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The additive identity is a unique element of a set which has the property that adding it to any element of the set leaves the value of that element unchanged. The identity is normally denoted by 0.

That is: for any X in the set, X + 0 = 0 + X = X

Whether or not the set is commutative, addition of the identity always is.

The additive inverse of one element of a set is a member of the set (not necessarily different nor unique) such that the sum of the two is the additive identity. The additive inverse of an element X is normally denoted by -X.

Thus, X + (-X) = (-X) + X = 0

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Q: How is the additive identity property different to the additive inverse property?
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