[continued from previous message]

the Cantorians have that almost all are irrational,
then there's also a model where half are rational.

The Infinitarcalcul and the Long Line of du Bois-Reymond,
are considered pretty great about the 1800's, then there's
that MacLaurin of the late 1700's is really pretty great.

In platonism one _finds_ not _defines_.

Then, one can define the standard reals or field reals
given a particular conflation of ordinary arithmetic and
algebra, and use ordinary set theory to establish cardinal
inequality of infinite cardinals, with only Cartesian functions,
yeah it's quite simple.

Borel vis-a-vis Combinatorics, anyone? That's about that
there are at least three Cantor spaces: sparse, square, and signal.

Thusly it's disambiguated among models of continuous domains,
with their extent, density, completeness, and measure,
line-reals, field-reals, and signal-reals, and each making
for what makes for least-upper-bound and measure 1.0,
the IVT and the FTC's, quite so simply.


The .999... vis-a-vis 1.0 is an accessible branching of
the course-of-passage of a continuous quantity like time,
and clock arithmetic, and the unbounded in making fractions
then decimal representation about dual representation,
them meeting in the modular, one of these ponts or bridges
of the analytical bridges to surpass the inductive impasse
that refuse their own result.

No difference? Differance.

--- SoupGate-DOS v1.05
 * Origin: you cannot sedate... all the things you hate (1:229/2)