tisdag 29 mars 2022 kl. 07:35:32 UTC+2 skrev Eram semper recta:
> On Monday, 28 March 2022 at 19:57:06 UTC+3, WM wrote:
> > Eram semper recta schrieb am Montag, 28. März 2022 um 06:48:59 UTC+2:
> > > On Monday, 28 March 2022 at 00:18:54 UTC+3, WM wrote:
> >
> > > > > They are complete well-formed numbers. They do not have to be represented in any particular radix system.
> > >
> > > > In principle they are instructions what to do: divide 1 by 3, if impossible multiply 1 by 10, write the result.
> > > Not at all.
> > 1/3 in words means "one divided by three".
> > > They are *NAMES* given to completed measures.
> > After the original meaning has been forgotten, they appear as names. Look, how many Millers are living in the USA? How many of them are producing flour?
> > > "Yes, we know how the set of real numbers is defined. But you cannot define all individuals. For that sake you need a formula."
> > > If Jim Burns even had a modicum of brains, then he would have responded:
> > >
> > > "But you just said p/q ( "real number") is the process definition (formula)", which shows that you contradict yourself all the time.
> > p/q is not a formula defining an individual fraction, like 1/3, but defining the general fraction.
> Of course p/q is not a formula - p/q represents the general NAME of a number.
>
> If p/q is not a "formula" as you call it, then neither is 1/3 because p/q is how 1/3 is represented.
>
> You're silly and I am wasting my time with you.
>
> >
> > Regards, WM
nope, Bob is a name

On Tuesday, 29 March 2022 at 05:49:35 UTC-3, Fritz Feldhase wrote:
> On Monday, March 28, 2022 at 7:29:53 PM UTC+2, sergio wrote:
> > On 3/28/2022 12:03 PM, WM wrote:
> > > Jim Burns schrieb am Montag, 28. März 2022 um 00:40:14 UTC+2:
> > > >
> > > > Consider the possibility that we don't particularly want to define all individuals.
> > > >
> > > If you want to map every individual then you must define every indivdual.
> > >
> > does that apply to numbers ? or are you still Out Of Math (OOM)?
> Well, he's never managed to actually DO math, since he's still defining each and every natural number, one after the other.

And presumably starting over multiple times, since he either forgot or intentionally dropped a few numbers along the way. Can't wait to see his life's accomplishments, his magnum opus.

zelos...@gmail.com submitted this idea :
> tisdag 29 mars 2022 kl. 07:35:32 UTC+2 skrev Eram semper recta:
>> On Monday, 28 March 2022 at 19:57:06 UTC+3, WM wrote:
>>> Eram semper recta schrieb am Montag, 28. März 2022 um 06:48:59 UTC+2:
>>>> On Monday, 28 March 2022 at 00:18:54 UTC+3, WM wrote:
>>>>>> They are complete well-formed numbers. They do not have to be
>>>>>> represented in any particular radix system.
>>>>> In principle they are instructions what to do: divide 1 by 3, if
>>>>> impossible multiply 1 by 10, write the result.
>>>> Not at all. 1/3 in words means "one divided by three".
>>>> They are *NAMES* given to completed measures. After the original meaning
>>>> has been forgotten, they appear as names. Look, how many Millers are
>>>> living in the USA? How many of them are producing flour? "Yes, we know
>>>> how the set of real numbers is defined. But you cannot define all
>>>> individuals. For that sake you need a formula." If Jim Burns even had a
>>>> modicum of brains, then he would have responded:
>>>>
>>>> "But you just said p/q ( "real number") is the process definition
>>>> (formula)", which shows that you contradict yourself all the time.
>>> p/q is not a formula defining an individual fraction, like 1/3, but
>>> defining the general fraction.
>> Of course p/q is not a formula - p/q represents the general NAME of a
>> number.
>>
>> If p/q is not a "formula" as you call it, then neither is 1/3 because p/q is
>> how 1/3 is represented.
>>
>> You're silly and I am wasting my time with you.
>>
>>>
>>> Regards, WM
> nope, Bob is a name

Bob Seger feels like number, but he isn't one.

https://www.youtube.com/watch?v=q1FRvwJP1pk

Eram semper recta schrieb am Dienstag, 29. März 2022 um 08:09:23 UTC+2:

> p/q means number where p and q are symbols or place-holders for parts of the number (name).
>
> p and q are NOT variables any more than say the x in x + 3 = 5 is a "variable".

Are you serious?
x = 2, no other value possible.
p and q: every value possible.

Regards, WM

Jim Burns schrieb am Montag, 28. März 2022 um 22:07:25 UTC+2:

> Note that a finite number of words can describe infinitely-
> -many things.

But only collectively, not individually. If you describe the set you don't describe its elements, unless there is only one or none.

Regards, WM

Jim Burns schrieb am Dienstag, 29. März 2022 um 05:46:21 UTC+2:
> On 3/28/2022 1:03 PM, WM wrote:

> > If you want to map every individual
> > then you must define every indivdual.
> We describe the objects we intend to study.

You intend to study all fractions and their indices. But you cannot find the dark fractions. So you claim that they have laft the matrix.

> If your dark realm does not satisfy the description,
> we haven't forgotten it,
> it's not part of what we intend to study.

You want to forget them.

> Your argument is that
> Cantor is wrong because
> his system implies undefinable points,
> so, if his system is used,
> there will be points undefinable.

My main point is that he claims that all fractions are definable and can be enumerated.
>
> Perhaps I missed it, but
> you've never answered the question
> "and then what?"

Then the notion of countable sets is nonsense, and then also the notion of uncountable sets is nonsense.

But it is still true that there are undefinable elements in actual infinity (or not existing elements in potential infinity).

Regards, WM

On 3/29/2022 8:50 AM, WM wrote:
> Jim Burns schrieb am Montag, 28. März 2022 um 22:07:25 UTC+2:
>
>> Note that a finite number of words can describe infinitely-
>> -many things.
>
> But only collectively, not individually, If you describe the set you don't describe its elements, unless there is only one or none.

What a ambiguous, cryptic, murky, nebulous, obscure, unintelligible, bleary, blurry, dim, faint, foggy, gauzy, hazy, misty, woozy
indeterminate, indistinct, indistinguishable, uncertain, undefinable, undefined, undetermined, inexplicable, inscrutable, mysterious
baffling, bewildering, confounding, confusing, mystifying, obfuscatory, perplexing, puzzling, and unfathomable statement of non-facts.

>
> Regards, WM

On 3/29/2022 9:02 AM, WM wrote:
> Jim Burns schrieb am Dienstag, 29. März 2022 um 05:46:21 UTC+2:
>> On 3/28/2022 1:03 PM, WM wrote:
>
>>> If you want to map every individual
>>> then you must define every indivdual.
>> We describe the objects we intend to study.
>
> You intend to study all fractions and their indices. But you cannot find the dark fractions.

there are no "dark fractions", troll.

>
>> If your dark realm does not satisfy the description,
>> we haven't forgotten it,
>> it's not part of what we intend to study.
>
> You want to forget them.

they never existed.

>
>> Your argument is that
>> Cantor is wrong because
>> his system implies undefinable points,
>> so, if his system is used,
>> there will be points undefinable.
>
> My main point is that he claims that all fractions are definable and can be enumerated.

Wrong. Cantor did not use your daffynition of "definable", you are quackers.

>>
>> Perhaps I missed it, but
>> you've never answered the question
>> "and then what?"
>
> Then the notion of countable sets is nonsense, and then also the notion of uncountable sets is nonsense.

your sentence is nonsense. Is this set countable, {1,2,3} ?

>
> But it is still true that there are undefinable elements in actual infinity (or not existing elements in potential infinity).

your "definable" daffynition with its beeps, taps, flashes, honks, colors of the rainbow, is quackers. How can you be serious at all ?

>
> Regards, WM

WM <askasker48@gmail.com> wrote:
> Alan Mackenzie schrieb am Samstag, 26. März 2022 um 11:57:25 UTC+1:

>>> I said that there is no infinite decimal representation without a
>>> formula prescribing every digit. 1/4 and 1/3 are such formulas.

>> How can you be serious? You don't understand, any more than John
>> Gabriel, what it means for a mathematical entity not to exist, do you?

>> Perhaps you might like to expand on what you think you mean by the
>> non-existence of such infinite decimal representations.

> It is hard to believe that you are unsure about it.

I'm not seeking to learn from you. Rather, I'm offering to teach you,
since you appear to be ignorant. I'm not at all unsure about it.

> Simplest example: If you write 1/3, then we know that 0.333... will
> never contain any other digit that 3. If you write
> 0.3333333333333333333333333333333, giving as many digits as you like,
> we cannot be sure that you mean 1/3.

You haven't answered the question, which was: what do you mean by the
"non-existence of an infinite decimal representation without a formula
prescribing every digit"?

Just because there may not be a formula known for some decimal
representation, how does that imply non-existence?

> Regards, WM

--
Alan Mackenzie (Nuremberg, Germany).

WM <askasker48@gmail.com> wrote:
> Jim Burns schrieb am Montag, 28. März 2022 um 22:07:25 UTC+2:

>> Note that a finite number of words can describe infinitely-
>> -many things.

> But only collectively, not individually. If you describe the set you
> don't describe its elements, unless there is only one or none.

In saying "the set of even numbers", for example, you do describe its
elements individually - each one is a multiple of two.

A great deal of mathematics concerns itself with properties each member
of an infinite set has. Such sets are described by finite numbers of
words.

> Regards, WM

--
Alan Mackenzie (Nuremberg, Germany).

Alan Mackenzie schrieb am Dienstag, 29. März 2022 um 19:29:44 UTC+2:
> WM <askas...@gmail.com> wrote:

> > Simplest example: If you write 1/3, then we know that 0.333... will
> > never contain any other digit that 3. If you write
> > 0.3333333333333333333333333333333, giving as many digits as you like,
> > we cannot be sure that you mean 1/3.
> You haven't answered the question, which was: what do you mean by the
> "non-existence of an infinite decimal representation without a formula
> prescribing every digit"?

Just what I said above: An infinite sequence cannot be given. Therefore you cannot know it without a finite formula, like "divide 1 by 3", generating it.
>
> Just because there may not be a formula known for some decimal
> representation, how does that imply non-existence?

What do you understand by existence? Does something that cannot be known exist? As a dark item?

Regards, WM

Alan Mackenzie schrieb am Dienstag, 29. März 2022 um 20:04:33 UTC+2:
> WM <askas...@gmail.com> wrote:
> > Jim Burns schrieb am Montag, 28. März 2022 um 22:07:25 UTC+2:
>
> >> Note that a finite number of words can describe infinitely-
> >> -many things.
>
> > But only collectively, not individually. If you describe the set you
> > don't describe its elements, unless there is only one or none.
> In saying "the set of even numbers", for example, you do describe its
> elements individually - each one is a multiple of two.

That is not what I mean by individually. Individually describing a number allows to distinguish it from all other numbers.
>
> A great deal of mathematics concerns itself with properties each member
> of an infinite set has. Such sets are described by finite numbers of
> words.

Of course. But all numbers described individually belong to a potentially infinite set. Most numbers will never be identified = described individually.

Regards, WM

WM <askasker48@gmail.com> wrote:
> Alan Mackenzie schrieb am Dienstag, 29. März 2022 um 19:29:44 UTC+2:
>> WM <askas...@gmail.com> wrote:

>> > Simplest example: If you write 1/3, then we know that 0.333... will
>> > never contain any other digit that 3. If you write
>> > 0.3333333333333333333333333333333, giving as many digits as you like,
>> > we cannot be sure that you mean 1/3.
>> You haven't answered the question, which was: what do you mean by the
>> "non-existence of an infinite decimal representation without a formula
>> prescribing every digit"?

> Just what I said above: An infinite sequence cannot be given. Therefore
> you cannot know it without a finite formula, like "divide 1 by 3",
> generating it.

So, your notion of "existence" is more restricted than the general usage
of the word. In addition to the normal usage of the word, you need to be
able to "give" the entity.

As something to think about, consider a random digit generator generating
a decimal representation. I don't think you would deny the sequence it
produces exists. However there is no formula for it - it can't be
"given".

>> Just because there may not be a formula known for some decimal
>> representation, how does that imply non-existence?

> What do you understand by existence?

In mathematics, something exists if it can be mathematically described
and doesn't give rise to contradictions.

> Does something that cannot be known exist?

Some somethings, yes. The random decimal expansion exists.

> As a dark item?

No. I don't know what you mena by "dark item".

> Regards, WM

--
Alan Mackenzie (Nuremberg, Germany).

WM <askasker48@gmail.com> wrote:
> Alan Mackenzie schrieb am Dienstag, 29. März 2022 um 20:04:33 UTC+2:
>> WM <askas...@gmail.com> wrote:
>> > Jim Burns schrieb am Montag, 28. März 2022 um 22:07:25 UTC+2:

>> >> Note that a finite number of words can describe infinitely-
>> >> -many things.

>> > But only collectively, not individually. If you describe the set you
>> > don't describe its elements, unless there is only one or none.

>> In saying "the set of even numbers", for example, you do describe its
>> elements individually - each one is a multiple of two.

> That is not what I mean by individually. Individually describing a
> number allows to distinguish it from all other numbers.

I think this is a linguistic problem. The word you need is not
"describe" but "specify". Another linguistic problem: in English the
word "allow" takes a noun (or a gerund), not an infinitive. So you
should have written that sentence as, for example:

Individually specifying a number allows you to distinguish it from all
other numbers.

>> A great deal of mathematics concerns itself with properties each
>> member of an infinite set has. Such sets are described by finite
>> numbers of words.

> Of course. But all numbers described individually belong to a
> potentially infinite set. Most numbers will never be identified > described individually.

This is of minor importance in mathematics. We can discuss the
properties of prime numbers, for example, without specifying each prime
number individually.

> Regards, WM

--
Alan Mackenzie (Nuremberg, Germany).

On 3/29/2022 1:15 PM, WM wrote:
> Alan Mackenzie schrieb am Dienstag, 29. März 2022 um 19:29:44 UTC+2:
>> WM <askas...@gmail.com> wrote:
>
>>> Simplest example: If you write 1/3, then we know that 0.333... will
>>> never contain any other digit that 3. If you write
>>> 0.3333333333333333333333333333333, giving as many digits as you like,
>>> we cannot be sure that you mean 1/3.
>> You haven't answered the question, which was: what do you mean by the
>> "non-existence of an infinite decimal representation without a formula
>> prescribing every digit"?
>
> Just what I said above: An infinite sequence cannot be given.

that is not what you said above. Try again.

>Therefore you cannot know it without a finite formula, like "divide 1 by 3", generating it.

Baloney, go study Number Representations

https://www.understood.org/articles/en/number-representations-an-evidence-based-math-strategy

>>
>> Just because there may not be a formula known for some decimal
>> representation, how does that imply non-existence?
>
> What do you understand by existence? Does something that cannot be known exist?

Sure! lots of planets out there, lots of sand under the rocks you like to count...

> As a dark item?

follow up with Dr Shrink to remove those pesky darkies

>
> Regards, WM

On 3/29/2022 10:02 AM, WM wrote:
> Jim Burns schrieb
> am Dienstag, 29. März 2022 um 05:46:21 UTC+2:
>> On 3/28/2022 1:03 PM, WM wrote:

>>> If you want to map every individual
>>> then you must define every indivdual.
>>
>> We describe the objects we intend to study.
>
> You intend to study all fractions and their indices.
> But you cannot find the dark fractions.
> So you claim that they have laft the matrix.

I claim that
only r/c
for which collections exist with counting-orders
which begin at 1 and end at r and at c
are r/c
for which collections exist with counting-orders
which begin at 1 and end at r and at c

If you change what's in the matrix as we proceed through
the discussion, you are equivocating. A fallacy.

>> If your dark realm does not satisfy the description,
>> we haven't forgotten it,
>> it's not part of what we intend to study.
>
> You want to forget them.

Do your dark fractions have r/c
for which collections exist with counting-orders
which begin at 1 and end at r and at c ?

If they do, r/c refers to them, too.

If they don't, r/c has never referred to them.

"Forget" how?

>> Your argument is that
>> Cantor is wrong because
>> his system implies undefinable points,
>> so, if his system is used,
>> there will be points undefinable.
>
> My main point is that he claims that
> all fractions are definable and can be enumerated.

k = (r+c-1)*(r+2-2)/2 + r

And then what?

>> Perhaps I missed it, but
>> you've never answered the question
>> "and then what?"
>
> Then the notion of countable sets is nonsense,

A finite non-empty collection
cannot match element-for-element
any of its proper subsets.

Each finite non-empty collection
can match element-for-element
some collection with a counting-order which
begins at 1 and
ends somewhere.

The collection of all
collections with a counting-order which
begins at 1 and
ends somewhere
cannot match element-for-element
any collection with a counting-order which
begins at 1 and
ends somewhere.

On the other hand,
the collection of all
collections with a counting-order which
begins at 1 and
ends somewhere
can match element-for-element
a collection with a counting-order which
begins at 1 and
does not end anywhere.

We can say that more compactly as
"The set of FISONs is countably infinite"

On Sunday, March 27, 2022 at 1:59:14 PM UTC-7, Jim Burns wrote:
> On 3/27/2022 12:48 PM, David Petry wrote:
>
> > Let me remind everybody about the argument that
> > Poincare (and others) made:

> It seems to me that the correctness of
> the mimicry of the intended _something_
> is more important than being finite or infinite
> or uncountable or inaccessible.

I'm sure that's very deep, but I don't understand it.

Would you say that all constructivists and intuitionists should listen to your sage advice?

Is the following something that you would say? "I (Jim Burns) don't understand the argument that Poincare gave, but, nevertheless, it is obvious to me that his argument is problematic. He ignored things he shouldn't have ignored, and I (J.B.) have pointed out what those things are."

On Sunday, March 27, 2022 at 2:31:42 PM UTC-7, WM wrote:
> david...@gmail.com schrieb am Sonntag, 27. März 2022 um 18:48:34 UTC+2:
> > On Saturday, March 19, 2022 at 9:35:13 AM UTC-7, WM wrote:
> > > There is no permutation of the Xs in
> > >
> > > XOOO...
> > > XOOO...
> > > XOOO...
> > > XOOO...
> > > ...
> > >
> > > such that all positions are covered by Xs.
> >
> > Would you agree that there is permutation of the X's and 0's such that all the 0's end up in the first column and all the other columns are "covered" by X's?
> No, that is obviously wrong. Here are the fractions m/n written out:

The problem is that it's not so obvious you're right.

> > I don't disagree with your conclusion, but I simply don't understand the argument you use to arrive at that conclusion. Do you think you have a better argument than the one Poincare gave us?

> My argument is not better, but it shows in a soimple way that the fractions cannot be counted.

You say your argument is simple, and yet hardly anyone here understands it! In what way is Poincare's argument not sufficiently simple?

I think you have some intuition that the rest of us don't share, and that you haven't been able to clearly articulate. Could I suggest that maybe you should work on clearly articulating that intuition?

Anyway, you've made up a very interesting listing of quotes from mathematicians who speak about the lack of necessity for Cantor's theory of infinite sets (is it still available on your website?). Do you still have plans to publish that? I think it would make an interesting reference work.

On Tuesday, 29 March 2022 at 16:44:31 UTC+3, WM wrote:
> Eram semper recta schrieb am Dienstag, 29. März 2022 um 08:09:23 UTC+2:
>
> > p/q means number where p and q are symbols or place-holders for parts of the number (name).
> >
> > p and q are NOT variables any more than say the x in x + 3 = 5 is a "variable".
> Are you serious?

Of course.

> x = 2, no other value possible.

Exactly! Therefore x is a CONSTANT.

> p and q: every value possible.

No, not every value.

circumference / diameter is not possible.

>
> Regards, WM

On Tuesday, 29 March 2022 at 16:51:08 UTC+3, WM wrote:
> Jim Burns schrieb am Montag, 28. März 2022 um 22:07:25 UTC+2:
>
> > Note that a finite number of words can describe infinitely-
> > -many things.
> But only collectively, not individually. If you describe the set you don't describe its elements, unless there is only one or none.

The above statement is true. See, when you are thinking correctly, I agree with you.

>
> Regards, WM

On Tuesday, 29 March 2022 at 21:15:33 UTC+3, WM wrote:
> Alan Mackenzie schrieb am Dienstag, 29. März 2022 um 19:29:44 UTC+2:
> > WM <askas...@gmail.com> wrote:
> > > Simplest example: If you write 1/3, then we know that 0.333... will
> > > never contain any other digit that 3. If you write
> > > 0.3333333333333333333333333333333, giving as many digits as you like,
> > > we cannot be sure that you mean 1/3.
> > You haven't answered the question, which was: what do you mean by the
> > "non-existence of an infinite decimal representation without a formula
> > prescribing every digit"?
> Just what I said above: An infinite sequence cannot be given. Therefore you cannot know it without a finite formula, like "divide 1 by 3", generating it.

Ah, now you're saying "divide 1 by 3" is the formula, but 1/3 DOES NOT mean "1 divided by 3". There is no division pending. In algebra, you cannot divide p by q if p<q. It's a NON-OPERATION. p goes to top of vinculum and q goes to the bottom. In geometry, it is however possible to divide any line segment into n equal parts.

> >
> > Just because there may not be a formula known for some decimal
> > representation, how does that imply non-existence?
> What do you understand by existence?

Existence implies "well-formed concept" - this and nothing else.

> Does something that cannot be known exist?

Yes. For example the constant pi. We know and can prove that any attempted measure of a circle's circumference using its diameter as unit results in a number approximation that is constant. However, we do not know the measure of pi. Your silly idea that a formula defines pi is in contradiction to many of your nutty claims. By your reasoning, a definition for the set of natural numbers implies that it exists.

Do you see this? As for the general question, it is misguided. Your question should be:

"Can anything exist without us knowing it?"

Yes. Your ignorance is exhibit A.

> As a dark item?

Drivel.
>
> Regards, WM

tisdag 29 mars 2022 kl. 16:02:25 UTC+2 skrev WM:
> Jim Burns schrieb am Dienstag, 29. März 2022 um 05:46:21 UTC+2:
> > On 3/28/2022 1:03 PM, WM wrote:
>
> > > If you want to map every individual
> > > then you must define every indivdual.
> > We describe the objects we intend to study.
> You intend to study all fractions and their indices. But you cannot find the dark fractions. So you claim that they have laft the matrix.
> > If your dark realm does not satisfy the description,
> > we haven't forgotten it,
> > it's not part of what we intend to study.
> You want to forget them.
> > Your argument is that
> > Cantor is wrong because
> > his system implies undefinable points,
> > so, if his system is used,
> > there will be points undefinable.
> My main point is that he claims that all fractions are definable and can be enumerated.
> >
> > Perhaps I missed it, but
> > you've never answered the question
> > "and then what?"
> Then the notion of countable sets is nonsense, and then also the notion of uncountable sets is nonsense.
>
> But it is still true that there are undefinable elements in actual infinity (or not existing elements in potential infinity).
>
> Regards, WM
You have yet to show any "dark" stuff exists

On Wednesday, 30 March 2022 at 07:51:39 UTC+3, Eram semper recta wrote:
> On Tuesday, 29 March 2022 at 16:44:31 UTC+3, WM wrote:
> > Eram semper recta schrieb am Dienstag, 29. März 2022 um 08:09:23 UTC+2:
> >
> > > p/q means number where p and q are symbols or place-holders for parts of the number (name).
> > >
> > > p and q are NOT variables any more than say the x in x + 3 = 5 is a "variable".
> > Are you serious?
> Of course.
> > x = 2, no other value possible.
> Exactly! Therefore x is a CONSTANT.
> > p and q: every value possible.
> No, not every value.
>
> circumference / diameter is not possible.
>
> >
> > Regards, WM

The fact that you misread so much of what I wrote is typical of the mainstream who never pay any attention to detail.

p/q is a symbolic fraction just like dy/dx. Both are treated exactly like numbers. It is 100% correct to write dy/dx = dy/dt x dt/dx.

Pay attention to detail!

onsdag 30 mars 2022 kl. 07:03:45 UTC+2 skrev Eram semper recta:
> On Tuesday, 29 March 2022 at 21:15:33 UTC+3, WM wrote:
> > Alan Mackenzie schrieb am Dienstag, 29. März 2022 um 19:29:44 UTC+2:
> > > WM <askas...@gmail.com> wrote:
> > > > Simplest example: If you write 1/3, then we know that 0.333... will
> > > > never contain any other digit that 3. If you write
> > > > 0.3333333333333333333333333333333, giving as many digits as you like,
> > > > we cannot be sure that you mean 1/3.
> > > You haven't answered the question, which was: what do you mean by the
> > > "non-existence of an infinite decimal representation without a formula
> > > prescribing every digit"?
> > Just what I said above: An infinite sequence cannot be given. Therefore you cannot know it without a finite formula, like "divide 1 by 3", generating it.
> Ah, now you're saying "divide 1 by 3" is the formula, but 1/3 DOES NOT mean "1 divided by 3". There is no division pending. In algebra, you cannot divide p by q if p<q. It's a NON-OPERATION. p goes to top of vinculum and q goes to the bottom. In geometry, it is however possible to divide any line segment into n equal parts.
> > >
> > > Just because there may not be a formula known for some decimal
> > > representation, how does that imply non-existence?
> > What do you understand by existence?
> Existence implies "well-formed concept" - this and nothing else.

That is your idea and your idea alone. It is not what others mean because your idea of "well-defined" is asinine

> > Does something that cannot be known exist?
> Yes. For example the constant pi. We know and can prove that any attempted measure of a circle's circumference using its diameter as unit results in a number approximation that is constant. However, we do not know the measure of pi. Your silly idea that a formula defines pi is in contradiction to many of your nutty claims. By your reasoning, a definition for the set of natural numbers implies that it exists.
>
> Do you see this? As for the general question, it is misguided. Your question should be:
>
> "Can anything exist without us knowing it?"
>
> Yes. Your ignorance is exhibit A.

Your ignorance is just as great

>
> > As a dark item?
>
> Drivel.
> >
> > Regards, WM

zelos...@gmail.com schrieb am Mittwoch, 30. März 2022 um 07:05:15 UTC+2:
> tisdag 29 mars 2022 kl. 16:02:25 UTC+2 skrev WM:

> > But it is still true that there are undefinable elements in actual infinity (or not existing elements in potential infinity).
> >
> You have yet to show any "dark" stuff exists

Here is a simple proof:

The finite initial segments {1, 2, 3, ..., n} of natural numbers ℕ contain the union of all their predecessors:

{1} = {1}
{1} U {1, 2} = {1, 2}
{1} U {1, 2} U {1, 2, 3} = {1, 2, 3}
{1} U {1, 2} U {1, 2, 3} U {1, 2, 3, 4} = {1, 2, 3, 4}
{1} U {1, 2} U {1, 2, 3} U {1, 2, 3, 4} U {1, 2, 3, 4, 5} = {1, 2, 3, 4, 5}
....

That implies that the sequence of *all* finite initial segments contains the union of all finite initial segments. This sequence however does not contain an infinite finite initial segment. If ℕ is actually infinite, it must contain more than all finite initial segments in addition. What is this additional contents?

Regards, WM