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Q: Does the set of rational numbers have an additive identity?

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There is only one set and it does have an additive identity.

Yes. The additive identity is 0.

I t is the number 0, which has the property that x + 0 = 0 + x = x for all rational numbers x.

Yes: it is 0.

Zero is the additive identity in the set of real numbers; when you add zero to any number, the number does not change its identity.

Yes, it does.

Wrong! Not only is zero a real number, but it is the additive identity for the set of integers, rational numbers as well as real numbers.

No. It has a different additive inverses for each element.

Yes. The multiplicative identity for the rational numbers is 1 (also can be written as 1/1).

Yes.

Yes, it is 1.

0 is the additive identity for the set of numbers.

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