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Rule

Identity Property of Addition

Adding to any number always results in the number itself.


Because of this, is called the Additive Identity.

Proof

 Informal Justification
Consider a number By the Reflexive Property of Equality, is equal to itself.
Let be another number. If is added to and subtracted from the left-hand side of the above equation, the equality still holds true.
Finally, is equal to
It has been shown that By the Commutative Property of Addition, is also equal to
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