0 and 1 are not prime numbers but apparently they have their own special names what are they?

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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).
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