, and more. Plus, get practice tests, quizzes, and personalized coaching to help you succeed.

Try it risk-freeWhat teachers are saying about Study.com

Already registered? Login here for access

Your next lesson will play in
10 seconds

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.

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.

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

2*x* + *y* = 2*x* + *y*

4.789 = 4.789

6^2 = 6^2

As you can see, each example is pretty much indicating the same thing, that each value is equal to itself. It is also important to note that all the numbers in the examples are real numbers, which is an essential part of this property.

The symmetric property of equality is the most similar to the reflexive property of equality, so many people get these two properties of equality mixed up! The **symmetric property of equality** states that if *x = y* then *y = x*. Can you see how this is different from the reflexive property of equality that simply states that *x*=*x*? The symmetric property adds a whole other variable to the picture, whereas the reflexive property is simply stating that a value is equal to itself.

The **reflexive property of equality** simply states that a value is equal to itself. Further, it states that for all real numbers, *x* = *x*. **Real numbers** include rational and irrational numbers, whole numbers and integers. Pretty much the only numbers not included in the real numbers category are negative square roots.

The reflexive property of equality may appear too obvious but it's important to state because if we did not, we would not know that we agree that *x* = *x* or be able to disprove mathematical statements like *x < x* or *x > x*?

To unlock this lesson you must be a Study.com Member.

Create your account

Are you a student or a teacher?

Already a member? Log In

BackWhat teachers are saying about Study.com

Already registered? Login here for access

Did you know… We have over 160 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

Not sure what college you want to attend yet? Study.com 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.

You are viewing lesson
Lesson
5 in chapter 13 of the course:

Back To Course

CAHSEE Math Exam: Tutoring Solution21 chapters | 211 lessons

- What Are the Different Parts of a Graph? 6:21
- Plotting Points on the Coordinate Plane 5:23
- How to Graph Reflections Across Axes, the Origin, and Line y=x 6:07
- Segment Addition Postulate: Definition & Examples 3:21
- The Reflexive Property of Equality: Definition & Examples 3:41
- X-Axis: Definition & Overview
- Y-Coordinates: Definition & Overview
- Go to CAHSEE - Geometry: Graphing Basics: Tutoring Solution

- AFOQT Information Guide
- ACT Information Guide
- Computer Science 335: Mobile Forensics
- Electricity, Physics & Engineering Lesson Plans
- Teaching Economics Lesson Plans
- FTCE Middle Grades Math: Connecting Math Concepts
- Social Justice Goals in Social Work
- Developmental Abnormalities
- Overview of Human Growth & Development
- ACT Informational Resources
- AFOQT Prep Product Comparison
- ACT Prep Product Comparison
- CGAP Prep Product Comparison
- CPCE Prep Product Comparison
- CCXP Prep Product Comparison
- CNE Prep Product Comparison
- IAAP CAP Prep Product Comparison

- Theories of Self-Esteem: Early & Modern
- Environmental Awareness: Definition, History & Importance
- Italian Culture: History, Values & Lifestyle
- Medieval Trial by Ordeal: Definition & History
- Cloud Runtime & Framework Services: Features & Providers
- First-Order Logic in AI: Identification, Uses & Calculations
- Five Senses Unit Plan
- Quiz & Worksheet - Different Kinds of Creativity
- Quiz & Worksheet - Egyptian Ankh
- Quiz & Worksheet - Dyeing Textiles
- Quiz & Worksheet - Symbols in Their Eyes Were Watching God
- Analytical & Non-Euclidean Geometry Flashcards
- Flashcards - Measurement & Experimental Design
- Science Lesson Plans
- 3rd Grade Math Worksheets & Printables

- Principles of Health: Certificate Program
- College Chemistry: Homework Help Resource
- Business Law Textbook
- Praxis Biology and General Science: Practice and Study Guide
- Praxis Psychology (5391): Practice & Study Guide
- Washington EOC - Algebra 1: Equivalent Expressions
- PSSA - ELA Grade 8: Word Choice & Tone
- Quiz & Worksheet - Modeling PE Programs with National & State Standards
- Quiz & Worksheet - Identifying Customer Needs
- Quiz & Worksheet - Employee Training Strategies
- Quiz & Worksheet - HRM Recruitment & Selection Laws
- Snowflakes: Quiz & Worksheet for Kids

- Why Communication Matters in the Workplace
- Medical Dosage Calculations & Formulas
- Jobs for Retired Teachers
- How to Pass a Chemistry Test
- AP English Literature Test & Study Guide
- How to Ace the GMAT
- Common Core State Standards in Missouri
- ELA Common Core Standards in Illinois
- NCBTMB Exam Information
- How to Use Study.com to Improve Your Grades
- Praxis Chemistry Test Difficulty
- Study.com Demo for Enterprise

- Tech and Engineering - Videos
- Tech and Engineering - Quizzes
- Tech and Engineering - Questions & Answers

Browse by subject