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On Wednesday, November 21, 2018 at 9:47:38 PM UTC-8, peteolcott wrote:
On 11/21/2018 10:07 PM, Ross A. Finlayson wrote:...
On Wednesday, October 31, 2018 at 9:11:42 PM UTC-7, Mike Terry wrote:
On 01/11/2018 02:28, peteolcott wrote:
On 10/31/2018 12:45 PM, Mike Terry wrote:
On 31/10/2018 16:22, peteolcott wrote:
On 10/30/2018 8:59 PM, Ben Bacarisse wrote:
peteolcott <Here@Home> writes:
Are you claiming that the points { R(0.0)I(n) : where n = 1,2,3,4... } >> include the point R(0.00001)I(0) ?
If you say yes to the second question, then we can conclude that the
answer to my first question would be "Yes - those points extend through >> the interval for at least the finite distance of 0.00001." (Noting that >> 0.00001 is a positive (*finite*) Real number, not an *infinitesimal*
length.)
Regards,
Mike.
The start point of Q and R is one geometric point beyond 0.0
and the last point of Q is one geometric point prior to 1.0.
Copyright 2018 Pete Olcott
Zeros are infinitesimal?
One geometric point beyond zero is one infinitesimal unit of measure.
A line segment from 0.0 to 1.0 that does not include the point at 0.0 begins at one infinitesimal unit of measure beyond 0.0.
Copyright 2018 Pete OlcottBorel vs. Calude?
This seems reasonable for combinatorics, here's
a link to an article of Calude about the
"approximation of omega, the halting constant",
(often or usually "Omega" or "Chaitin's Omega")
https://www.cs.auckland.ac.nz/%7Ecristian/approxcompactIJBC.pdf
"The value of an Omega number is highly machine-dependent;
in some cases, it is possible to prove that no bit can be computed."
"Computing upper bounds is ...".
"Of course, we can compute exact 0 digits,
but as a result of balancing the lower and upper bounds."
This is the halting probability also this halting
"constant" because each machine over all its inputs
does have its result for whether it halts, in the
"probability" that any of the other events in machines
have.
I.e., that it's a "probability" not a "constant", on
an input, of as probability the space of the inputs,
which for example in constants is a constant.
(For example one half.)
This is Banach-Tarski the measure theory quasi-invariant
(you know, invariant about measure) here the area and
volumetric, the doubling space, then also to the uniform
media or here "grainy". Borel vs. Combinatorics is that
in the middle that the space has density one half, i.e.
it's "constant" in probabilities (which are between zero
and one).
Infinitesimals, those are for examples what infinitesimals
are for the complete ordered field, for example they don't
exist, besides zero, here it is Bourbaki for "zero has the
value of all the infinitesimals". Infinitesimals in standard
infinitesimals are like 1/oo and they add up to oo/oo = 1.
(I.e., they add up that way whether "from zero" or not.)
And only that.
Any "infinitesimals" has "infinity" here basically the
numbers, 1, 2, 3, out to infinity or "INFINITY".
There are that many infinitesimals or they are as small
as the infinite is large. This though is then besides
as about the value and differences from zero, that whether
or not the numbers, are as about symmetry, reversibility,
infinitesimals are arithmetic like infinities then that
whether or not the infinities exist over the infinitesimals
has that in the micro it for example is a definition in numbers
starting with one first, then dividing, as the first case for
induction, running out the case because it's accomplished by
induction, then that all the results of the complete ordered
field are in that (because of the unit segment).
So, "Borel vs. Combinatorics",
or "Borel vs. Calude",
I think they all win (even versus).
This was "Borel vs. Combinatorics, I win".