In arithmetic, the additive identity is 0.

This means that you can add 0 to any number...  and it keeps its identity!  The number stays the same!

Let's look at the number 5.  Anyway we try to add 0 to it, the 5 just keeps coming back as the answer.

5 + 0 = 5

0 + 5 = 5

Go ahead and try it with any number you can thing of...  It always works!

And, when something always works in math, we make it a property:

The Additive Identity Property:

The additive identity is 0 because

a + 0 = a
 
and

 
0 + a = a

This is often written in one line...

a + 0 = a = 0 + a

Where a is any real number.

 

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