Re: Real Number --- Merely numbers whose digits can be infinitely long

On 05/02/2024 08:23 PM, Ross Finlayson wrote:

On 05/02/2024 07:58 PM, Keith Thompson wrote:

wij <wyniijj5@gmail.com> writes:

On Thu, 2024-05-02 at 18:02 -0700, Keith Thompson wrote:

wij <wyniijj5@gmail.com> writes:
[snip]

Nothing is different from the math. you understand (except several
corner cases
which you will never need to worry about).

>
So there's nothing novel in your notation, and I needn't waste any more
time asking questions about it that you're unwilling and/or unable to
answer.
>
Is that a fair summary?
>
(I'll ignore the "corner cases" you allude to.)

>
No, nothing novel there changed the usual usage of 'fixed point number'.

>
I have no idea whether that was an attempt to answer my question.  If it
was such an attempt, it failed.
>
The term "fixed point number" is quite distinct from both "rational
number" and "real number".  I don't know which you're trying to define.
Fixed point numbers, in my experience, are a computer representation,
not a mathematical abstraction.  But your subject header talks about
real numbers.
>
Feel free to attempt to clarify if you're so inclined.  Or don't.
>

>
https://en.wikipedia.org/wiki/Numerical_tower
>
The line-reals are naturals n/d, 0 <= n <= d, d goes to infinity,
it has extent, density, completeness, measure [0,1], measure 1.0.
>
The field-reals are the equivalence classes of sequences that
are Cauchy, and that's the standard definition of the complete
ordered field, including when Dedekind cuts (of rationals) won't do.
>
The signal-reals are as that the rationals are huge,
when doubling them results a continuous domain.
>
>
It gets involved doubling and halving measures and spaces
and real non-standard analytical character and new results
in numerical series and methods in the Cantor space or
"2 ^ omega" of each of these different models of real numbers.
Then standard ordinary set theory is left consistent by just
making another result in set theory in function theory.
>
That _always_ exists.
>
>

The infinite expressions and completions and closures
and the inductive and deductive and non-inductive and
anti-inductive in the infinite expressions, for the
infinite limits and continuum limits, of course has
that mathematics has great examples of the results of
deductive inference as the abductive over inductive inference,
as what arrives at the continuum has at least these three
different and distinct definitions, that arrive together
as inter-compatible if not inter-changeable, that is
quite better than even the standard way today, as it
really shows that mathematics has these various laws
of large numbers for their various regularities for
their various rulialities for their various common
consequences of each their fixed completions,
why it is so that line-reals, field-reals, signal-reals
are more replete the complete linear continuum, and
as about the integer continuum, the linear continuum,
and the long-line continuum, in all the objects of
the real analysis.
So, a premier mathematician of this age, knows these things.