“The surprising fact is the amount of infinitesimal and
infinitely large numbers which such a positional numeral system can represent.:”
On Sergeyev’s Grossone: How to compute effectively with
Infinitesimal and Infinitey large Numbers.
The ability for the gross powers to be recursively defined
in terms of prior gross one numbers allows for this large but not cardinally inaccessible
size of representation. How far it can
be empirically utilized where other larger infinites are at play remains to be
seen and how to populate a set of grosspowers and grossdigits via path analysis for instance (where the two
directional arrows represent undetermined divisions within the a posteriori
instantiated empirics) needs to be materialized.
Consider any given set of distribution points as having an
association with some number with the Natural Number set N as a grossnumber
This particular division would be suitable wherein the
distributions shows two lineages and where the the track^node^mass^baseline organizational
difference between the two is simply a shift relative to the baseline.
One way to find this shift as the data for both lineages are
populated into the outline and framework is by the constraint that N also
presents grossone squared at the same time. One is thus left with the more less
difficult task of describing the track^node^mass^baseline coefficients as the
cross (vicariant) diagonal through ordered pairs of actual distribution
To do this the lineages without shift (relative to sister) are demonstrated in the upper half of the x illustrated diagonal. How high grossone minus one goes before it is subtracted (in data actually inputted) may depend on the masses actually present. The lower end of the x may be those areas wherein the node antinodes are clearly directed to the baseline.