Re: how to list all of the real numbers

In article <1187994742.323515.123460@xxxxxxxxxxxxxxxxxxxxxxxxxxxx>,
"Ross A. Finlayson" <raf@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.



I don't know what you mean by "definitely distinct" and "indefinitely
distinct". But according to Euclid's 1st postulate, if any two points
*are not the same*, then a line can be drawn between them. Any
concept of "adjacent points" is provably inconsistent in geometry.


Euclid's postulates have long been accepted to define geometry.

At least Euclidean geometry, but the are others. But in all but special
or finite geometries, between any two points a line exists.

The continuum of real numbers, where any numbers between zero and one
are real numbers else they wouldn't be between zero and one, including
the nilpotent infinitesimal iota and iota-sums and iota-multiples,
such that infinitely many iota's in multiple equal exactly one, leads
to reformulation of the infinitesimal analysis as infinitesimal
analysis, where that is nonstandard and not necessarily Non-Standard.

<snip>

This run-on sentence is ill-defined and not even well thought out.
You need to break this into steps. By doing so, the errors will
become more apparent.


No, it's readable.

Word by word readable but as a whole imparsible.


Yes, much of early analysis lacked the rigor it has today. Even many
of Euler's proofs were playgrounds of inconsistencies and unwarranted
assumptions. When Weierstrass and Bolzano came upon the scene, they
added the rigorous approach to analysis so that it would be on as
firm a foundation as Geometry had always been.


I think there is more than one approach.

At least two: there is the rigorous approach and the Ross approach.

....

There are a wide variety of reasonable and useful considerations of
infinity in the numbers.

With none of which is Ross competent.


Regardless, I fail to see the point you are trying to make about this
function. The existence (or non-existence) Dirac delta's
axiomitization is completely irrelevant to the topology or cardinality
of R.

No, they're inextricably related.

Since the Dirac delta is not a real function, how is it related?

Can you please give me an example of this "equivalency function"? For
instance, which finite natural number maps to pi?

...


You would have that there would always be statements about the real
numbers that, although true, you could never prove. I, instead, would
have that there is some true set of real numbers about which all facts
are provable.

Goedel's work suggests otherwise.
.

Relevant Pages

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