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-3 does not have a multiplicative identity in the set of real numbers.
It is the additive identity for integers, rational numbers, real numbers, complex numbers.
They both considered "identity elements". 0 is actually the identity element under addition for the real numbers, since if a is any real number, a + 0 = 0 + a = a. Mathematicians refers to 0 as the additive identity (or better said, the reflexive identity of addition). 1 is a separate and special entity called 'Unity' or 'Identity element'. 1 is actually the identity element under multiplication for the real numbers, since a x 1 = 1 x a = a. Mathematicians refers to 1 as the multiplicative identity (or better said, the reflex identity of multiplication).
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.
not a real number * * * * * Zero is very much a real number. In fact it is the additive identity for the set of real numbers.