Another quantum leap happens in the harmonic series........using the zero dimension........a clue in itself...........zeros in analysis.............................and the fractions..............can be added or combined.........both seem to be important...........................as in 1 can be two.............1/1.............1 + 1 = 2..............or eleven.............how can one be two and/or eleven at the same time?  Quantum superposition.................

Harmonic Series The series (1) is called the harmonic series. It can be shown to diverge using the integral test by comparison with the function . The divergence, however, is very slow. Divergence of the harmonic series was first demonstrated by Nicole d'Oresme (ca. 1323-1382), but was mislaid for several centuries (Havil 2003, p. 23; Derbyshire 2004, pp. 9-10). The result was proved again by Pietro Mengoli in 1647, by Johann Bernoulli in 1687, and by Jakob Bernoulli shortly thereafter (Derbyshire 2004, pp. 9-10). Progressions of the form (2) are also sometimes called harmonic series (Beyer 1987). Oresme's proof groups the harmonic terms by taking 2, 4, 8, 16, ... terms (after the first two) and noting that each such block has a sum larger than 1/2, (3) (4) and since an infinite sum of 1/2's diverges, so does the harmonic series. The generalization of the harmonic series