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Editor’s collection of notes:
Pre-Algebra
Property, Equality: Reflexive
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used in mathematical proofs
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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?
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.
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
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