I think it's funny that many will readily accept some least infinite,
but not some greatest infinitesimal: the differential.
I also think it's sad.
That's OK, though, Fraenkel says we'll recover, to Cantor's bacilli: the
infinitesimals.
It's funny how differentials are defined in terms of generally
orthogonal contra-ordinates. Infinities in analysis are defined much
the same way in the asymptotic, in terms of functional analysis.
The geometric mutations in the large and small in the polydimensional in
real numbers might be approached in this manner: consider instead of
defining geometry in terms of points then lines, instead in terms of the
point, then the space. Then, where such numbers as squares and etcetera
have these perfect geometric analogs in the classically analytic, it's
actually the numbers. Meromorphologists divide by zero, in a generally
reasonable, if not generally accessible, manner.
That's from a very minimalist yet expansionist perspective, someday more
people will understand.
Goedel's theory of theories is a Goedel theory.
Regards,
Ross F.