Re: A dark quantity

On 02/05/2024 04:51 AM, Richard Damon wrote:

On 2/5/24 4:07 AM, WM wrote:

Le 04/02/2024 à 13:48, Richard Damon a écrit :

On 2/4/24 3:37 AM, WM wrote:

Le 03/02/2024 à 12:52, Richard Damon a écrit :
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It just jumps to infinity.

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That is true for visible unit fractions. But it means that ℵ unit
fractions of this jump cannot be distinguished.

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Nope, NUF(x) just jumps because it is ill-defined, to count from an end
that doesn't have an ed.
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Why is "More than one" impossible?

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Because 1/n - 1/(n+1) > 0.
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How does that follow?

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Don't be so stupid.

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Really? You can't actually SHOW how you get there?
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Your problem is that for you to actually SHOW how to prove your claim,
you will need to make explicit the assumption (aka axioms) that you are
using, and those appear to be so obviously flawed (at least to someone
who understands what infinity actually is) so you need to hide them.
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To you, "Darkness" is just a crutch to hide things you can not handle,
due to your use of limiting axioms. Your thought processes are just too
simple to handle the things you are looking at, so you call the ensuing
confusion and mental tension "darkness" so you don't need to look at it.
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since 1/n - 1/(n+1) > 0,
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So, for any point 1/n, there is a smaller point 1/(n+1) below it,

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For any chosen point 1/n are ℵ smaller unit fractions below it. That
means any attempt to distinguish them must fail.

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WHy?
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You don't think we can distinguish an infinite number of points?
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We have an infinite number of names to give them.
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So there is no point in the Finite Numbers for NUF(x) to be 1, so it
has to jump if we are only looking at Finite Numbers.

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This junmp cannot be further analyzed.

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Maybe, with your logic, but doesn't mean it can't happen.
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You just don't understand how logic works, and are getting "darkness"
as a result of not being able to look at thing that are clearly there.

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If you could look at the unit fractions in the jump, then there was no
jump. But you can't. Every attempt leaves ℵ unit fractions not
distingusihed. Yor claim that all could be distinguished or chosen
fails.
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Regards, WM
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Nope. You are trying to distingush something that doesn't exist, that
first unit fraction.
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Trying to do logic on things that don't exist can create all sorts of
problems.

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Like the Russell set?
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(Here this is a reference to that if you start with only the
finite numbers as the sets that don't contain themselves,
then quantify over that, then the inductive set is also
the Russell set.  Anyways ZF just defines a non-Russell inductive set,
but, while it's convenient and represents the usual notion of
the bounded fragments, isn't really logical and wouldn't
otherwise "really" exist.  This caused Frege a great amount
of righteous disconsolation, while of course Frege's models
for arithmetic and so on are just fine for finite combinatorics,
and the unbounded of that.)
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I mean, I know standard analysis, and for example why that the
definition of the members of the complete ordered field is as are
the equivalence classes of sequences that are Cauchy, in the
usual model according to descriptive set theory.
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Then, for iota-values, that look sort of this way,
it's kind of the idea that they're the divided unit.
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1
_
oo
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1, x2, x3, ..., xoo
-------------------
      oo
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0, ..., 1
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I really suggest that you study Vitali's result, why, there are
sets of reals, that are non-measurable, and why, there are
doubling-spaces, that dividing or "fractions" results the
"degenerate intervals" of a deconstructive account,
that it's exactly so the adding those back together results
a doubling-space, for the "re-Vitali-ization" of measure theory.
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I.e., MW/WM may have the attributes of a crankety troll,
there are much larger seeming that formalize iota-values
for line-reals, for re-Vitali-izing measure theory,
for quasi-invariant measure theory, about Vitali and Hausdorff
and doubling spaces, about the nature of the continuous
and the nature of the discrete and the function between them.
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Really, most people's curiousity about foundations of mathematics,
is to explain the continuous vis-a-vis the discrete.
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I mean, logic already makes the counting arguments and finite
combinatorics totally simple, they expect something more
from mathematics.
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