Re: How many different unit fractions are lessorequal than all unit fractions? (infinitary)

On 10/19/2024 03:30 PM, Ross Finlayson wrote:

On 10/19/2024 03:16 PM, Ross Finlayson wrote:

On 10/19/2024 02:57 PM, FromTheRafters wrote:

WM used his keyboard to write :

On 19.10.2024 20:22, Alan Mackenzie wrote:

WM <wolfgang.mueckenheim@tha.de> wrote:

>

An infinite set is one which has a proper subset which can be
put into 1-1 correspondence with the original set.  That is the
definition.

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According to Dedekind every set {1, 2, 3, ..., n} is in correspondence
with the set {2, 4, 6, ..., 2n} which covers twice the interval,
containing numbers not in the original set. This does not change when
the whole set ℕ is multiplied by 2. The result covers twice the
interval, containing numbers not in the original set ℕ.

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Intervals now? Discrete ones or real ones?

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The usual term for how an interval could be anything
less is called a "de-generate" interval, that it's not
generated by infinite divisibility a generate (n.),
sort of like "quasi-invariant", "pseudo-differential",
"degenerate interval", this kind of thing.
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I.e. that's the term for that concept the idea.
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If you have it, ....
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Sort of like, "calling something that's
unknown or undefined or strange 'weird'
is, in a sense of language, like 'degenerate'".
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That is to say it's stupid.
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So, the "degenerate interval" of mathematics
isn't necessarily good nor bad, in the usual
vulgar sense that it's bad, and is intended
to reflect that when the prototype event of
the term-wise addition and the _carry_ bit,
_carries_, in the sense of an un-bounded
sequence that the sequence "rolling over"
is called "carry", when the otherwise
un-limited operation, here halving as
a placeholder for "the property of being
divisible as dividing into two parts",
then the notion of "degenerate" interval
is what according to deductive inference
must have been arrived at.
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I.e. it so follows.
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Then, not so much speaking to the massively
degenerate the dumbing-down of the feuilletons
and concepts of popular culture like the queering
of differences or such crap, there are already
words for these concepts that are under-defined
in usually the standard, because mathematics
is thoroughly explored both standard and non-standard.
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Stupid-heads
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It's kind of like "continuous point-sets",
these "degenerate intervals", a lot like in fact,
being that "according to induction: lines can
not be made of points nor points made of lines".
Yet, they are, ..., made of each other.
Atomism is the usual classical superclassical theory,
if there's a theory that's sort of anything other
than amorphism, or after animatism and animism.
Then, the "infinitely-divisible" and the "infinite",
sort of have to get along, in a sort of heno-theory
where points or lines are elementary, for example a
theory where points and lines are each elementary.
The idea of "henotheory", I was reading a book called
something like "Structural Depths in Indian Thought",
where there's discussed henotheology where the
primary or central elements sort of rotate, where for
examples of these theories all somehow share the
same theory.
set theory
part theory
set theory
class theory
set theory
ordering theory
This is where set theory is "a theory with one relation: elt",
and that class theory and part theory and ordering theory
are simply other sorts usual theories with one relation,
then with regards to the usual transitivity of it with regards
to usually enough classes.
number theory
geometry
These are the usual big theories, mathematical.
function theory
topology
These are the usual glue theories, mathematical.
arithmetic
algebra
analysis
These are reasonably enough applied.
So, the heno-theory, or heno-mathematics,
helps reflect that it's a universe of mathematical objects,
and the same structure, is each the theories.
It must be: there's nothing else for it to be,
and nothing else to be it.
So, is there a mathematics at all?
And not just a mere science of it? A mouthing?
Isn't mathematics true?