Definition
Additive identity
The additive identity is zero, because adding zero leaves a number unchanged.
What it means
Zero means no extra amount. Add no extra amount to a number and you still have the same number. It works on either side of the addition sign.
Remember it
Adding nothing changes nothing.
Example
Start with 27 counters. Adding 0 counters leaves 27, so 27 + 0 = 27. Starting with 0 and then adding 27 also gives 27, so 0 + 27 = 27.
Watch for
Zero is the identity for addition, but an operation involving zero does not always leave a number unchanged: 27 × 0 = 0.
Common mix-up
Do not swap the two identity numbers: zero is the additive identity, while one is the multiplicative identity.
Exact meaning
The additive identity is the number zero: for any number a for which addition is defined, a + 0 = 0 + a = a.