Re: how to list all of the real numbers

In article <1188070175.377352.165110@xxxxxxxxxxxxxxxxxxxxxxxxxxxx>,
"Ross A. Finlayson" <raf@xxxxxxxxxxxxxxx> wrote:

On Aug 24, 6:17 pm, Virgil <vir...@xxxxxxxxxxx> wrote:
In article <1187994742.323515.123...@xxxxxxxxxxxxxxxxxxxxxxxxxxxx>,
"Ross A. Finlayson" <r...@xxxxxxxxxxxxxxx> wrote:

If both of O < c and O > c hold, cardinals are non-trichotomous or the
reals aren't a set.

If 0 < c and c < 0, cardinals are trichotomous and the reals are a set,
and anything else anyone wants to claim is also true.



No, if that is so then where the reals are a set cardinals wouldn't be
trichotomous, because the ordering properties don't hold, not directly
via violation of excluded middle, to inconsistency and Russell is the
pope.

In every order relation of my acquaintance, 0 < c AND c < 0 is a
contradiction, which implies everything and anything.

That the cardinality of the continuum would be consistently equivalent
to a wide variety of cardinals, but not any particular one, is well-
known and swept under the rug.

Are you claiming that merely knowing which aleph or beth fits the
cardinality of the continuum causes inconsistencies?
.

Relevant Pages

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