On 12/16/2023 9:47 AM, WM wrote:
> Le 16/12/2023 à 13:13, FromTheRafters a écrit :
>> WM was thinking very hard :
>>> Le 15/12/2023 à 21:52, Jim Reburns a écrit :
>
>>>> Not true, impossible. All at once is an oximoronic statement.
>>>
>>> Enumerating is a stepwise process.
>>
>> No it isn't. This is just a bijective function being applied to the
>> whole set. Nothing about steps at all.
>
> This answer shows that unrealistic fools have seized power and try to
> shut down mathematics. Counting is done step by step.

You dip shit!!!!! Oh man. WM in elementary school looks at a question:

0 + 7 = ?

WM gives the teacher a fucking cassette tape with a recording of him saying:

zero, one, two, three, four, five, six, seven

WOW!!!

>>
>>> For algebraic numbers the polynomials of height n have to be searched
>>> one after the other.
>>
>> Have they found them all yet?
>
> No infinite set will ever be counted.
>
> Regards, WM
>
>

On 16.12.2023 21:51, Richard Damon wrote:

> That is one of the strange properties of unboundely small values, while
> any distance is finite, you can have an infinite number of them before
> any finite distance.

That is not a strange property but the belief of a crank.

Regards, WM

On 16.12.2023 19:03, Richard Damon wrote:
> On 12/16/23 12:53 PM, WM wrote:

>> No. ∀n ∈ ℕ: 1/n - 1/(n+1) = d_n > 0 is basic.
>>
> Which doesn't say what you want it to say,
>
> The LOGIC you apply to that statement

says that even one non-vanishing distance is > 0.

> can't handle unbounded values

shows the nonsense entertained by matheologians in brightest light.

Regards, WM

On 12/17/23 7:38 AM, WM wrote:
> On 16.12.2023 21:51, Richard Damon wrote:
>
>> That is one of the strange properties of unboundely small values,
>> while any distance is finite, you can have an infinite number of them
>> before any finite distance.
>
> That is not a strange property but the belief of a crank.
>
> Regards, WM
>

Then try to show otherwise!

Give me the finite value that has no finite value below it.

How would you even try to create such a number.

Your arguement is based on the fallacy of assuming such a number exists,
which is a fallacy.

That your brain is unable to comprehend how this might work is a problem
with your brain, not mathematics.

Your problem is just that it can't handle unbounded sets.

On 12/17/23 7:41 AM, WM wrote:
> On 16.12.2023 19:03, Richard Damon wrote:
>> On 12/16/23 12:53 PM, WM wrote:
>
>>> No. ∀n ∈ ℕ: 1/n - 1/(n+1) = d_n > 0 is basic.
>>>
>> Which doesn't say what you want it to say,
>>
>> The LOGIC you apply to that statement
>
> says that even one non-vanishing distance is > 0.

Since ALL unit fractions have non-vanishing distance and are > 0, yes,
there exsits at least one of them.

But nowhere does that say that there is a "smallest" non-vanishing
distance that no smaller exist.

>
>> can't handle unbounded values
>
> shows the nonsense entertained by matheologians in brightest light.

No, shows that YOU create nonsense to try to explain something you can
not understand due to your own limits.

This is a common technique of "primitive" man.

>
> Regards, WM
>

Le 17/12/2023 à 13:55, Richard Damon a écrit :

> That your brain is unable to comprehend how this might work is a problem
> with your brain, not mathematics.
>
You said: while any distance is finite, you can have an infinite number of
them
before any finite distance.

How do you distinguish then some of these infinitely many unit fractions
which lie before any finite distance but are not dark?

Regards, WM

On 12/17/2023 7:38 AM, WM wrote:
> On 16.12.2023 21:51, Richard Damon wrote:

>> That is one of the strange properties of
>> unboundely small values,
>> while any distance is finite,
>> you can have an infinite number of them
>> before any finite distance.
>
> That is not a strange property
> but the belief of a crank.

0 < ⅟x < n < n⁺¹

⅟x⋅x⋅⅟n < n⋅x⋅⅟n
⅟n < x

n⋅⅟n⋅⅟n⁺¹ < n⁺¹⋅⅟n⋅⅟n⁺¹
1/n⁺¹ < 1/n

0 < ⅟n⁺¹ < ⅟n < x

https://en.wikipedia.org/wiki/Programme_for_International_Student_Assessment

Le 17/12/2023 à 16:24, Jim Burns a écrit :
> On 12/17/2023 7:38 AM, WM wrote:
>> On 16.12.2023 21:51, Richard Damon wrote:
>
>>> That is one of the strange properties of
>>> unboundely small values,
>>> while any distance is finite,
>>> you can have an infinite number of them
>>> before any finite distance.
>>
>> That is not a strange property
>> but the belief of a crank.
>
Here you have found a congenial fellow. Let an infinite number of bObs
disappear and let an infinite number of finite distances disappear. But
oppose darkness vehemently.

Regards, WM

On 12/17/23 8:27 AM, WM wrote:
> Le 17/12/2023 à 13:55, Richard Damon a écrit :
>
>> That your brain is unable to comprehend how this might work is a
>> problem with your brain, not mathematics.
>>
> You said: while any distance is finite, you can have an infinite number
> of them before any finite distance.
>
> How do you distinguish then some of these infinitely many unit fractions
> which lie before any finite distance but are not dark?
>
> Regards, WM
>
>

We can give every one of them a unique name, as they are one over some
natural number, which all have names.

On 12/17/23 12:31 PM, Richard Damon wrote:
> On 12/17/23 8:27 AM, WM wrote:
>> Le 17/12/2023 à 13:55, Richard Damon a écrit :
>>
>>> That your brain is unable to comprehend how this might work is a
>>> problem with your brain, not mathematics.
>>>
>> You said: while any distance is finite, you can have an infinite
>> number of them before any finite distance.
>>
>> How do you distinguish then some of these infinitely many unit
>> fractions which lie before any finite distance but are not dark?
>>
>> Regards, WM
>>
>>
>
> We can give every one of them a unique name, as they are one over some
> natural number, which all have names.
>

In fact, I will ask why you think there is any problem giving them a name.

After all at the point 1/n the length of the flat point before it is of
lenght 1/n - 1/(n+1) = 1/(n*(n+1)), so even if all the proceeding lines
were the same length, we would have at least n+1 more gaps, and the fact
that they get smaller we get even more.

So even without actually traveling to that smaller space, we can see
that given we are at 1/n, we can get to at least 1/(2n) in the space
available, so ther is always room for more.

This demonstrates that this is an unbounded set and thus we won't see a
bound on the way.

We can always find a LOWER bound for the number of smaller unit
fractions that must exist, but never an UPPER Bound, and the fact that
the lower bound continues to increase at an increasing rate shows there
is not actual bound.

Le 17/12/2023 à 18:31, Richard Damon a écrit :
> On 12/17/23 8:27 AM, WM wrote:
>> Le 17/12/2023 à 13:55, Richard Damon a écrit :
>>
>>> That your brain is unable to comprehend how this might work is a
>>> problem with your brain, not mathematics.
>>>
>> You said: while any distance is finite, you can have an infinite number
>> of them before any finite distance.
>>
>> How do you distinguish then some of these infinitely many unit fractions
>> which lie before any finite distance but are not dark?
>>
> We can give every one of them a unique name, as they are one over some
> natural number, which all have names.

Then give one of those unit fractions which lie before any finite distance
a name.

Regards, WM

Le 17/12/2023 à 18:53, Richard Damon a écrit :
> On 12/17/23 12:31 PM, Richard Damon wrote:
>> On 12/17/23 8:27 AM, WM wrote:

>>> You said: while any distance is finite, you can have an infinite
>>> number of them before any finite distance.
>>>
>>> How do you distinguish then some of these infinitely many unit
>>> fractions which lie before any finite distance but are not dark?
>>>
>> We can give every one of them a unique name, as they are one over some
>> natural number, which all have names.
>
> In fact, I will ask why you think there is any problem giving them a name.

That's easy. Every name you give belongs to a unit fraction which dos not
lie before any finite distance.
>
> After all at the point 1/n the length of the flat point before it is of
> lenght 1/n - 1/(n+1) = 1/(n*(n+1)), so even if all the proceeding lines
> were the same length, we would have at least n+1 more gaps, and the fact
> that they get smaller we get even more.
>
> So even without actually traveling to that smaller space, we can see
> that given we are at 1/n, we can get to at least 1/(2n) in the space
> available, so there is always room for more.

All named unit fractions have finite distances from 0. I am asking for
those which "lie before any finite distance" but are not dark.

Regards, WM

On 12/17/23 2:17 PM, WM wrote:
> Le 17/12/2023 à 18:31, Richard Damon a écrit :
>> On 12/17/23 8:27 AM, WM wrote:
>>> Le 17/12/2023 à 13:55, Richard Damon a écrit :
>>>
>>>> That your brain is unable to comprehend how this might work is a
>>>> problem with your brain, not mathematics.
>>>>
>>> You said: while any distance is finite, you can have an infinite
>>> number of them before any finite distance.
>>>
>>> How do you distinguish then some of these infinitely many unit
>>> fractions which lie before any finite distance but are not dark?
>>>
>> We can give every one of them a unique name, as they are one over some
>> natural number, which all have names.
>
> Then give one of those unit fractions which lie before any finite
> distance a name.
>
> Regards, WM
>
>

Non-existant.

And WM is an idiot.

On 12/17/23 2:22 PM, WM wrote:
> Le 17/12/2023 à 18:53, Richard Damon a écrit :
>> On 12/17/23 12:31 PM, Richard Damon wrote:
>>> On 12/17/23 8:27 AM, WM wrote:
>
>>>> You said: while any distance is finite, you can have an infinite
>>>> number of them before any finite distance.
>>>>
>>>> How do you distinguish then some of these infinitely many unit
>>>> fractions which lie before any finite distance but are not dark?
>>>>
>>> We can give every one of them a unique name, as they are one over
>>> some natural number, which all have names.
>>
>> In fact, I will ask why you think there is any problem giving them a
>> name.
>
> That's easy. Every name you give belongs to a unit fraction which dos
> not lie before any finite distance.

Why does it need to lay before "ANY" finite distance, as that presumes
that there IS a "first" finite difference

>>
>> After all at the point 1/n the length of the flat point before it is
>> of lenght 1/n - 1/(n+1) = 1/(n*(n+1)), so even if all the proceeding
>> lines were the same length, we would have at least n+1 more gaps, and
>> the fact that they get smaller we get even more.
>>
>> So even without actually traveling to that smaller space, we can see
>> that given we are at 1/n, we can get to at least 1/(2n) in the space
>> available, so there is always room for more.
>
> All named unit fractions have finite distances from 0. I am asking for
> those which "lie before any finite distance" but are not dark.
>
> Regards, WM
>

Why?

That would be asking me to find your non-existant "Dark" numbers.

Your problem is you are presuming a "bound" at that end that something
needs to be before.

If there is no smallest unit fraction, then there doesn't need to be
something before that which doesn't exist.

On 12/17/23 2:17 PM, WM wrote:
> Le 17/12/2023 à 18:31, Richard Damon a écrit :
>> On 12/17/23 8:27 AM, WM wrote:
>>> Le 17/12/2023 à 13:55, Richard Damon a écrit :
>>>
>>>> That your brain is unable to comprehend how this might work is a
>>>> problem with your brain, not mathematics.
>>>>
>>> You said: while any distance is finite, you can have an infinite
>>> number of them before any finite distance.
>>>
>>> How do you distinguish then some of these infinitely many unit
>>> fractions which lie before any finite distance but are not dark?
>>>
>> We can give every one of them a unique name, as they are one over some
>> natural number, which all have names.
>
> Then give one of those unit fractions which lie before any finite
> distance a name.
>
> Regards, WM
>
>

Note, "Any" means I can choose one. and 1/4 is before 1/2 so meets the
actual meaning of your quesiton.

You mean give a unit fraction that is before EVERY unit fraction, but
that is logically impossible, how can there be a member of a set that
isn't part of the set it is supposed to be part of.

You could fix that by saying every other unit fraction, but that implies
that the set is bounded, which it isn't, so you are just showing you
don't understand your own logic.

On 12/17/2023 12:20 PM, WM wrote:
> Le 17/12/2023 à 16:24, Jim Burns a écrit :
>> On 12/17/2023 7:38 AM, WM wrote:
>>> On 16.12.2023 21:51, Richard Damon wrote:

>>>> That is one of the strange properties of
>>>> unboundely small values,
>>>> while any distance is finite,
>>>> you can have an infinite number of them
>>>> before any finite distance.
>>>
>>> That is not a strange property
>>> but the belief of a crank.
>
> Here you have found a congenial fellow.
> Let an infinite number of bObs disappear

For each ⟨i,j⟩
swap ⟨i,j⟩↔⟨kᵢⱼ,1⟩ exists.
kᵢⱼ = i+(i+j-1)(i+j-2)/2

Before ⟨i,j⟩↔⟨kᵢⱼ,1⟩
each swap keeps kᵢⱼ/1 in ⟨kᵢⱼ,1⟩

After ⟨i,j⟩↔⟨kᵢⱼ,1⟩
each swap keeps kᵢⱼ/1 in ⟨i,j⟩

After all ⟨i,j⟩↔⟨kᵢⱼ,1⟩
each ⟨i,j⟩ holds index kᵢⱼ/1
and not.holds not.index i/jᙾ¹

....because arithmetic.

> Here you have found a congenial fellow.

....meaning: one who accepts arithmetic.

I admit that I accept arithmetic.

https://en.wikipedia.org/wiki/Programme_for_International_Student_Assessment

> and let an infinite number of
> finite distances disappear.
> But oppose darkness vehemently.
>

On 12/17/2023 12:20 PM, WM wrote:
> Le 17/12/2023 à 16:24, Jim Burns a écrit :
>> On 12/17/2023 7:38 AM, WM wrote:
>>> On 16.12.2023 21:51, Richard Damon wrote:

>>>> That is one of the strange properties of
>>>> [unboundedly] small values,
>>>> while any distance is finite,
>>>> you can have an infinite number of them
>>>> before any finite distance.
>>>
>>> That is not a strange property
>>> but the belief of a crank.
>
> Here you have found a congenial fellow.
> Let an infinite number of bObs disappear
> and
> let an infinite number of finite distances
> disappear.
> But oppose darkness vehemently.

I oppose
visibleᵂᴹ‖darkᵂᴹ n‖n+1
because it's your (WM's) darkᵂᴹ
and you (WM) oppose
visibleᵂᴹ‖darkᵂᴹ n‖n+1

Opposing visibleᵂᴹ‖darkᵂᴹ n‖n+1
and not.opposing darkᵂᴹ n in ⟨0,…,n⟩
is contradictory.

Perhaps
you consider not-asserting contradictions
to be vehemence, and
you oppose vehemence.
That would explain a lot (psychologically).

Define
super.visibleᵂᴹ n to be
visibleᵂᴹ n with
each number before n visibleᵂᴹ

If n in ⟨0,…,n⟩ is darkᵂᴹ
then
in ⟨0,…,n⟩ iₓ‖iₓ+1 exists which is
last.super.visibleᵂᴹ‖first.not.super.visibleᵂᴹ

last.super.visibleᵂᴹ iₓ is visibleᵂᴹ
first.not.super.visibleᵂᴹ iₓ+1 is darkᵂᴹ

iₓ‖iₓ+1 is visibleᵂᴹ‖darkᵂᴹ

However,
that contradicts
no n‖n+1 is visibleᵂᴹ‖darkᵂᴹ

Ergo vehemence.

Le 17/12/2023 à 21:17, Richard Damon a écrit :
> On 12/17/23 2:17 PM, WM wrote:

>>> We can give every one of them a unique name, as they are one over some
>>> natural number, which all have names.
>>
>> Then give one of those unit fractions which lie before any finite
>> distance a name.

> Non-existant.
>
You said: That is one of the strange properties of unboundely small
values, while any distance is finite, you can have an infinite number of
them before any finite distance.

Now they are no longer existant?

Regards, WM

Le 17/12/2023 à 21:18, Richard Damon a écrit :
> On 12/17/23 2:22 PM, WM wrote:
>> Le 17/12/2023 à 18:53, Richard Damon a écrit :
>>> On 12/17/23 12:31 PM, Richard Damon wrote:
>>>> On 12/17/23 8:27 AM, WM wrote:
>>
>>>>> You said: while any distance is finite, you can have an infinite
>>>>> number of them before any finite distance.
>>>>>
>>>>> How do you distinguish then some of these infinitely many unit
>>>>> fractions which lie before any finite distance but are not dark?
>>>>>
>>>> We can give every one of them a unique name, as they are one over
>>>> some natural number, which all have names.
>>>
>>> In fact, I will ask why you think there is any problem giving them a
>>> name.
>>
>> That's easy. Every name you give belongs to a unit fraction which dos
>> not lie before any finite distance.
>
> Why does it need to lay before "ANY" finite distance, as that presumes
> that there IS a "first" finite difference

That is one of the strange properties of unboundely small values, while
any distance is finite, you can have an infinite number of them before any
finite distance.

>>> After all at the point 1/n the length of the flat point before it is
>>> of lenght 1/n - 1/(n+1) = 1/(n*(n+1)), so even if all the proceeding
>>> lines were the same length, we would have at least n+1 more gaps, and
>>> the fact that they get smaller we get even more.
>>>
>>> So even without actually traveling to that smaller space, we can see
>>> that given we are at 1/n, we can get to at least 1/(2n) in the space
>>> available, so there is always room for more.
>>
>> All named unit fractions have finite distances from 0. I am asking for
>> those which "lie before any finite distance" but are not dark.

>
> Why?
>
> That would be asking me to find your non-existant "Dark" numbers.

So it is. That is one of the strange properties of unboundely small
values, while any distance is finite, you can have an infinite number of
them before any finite distance. They are dark.

Regards, WM

Le 17/12/2023 à 21:21, Richard Damon a écrit :
> On 12/17/23 2:17 PM, WM wrote:

> Note, "Any" means I can choose one.

No, any means there is no other. Any includes the first distance between
two unit fractions.

> You mean give a unit fraction that is before EVERY unit fraction, but
> that is logically impossible, how can there be a member of a set that
> isn't part of the set it is supposed to be part of.

So you agree that the unit fractions and their distances are all there and
that NUF can not increase by more than 1 without being constant for a
finite period,

As it starts with 0, the first increase is by 1.

Regards, WM

Le 18/12/2023 à 02:35, Jim Burns a écrit :
> On 12/17/2023 12:20 PM, WM wrote:

> Perhaps
> you consider not-asserting contradictions
> to be vehemence, and

I consider Bob leaving the matrix as impossible.
>
> Define
> super.visibleᵂᴹ n to be
> visibleᵂᴹ n with
> each number before n visibleᵂᴹ

Each number before a visible number is visible. This is the definitions of
visible n: A FISON {1, 2, 3, ..., n} exists.

Regards, WM

On 12/18/23 6:16 AM, WM wrote:
> Le 17/12/2023 à 21:17, Richard Damon a écrit :
>> On 12/17/23 2:17 PM, WM wrote:
>
>>>> We can give every one of them a unique name, as they are one over
>>>> some natural number, which all have names.
>>>
>>> Then give one of those unit fractions which lie before any finite
>>> distance a name.
>
>> Non-existant.
>>
> You said: That is one of the strange properties of unboundely small
> values, while any distance is finite, you can have an infinite number of
> them before any finite distance.
>
> Now they are no longer existant?
>
> Regards, WM
>
>

Before any given finite point, there are infinitely many smaller points.

To try to form the set of ALL finite points is an impossible task.

It doesn't even work for finite sets:

What letter of the alphabet is earlier than all the letters of the
alphabet? (That includes itself!)

Yes, for set that are bounded, you can change it to before all other
elements, but since the Natural Numbers and Unit Fractions are
Unbounded, that alternate doesn't work.

So, your "darkness" property is based on the exisnce of things tht do
not exist.

On 12/18/23 6:19 AM, WM wrote:
> Le 17/12/2023 à 21:18, Richard Damon a écrit :
>> On 12/17/23 2:22 PM, WM wrote:
>>> Le 17/12/2023 à 18:53, Richard Damon a écrit :
>>>> On 12/17/23 12:31 PM, Richard Damon wrote:
>>>>> On 12/17/23 8:27 AM, WM wrote:
>>>
>>>>>> You said: while any distance is finite, you can have an infinite
>>>>>> number of them before any finite distance.
>>>>>>
>>>>>> How do you distinguish then some of these infinitely many unit
>>>>>> fractions which lie before any finite distance but are not dark?
>>>>>>
>>>>> We can give every one of them a unique name, as they are one over
>>>>> some natural number, which all have names.
>>>>
>>>> In fact, I will ask why you think there is any problem giving them a
>>>> name.
>>>
>>> That's easy. Every name you give belongs to a unit fraction which dos
>>> not lie before any finite distance.
>>
>> Why does it need to lay before "ANY" finite distance, as that presumes
>> that there IS a "first" finite difference
>
> That is one of the strange properties of unboundely small values, while
> any distance is finite, you can have an infinite number of them before
> any finite distance.

Right, so NUF(x) is infinite for ANY finite number, and thus for ANY
unit fraction, so it is NEVER 1 at any, so there is no smallest unit
fraction.

>
>>>> After all at the point 1/n the length of the flat point before it is
>>>> of lenght 1/n - 1/(n+1) = 1/(n*(n+1)), so even if all the proceeding
>>>> lines were the same length, we would have at least n+1 more gaps,
>>>> and the fact that they get smaller we get even more.
>>>>
>>>> So even without actually traveling to that smaller space, we can see
>>>> that given we are at 1/n, we can get to at least 1/(2n) in the space
>>>> available, so there is always room for more.
>>>
>>> All named unit fractions have finite distances from 0. I am asking
>>> for those which "lie before any finite distance" but are not dark.
>
>>
>> Why?
>>
>> That would be asking me to find your non-existant "Dark" numbers.
>
> So it is. That is one of the strange properties of unboundely small
> values, while any distance is finite, you can have an infinite number of
> them before any finite distance. They are dark.
>
> Regards, WM
>
>

They are not "Dark", they are just more of the finite unit fractions.

There is no smallest unit fraction, or even smallest definable unit
fraction, so no need to make some of them "dark", as all of them are
"definable" or "nameable" or even usable individually (even if not all
at once).

On 12/18/23 6:22 AM, WM wrote:
> Le 17/12/2023 à 21:21, Richard Damon a écrit :
>> On 12/17/23 2:17 PM, WM wrote:
>
>> Note, "Any" means I can choose one.
>
> No, any means there is no other. Any includes the first distance between
> two unit fractions.

Which means the existance of a smallest unit fraction, which means the
unit fractions are bounded on the smallest value side, which means the
Natural Numbers are bounded on the high side, which is a FALSE
statement, so can't apply.

>
>> You mean give a unit fraction that is before EVERY unit fraction, but
>> that is logically impossible, how can there be a member of a set that
>> isn't part of the set it is supposed to be part of.
>
> So you agree that the unit fractions and their distances are all there
> and that NUF can not increase by more than 1 without being constant for
> a finite period,
>
> As it starts with 0, the first increase is by 1.
>
> Regards, WM
>
>

Nope, NUF goes from 0 to 1 in the range of infintesimal numbers which
are NOT "Unit Fractions" so outside the actual domain of the numbers
described

You need to clarify what number system you are working in. If we are
talking about the Natural Number (which can be built on some simple set
theory) then these infintesimals, (or the transfinite numbers) don't exist.

If you want to include them, then you need to define WHICH set of
transfinites you are workig with, and use the mathematics that the
chosen set obeys. For instance, your claim of counting one at a time
doesn't apply (it doesn't even apply to the Natural Numbers).

Thus, your whole arguement seems to break down to a category error of
trying to deal with numbers that don't exist in the number system your
set theory is defining.

Le 18/12/2023 à 15:21, Richard Damon a écrit :

> Before any given finite point, there are infinitely many smaller points.

That means these are points, ℵ₀ unit fractions, which cannot be
distinguished from each other by defining a point between them.
>
> So, your "darkness" property is based on the exisnce of things that do
> not exist.

The darkness property is based upon the non-existence of separators
between the ℵ₀ unit fractions.

Regards, WM