The Reflexive Property of Equality: Definition & Examples
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 is not true? Because of this property of equality, we can affirm that statements like x < x are false.
Examples
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
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