Re: An uncountable countable set

Virgil wrote:

Coming from TO it damns Ross.

Virgil, shut up.

ZFC and IST, Nelson's Internal Set theory, and Robinson's hyperreals
are quite compatible with each other, for example how ZFC is
coconsistent with IST.

ZF is inconsistent. There is no set of sets in ZF.

Robinson's hyperreals are basically what are referred to here as
Newton's notion of the reals, with fluents and fluxions, extended with
infinite values. The hyperintegers are similarly a notion of the
finite natural numbers having appended infinite, natural numbers.

Fluxions after the first unit's aren't generally used in analysis, but
they can be in chaining derivatives, composition, as Newton's are
nilpotent. The sum of any number of zeros is zero.

There are quite the few other even more alternative and nonstandard
formulations of the real numbers than the hyperreals, so constructed in
and known from the literature, re Schmieden and Laugwitz, Bishop and
Cheng, myself, etcetera.

There are as well useful compactifications or projective extensions of
the real numbers with the as you say "point at infinity."

Ross

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