For ten points, give this multiplicative identity, the first positive integer.
The sum of the reciprocals of Sylvester's Sequence converge to this number, and in ZF set theory, it is defined as the set whose only element is the empty set. This only odd number in the range of Euler's totient is the largest output possible of the Mobius function, and Egyptian fractions have this number as the numerator. (*) Zero-factorial is equal to this number, as is i to the fourth power. Events which will definitely occur have probability equal to this number, and, like zero, all powers of this number are equal to it. For ten points, give this multiplicative identity, the first positive integer.
The sum of the reciprocals of Sylvester's Sequence converge to this number, and in ZF set theory, it is defined as the set whose only element is the empty set.
{one}