On Friday, 19 August 2022 at 20:31:29 UTC+2, dklei...@gmail.com wrote:
> On Thursday, August 18, 2022 at 11:02:48 PM UTC-7, Skep Dick wrote:
> > On Friday, 19 August 2022 at 06:17:23 UTC+2, dklei...@gmail.com wrote:
> > > Still meaningless. There is no "last" digit.
> > There is a last digit to ANYONE who can look past completed infinities!
> >
> > That is you (according to you).
> >
> You don't like this but I say whether infinite objects are real or not is a
> matter for philosophers - not you or me.
No. This is not a philosophical issue. This is a Kolmogorov complexity issue.

We know how to create finite representations/encodings of infinite objects.
Writing a generator for ALL the Natural numbers in any programming language is trivial.

What is not trivial is getting the generator to "complete" the process of generating ALL Natural numbers.

> When I contemplate an infinite I see no last member. There are always
> more members. There are just as many more members as there are
> original members.
Then what did you mean when you said "completed" process/infinity?

Because when I use that word I use its standard English meaning.

Synonymous with entire; finished; having come to an end; entirely done.

And I would never use that word to describe the natural number generator.
It's never done, It's never finished, complete; or come to an end.

On Friday, 19 August 2022 at 20:48:02 UTC+2, dklei...@gmail.com wrote:
> On Friday, August 19, 2022 at 4:46:10 AM UTC-7, Skep Dick wrote:
> >
> > Show me the number 0! Not the symbol representing it.
> >
> Most mathematicians would, given this context, take 0 to mean
> the empty set. Then the successor of any number N would be N
> plus the set whose only member is N.
That's not really an answer. Show me the empty set. Not the syhmbols representing it - the empty set itself.

This is a fundamental problem with representation systems. When you represent nothing does it become something or is it still nothing?

Is nothing something; or is it just NO(thing)?

On Friday, 19 August 2022 at 19:41:08 UTC+2, richar...@gmail.com wrote:
> On 8/19/22 12:44 PM, Skep Dick wrote:
> > On Friday, 19 August 2022 at 17:55:29 UTC+2, richar...@gmail.com wrote:
> >> What don't I understand?
> >>
> >> The Real Number System HAS a Definition, and rules (like its Algebra)
> >>
> >> If you claim to be working in the Real Number system, you need to follow
> >> its rules. (This includes that infinity is NOT a Real Number).
> >>
> >> If you want to Extend the Real Number System, fine, Just say you are
> >> working in an Extended Real Number System. But when you do, remember
> >> that you have to figure out what Algebra works in that system. You can't
> >> just assume the Alrgebra of the Real Number System works.
> >>
> >> This is why clarity is important.
> >>
> >> I don't have a clear enough understanding of your extentions (not sure
> >> if you do either, but that is less important), but it IS an extension,
> >> and so needs to be treated as one.
> >>
> >> You might want to study some of the Extended Real Number Systems and the
> >> Trans-Finite number systems to see if anyone else has worked in the same
> >> direction you are thinking.
> >
> > Jesus fucking christ. This moron will drive himself off a cliff just because the rules said so.
> >
> > No! You absolutely DON'T have to follow any rules! The intensional properties of your system don't matter as long as your extensional properties are satisfied.
> >
> > This is how interfaces work! Adhere to the contract externally - do whatever the hell you want internally. It's just irrelevant implementation detail!
> But if your system is open, so others can work in it, you can't do that.
Fucking idiot. That's not what an open system IS.

Humans INTERACT WITH the open system.
Humans don't WORK IN the open systems.

https://en.wikipedia.org/wiki/Open_system_(systems_theory)

> I will note, that the whole discission with you has just proved your a
> Hypocrite, as you keep on trying to get people to accept YOUR
> definitions, but you refuse to even try to adapt to their.
Fucking idiot. This is not about definitions.

Some people may define this as red: 🔴
Some people may define this as green: 🔴
Some people may define this as blue: 🔴

All of the above bindings are valid.

The problem comes when we start de-referencing bindings!

What does de-referencing 0 mean? What object is it?
What does de-referencing ∞ mean? What object is it?

> Without Rules, there is no logic. (At its core, logic is applying Rules
> to knowledge to get more Knowledge).
Q.E.D you don't actually understand the difference between "rules of logic"; and "logic of rules".

Proof nets.

> For example, you were asking for a "Well-Defined Definition", but that
> ment you were IMPOSING A RULE about how to define things.
Nonsense. I am using the standard, socially accepted concept "well-defined" objects.

Recursive self-definition. A.k.a name-binding!

Which I cannot demonstrate to you via this medium because it doesn't allow for different font/text colors.

But I shall attempt to describe it anyway...

The color of this sentence is red. <--- Imagine that the font-color is the conventional meaning of red.
The color of this sentence is red. <--- Imagine that the font-color is the conventional meaning of green.
The color of this sentence is red. <--- Imagine that the font-color is the conventional meaning of blue.

Or demonstrated in a much richer computational model!
https://docs.google.com/document/d/1z9MRa2EB7gJwOPWSZrhIdFFsmtzr7RDDOxIgyRhln1M/edit?usp=sharing

Use it; or don't use it.

> The problem with you method is that you have no idea if what you are
> doing makes any sense, as if you don't know and follow the constraints
> in the methods you are using, you have no promise they will give
> reasonable results.
You can't even well-define "reasonable" you moron :)

> It seems you have already jumped of the cliff.
You have that backwards. Your brain is already splatteerd on the rocks below.

You've represented (and you are actively referencing/dereferencing) a NULL-object in your system.

> Note, The Rules don't tell you what you HAVE to do, they tell you what
> you need to do to get the results promised by the system.
You don't even know what PROMISES are. You fucking idiot.

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

> You are ALWAYS free to alter the system to look at something new, but
> HONESTY requires that you make it clear how you are devating, and that
> you take into account you deviations (a good reason to make them clear).
That sure seems like a lame attempt to bind your definition to the symbol "HONESTY".

> I am not saying you HAVE to use the Real Numbers, but if you claim to be
> doing so, you need to follow the Rules of them or you are just a LIAR.
You can't even solve the LIAR's paradox you fucking cunt!

You can't tell the difference between truth and lies!
Neither can Mathematics. They are just inverses under negation!

Modality.

> You can use what every methods you want, as long as you are honest about
> them and what you are doing, and give others the right to do the same.
I am honest about being dishonest, you shit-for-brains.

I am consistently inconsistent!
I am logical about being illogical.

Undecidability! Do you actually grok it?

The moment you try to bind me to your symbols your system blows up.

On 8/20/22 3:31 AM, Skep Dick wrote:
> On Friday, 19 August 2022 at 20:48:02 UTC+2, dklei...@gmail.com wrote:
>> On Friday, August 19, 2022 at 4:46:10 AM UTC-7, Skep Dick wrote:
>>>
>>> Show me the number 0! Not the symbol representing it.
>>>
>> Most mathematicians would, given this context, take 0 to mean
>> the empty set. Then the successor of any number N would be N
>> plus the set whose only member is N.
> That's not really an answer. Show me the empty set. Not the syhmbols representing it - the empty set itself.
>
> This is a fundamental problem with representation systems. When you represent nothing does it become something or is it still nothing?
>
> Is nothing something; or is it just NO(thing)?
>

Its a fundamental problem with a "Show me ..." question. YOu can only
"Show" something concrete, which means that for things that are somewhat
abstract "showing" is hard (to impossible) to do.

For something as abstract as a "Number", which only exists as something
to our senses in a representation, asking to show the thing and not a
representation just shows you don't understand what you are asking for.

On Saturday, 20 August 2022 at 12:37:05 UTC+2, richar...@gmail.com wrote:
> Its a fundamental problem with a "Show me ..." question. YOu can only
> "Show" something concrete
So conretize it!

Reify it! https://en.wikipedia.org/wiki/Reification_(computer_science)

Realize it! https://en.wikipedia.org/wiki/Realizability

Construct it! https://en.wikipedia.org/wiki/Constructivism_(philosophy_of_mathematics)

>which means that for things that are somewhat abstract "showing" is hard (to impossible) to do.
> For something as abstract as a "Number", which only exists as something
> to our senses in a representation, asking to show the thing and not a
> representation just shows you don't understand what you are asking for.
Hahahahahahahaha. Fucking moron.

Numbers used to represent quantities! There was nothing abstract about 1-indexed number-systems.

2 eggs <->🥚🥚
1 egg <-🥚

Add an egg.

It's only when zero-indexing happened is when things became abstract.

0 eggs <-> NO(🥚)

It's a counter-factual.

In plain English. 0 may be a number, but it's NOT a quantity! It's a countrer-factual to a quantity.

It's the Maybe monad. https://en.wikipedia.org/wiki/Monad_(functional_programming)#An_example:_Maybe

2 eggs <-> Just(2) <-> 🥚🥚
1 egg <-> Just(1) <-> 🥚
0 eggs <-> Nothing <-> NO(🥚)

Hindu-Arabic numberal systems went and forgot that fact, so you need to remind yourself the difference between Unit types and Empty types.

On Saturday, 20 August 2022 at 12:37:05 UTC+2, richar...@gmail.com wrote:
> Its a fundamental problem with a "Show me ..." question. YOu can only
> "Show" something concrete, which means that for things that are somewhat
> abstract "showing" is hard (to impossible) to do.
>
> For something as abstract as a "Number", which only exists as something
> to our senses in a representation, asking to show the thing and not a
> representation just shows you don't understand what you are asking for.
But most of all people in their 20s/30s (lacking all of your "knowledge" and "experience") are doing it.

https://github.com/MrChico/agda-stdlib/blob/clean/src/Data/Real.agda

But you are full of excuses!

Andy Walker <anw@cuboid.co.uk> writes:

> On 19/08/2022 14:57, Ben Bacarisse wrote:
>>>> [...] I'm not sure you gave enough
>>>> information for anyone who does /not/ know the rules to work it out.
>>> I didn't. But you introduced Hackenbush!
>> Only because that's the interpretation I needed to square what you
>> wrote. If they are a not Hackenbush numbers, then why do you say that
>> R(L) > 0? The problem, for the reader, is why "Walker" numbers have
>> RL(LR) = 1/3 but R(L) > 0.
>
> One interpretation of strings of R's and L's is as Hackenbush
> numbers; there are others. But 0 is represented by the empty string,
> so [in the scenario I posed] no other string is 0. In particular, it
> has the sign given by its first letter; in "R(L)", you start by going
> right and can never get back to the origin.

Yes, saying that no two distinct strings denote equal values removes any
ambiguity.

>> Given the name you used ("balanced binary"), the most natural
>> interpretation is of a binary representation who infinite strings are
>> the limits of infinite digit sums which works for RL(LR) but not,
>> apparently, for R(L).
>
> I don't think "balanced binary" implies anything about limits,
> an invention of real analysis. We're just playing games with strings.
> You can interpret that either as having fun, or as a genuine game [eg
> a simplified version of Hackenbush].

Had you presented the ordering rules for strings, I'd agree. But the
name will suggest (to may readers) an encoding based on powers of two.
And you even gave examples of doing that. Many people will know how to
arrive at a value for RL(LR) using limits and they will get a result
that you confirm: 1/3. How else should any reader confirm that RL(LR) =
1/3?

>> And if they /are/ Hackenbush numbers, then saying that RL(LR) = 1/3 is
>> really throwing a spanner in the works (for the learner), because (but
>> here I am out of my confort zone) RL(LR) might be "identified" with 1/3
>> because there is no closer Hackenbush number to 1/3.
>
> I don't expect learners to glean "everything" about surreals
> from a page or so of text; but they've been pointed at Conway's and
> Knuth's books.

The trouble, I think, is that there was nothing to link the post to this
avenue of further study. That's why a keyword or two might have helped.

>>> [I'm not proposing to write a textbook here; anyone with a
>>> mathematical background and who is not already familiar with the
>>> surreals can look it up. I just wanted to give some pointers.]
>> Then I think you need to give a keyword to help people look it up. Did
>> you try searching for "balanced binary"?
>
> Ah. No, sorry. I assumed, obviously incorrectly, that it was
> a sufficiently-well understood concept, at least in CS.

I'm not sure how widely known it is, but can't see an obvious place for
it to come up in a typical CS course (I don't think it did where I
taught). Mind you, I don't think the comp.theory readership is dense in
CS-graduates.

> It's discussed
> in Knuth's "The Art of Computer Programming" somewhere [but I don't
> have that on my shelves so can't give an actual reference].

Hmm... "Balanced binary" is in TAOCP's index, but it's pretty much what
I thought some readers might confuse your numbers with (i.e. not
Hackenbush numbers). That's why some other keywords would probably have
helped.

Then again, the sad fact is that it's possible that no one else did more
than glance at your post anyway, despite it being one of the more
interesting ones to pop up here in the PO/SD noise.

--
Ben.

On 8/20/22 7:01 AM, Skep Dick wrote:
> On Saturday, 20 August 2022 at 12:37:05 UTC+2, richar...@gmail.com wrote:
>> Its a fundamental problem with a "Show me ..." question. YOu can only
>> "Show" something concrete
> So conretize it!
>
> Reify it! https://en.wikipedia.org/wiki/Reification_(computer_science)
>
> Realize it! https://en.wikipedia.org/wiki/Realizability
>
> Construct it! https://en.wikipedia.org/wiki/Constructivism_(philosophy_of_mathematics)

Which are just ways to create a representation of it.

You just broke your own rules, maybe because you forgot what you first
asked.

Your logic seems to be inconsistent.

>
>> which means that for things that are somewhat abstract "showing" is hard (to impossible) to do.
>> For something as abstract as a "Number", which only exists as something
>> to our senses in a representation, asking to show the thing and not a
>> representation just shows you don't understand what you are asking for.
> Hahahahahahahaha. Fucking moron.
>
> Numbers used to represent quantities! There was nothing abstract about 1-indexed number-systems.
>
> 2 eggs <->🥚🥚
> 1 egg <-🥚
>
> Add an egg.

The show me "Two" without the "Egg"

The "Twoness" is an abstract quality.

>
> It's only when zero-indexing happened is when things became abstract.
>
> 0 eggs <-> NO(🥚)
>
> It's a counter-factual.
>
> In plain English. 0 may be a number, but it's NOT a quantity! It's a countrer-factual to a quantity.
>
> It's the Maybe monad. https://en.wikipedia.org/wiki/Monad_(functional_programming)#An_example:_Maybe
>
> 2 eggs <-> Just(2) <-> 🥚🥚
> 1 egg <-> Just(1) <-> 🥚
> 0 eggs <-> Nothing <-> NO(🥚)
>
> Hindu-Arabic numberal systems went and forgot that fact, so you need to remind yourself the difference between Unit types and Empty types.
>

So it depends on which system you are working in, and how you want to
define a number.

Natural Numbers have a very direct relation to counting things.

Integers add some abstractions to allow for 0 or negative quantities,
but are still basically counts but with an abstraction.

Rationals extend this by allowing us to divide into equal parts, at this
point simple physical models can still demonstrate the concepts. We can
imagine counting something like a third, by taking a whole and
partitioning it, so we are still counting but in another direction.

We can then move to Reals, which move from what can be "counted" to what
is Measured. We move from "How Many" to "How Much"

On 8/20/22 4:06 AM, Skep Dick wrote:
> On Friday, 19 August 2022 at 19:41:08 UTC+2, richar...@gmail.com wrote:
>> On 8/19/22 12:44 PM, Skep Dick wrote:
>>> On Friday, 19 August 2022 at 17:55:29 UTC+2, richar...@gmail.com wrote:
>>>> What don't I understand?
>>>>
>>>> The Real Number System HAS a Definition, and rules (like its Algebra)
>>>>
>>>> If you claim to be working in the Real Number system, you need to follow
>>>> its rules. (This includes that infinity is NOT a Real Number).
>>>>
>>>> If you want to Extend the Real Number System, fine, Just say you are
>>>> working in an Extended Real Number System. But when you do, remember
>>>> that you have to figure out what Algebra works in that system. You can't
>>>> just assume the Alrgebra of the Real Number System works.
>>>>
>>>> This is why clarity is important.
>>>>
>>>> I don't have a clear enough understanding of your extentions (not sure
>>>> if you do either, but that is less important), but it IS an extension,
>>>> and so needs to be treated as one.
>>>>
>>>> You might want to study some of the Extended Real Number Systems and the
>>>> Trans-Finite number systems to see if anyone else has worked in the same
>>>> direction you are thinking.
>>>
>>> Jesus fucking christ. This moron will drive himself off a cliff just because the rules said so.
>>>
>>> No! You absolutely DON'T have to follow any rules! The intensional properties of your system don't matter as long as your extensional properties are satisfied.
>>>
>>> This is how interfaces work! Adhere to the contract externally - do whatever the hell you want internally. It's just irrelevant implementation detail!
>> But if your system is open, so others can work in it, you can't do that.
> Fucking idiot. That's not what an open system IS.
>
> Humans INTERACT WITH the open system.
> Humans don't WORK IN the open systems.
>
> https://en.wikipedia.org/wiki/Open_system_(systems_theory)

But I am using it differently.

An open system is a system that is open for others to use, change, to
WORK IN.

Linux is an Open System vs Windows is a Closed System, as we just get to
see the "outside" of the system.

Note, in my model we WORK IN a system because we adopt its rules are are
partcipating in the behavior of the system. It allows us to actually
understand and see the abstractions in it.

Maybe your refusal to put yourself into the systems is the reason you
can't understand the abstractions of the system.

This is just one of the lies you admit you do.

>
>> I will note, that the whole discission with you has just proved your a
>> Hypocrite, as you keep on trying to get people to accept YOUR
>> definitions, but you refuse to even try to adapt to their.
> Fucking idiot. This is not about definitions.
>
> Some people may define this as red: 🔴
> Some people may define this as green: 🔴
> Some people may define this as blue: 🔴

And only the ones that define it according to the established definition
are aligned with the established system, and thus "right" in that system.

This is another of your lies that you admit you do.

>
> All of the above bindings are valid.

Depends on what you want to call valid.

To you, it seems irrelevent.

>
> The problem comes when we start de-referencing bindings!
>
> What does de-referencing 0 mean? What object is it?
> What does de-referencing ∞ mean? What object is it?

But we aren't computers so we don't actually need to "de-reference" a
binding.

>
>> Without Rules, there is no logic. (At its core, logic is applying Rules
>> to knowledge to get more Knowledge).
> Q.E.D you don't actually understand the difference between "rules of logic"; and "logic of rules".

No, I think you do understand it.

>
> Proof nets.
>
>> For example, you were asking for a "Well-Defined Definition", but that
>> ment you were IMPOSING A RULE about how to define things.
> Nonsense. I am using the standard, socially accepted concept "well-defined" objects.
>
> Recursive self-definition. A.k.a name-binding!
>
> Which I cannot demonstrate to you via this medium because it doesn't allow for different font/text colors.
>
> But I shall attempt to describe it anyway...
>
> The color of this sentence is red. <--- Imagine that the font-color is the conventional meaning of red.
> The color of this sentence is red. <--- Imagine that the font-color is the conventional meaning of green.
> The color of this sentence is red. <--- Imagine that the font-color is the conventional meaning of blue.

And, unless you have indicated you aren't in the standard meaning of the
color words, only the first sentence is "correct"

Yes, if you escape out of conventional meaning, you can talk about being
more abstract in your binding of meaning, but you need to be careful, or
you lose all sense of meaning.

>
> Or demonstrated in a much richer computational model!
> https://docs.google.com/document/d/1z9MRa2EB7gJwOPWSZrhIdFFsmtzr7RDDOxIgyRhln1M/edit?usp=sharing
>
> Use it; or don't use it.

And if you throw away all conventions, you have no base to start anything.

>
>> The problem with you method is that you have no idea if what you are
>> doing makes any sense, as if you don't know and follow the constraints
>> in the methods you are using, you have no promise they will give
>> reasonable results.
> You can't even well-define "reasonable" you moron :)

I don't need to, as it IS defined. Maybe not in your broken system, but
it is in the one that you actually are living in, even if you reject it.

From the dictionary:
1 a : being in accordance with reason
a reasonable theory
b : not extreme or excessive
reasonable requests
c : MODERATE, FAIR
a reasonable chance
a reasonable price
d : INEXPENSIVE
2 a : having the faculty of reason
b : possessing sound judgment
a reasonable man

1a with perhaps a bit of 1b seems to fit.

If you want more, then you run into the problem that you definition of
"well-defined" isn't actually able to be "well-defined" because ALL
definitions, when you expand them eventually become cirucular are refer
to words that are only later defined. That is why we need to understand
our First Principles, which form our base.

>
>> It seems you have already jumped of the cliff.
> You have that backwards. Your brain is already splatteerd on the rocks below.
>
> You've represented (and you are actively referencing/dereferencing) a NULL-object in your system.

What NULL-object, I don't directly work with object pointers, as that
isn't my model of logic.

>
>> Note, The Rules don't tell you what you HAVE to do, they tell you what
>> you need to do to get the results promised by the system.
> You don't even know what PROMISES are. You fucking idiot.
>
> https://en.wikipedia.org/wiki/Futures_and_promises

Whose says that I am using it in that meaning?

Its isn't even applicable, since I was talkinga about systems of LOGIC
and that is about program execution. Thus, not applicable.

YOU seem to be violating your own precepts. Your system is inconsistent.

FAIL.

>
>> You are ALWAYS free to alter the system to look at something new, but
>> HONESTY requires that you make it clear how you are devating, and that
>> you take into account you deviations (a good reason to make them clear).
> That sure seems like a lame attempt to bind your definition to the symbol "HONESTY".
>
>> I am not saying you HAVE to use the Real Numbers, but if you claim to be
>> doing so, you need to follow the Rules of them or you are just a LIAR.
> You can't even solve the LIAR's paradox you fucking cunt!
>
> You can't tell the difference between truth and lies!
> Neither can Mathematics. They are just inverses under negation!
>
> Modality.

But if X is established, ~x is false.

Truth IS established.

>
>> You can use what every methods you want, as long as you are honest about
>> them and what you are doing, and give others the right to do the same.
> I am honest about being dishonest, you shit-for-brains.

Glad you admit it.

If you are dishonest, why should we listen to you.

>
> I am consistently inconsistent!
> I am logical about being illogical.
>
> Undecidability! Do you actually grok it?
>
> The moment you try to bind me to your symbols your system blows up.
>
>
>
>

On Saturday, August 20, 2022 at 12:28:34 AM UTC-7, Skep Dick wrote:
> On Friday, 19 August 2022 at 20:31:29 UTC+2, dklei...@gmail.com wrote:
> > On Thursday, August 18, 2022 at 11:02:48 PM UTC-7, Skep Dick wrote:
> > > On Friday, 19 August 2022 at 06:17:23 UTC+2, dklei...@gmail.com wrote:
> > > > Still meaningless. There is no "last" digit.
> > > There is a last digit to ANYONE who can look past completed infinities!
> > >
> > > That is you (according to you).
> > >
> > You don't like this but I say whether infinite objects are real or not is a
> > matter for philosophers - not you or me.
> No. This is not a philosophical issue. This is a Kolmogorov complexity issue.
>
> We know how to create finite representations/encodings of infinite objects.
> Writing a generator for ALL the Natural numbers in any programming language is trivial.
>
> What is not trivial is getting the generator to "complete" the process of generating ALL Natural numbers.
> > When I contemplate an infinite I see no last member. There are always
> > more members. There are just as many more members as there are
> > original members.
> Then what did you mean when you said "completed" process/infinity?
>
> Because when I use that word I use its standard English meaning.
>
> Synonymous with entire; finished; having come to an end; entirely done.
>
> And I would never use that word to describe the natural number generator.
> It's never done, It's never finished, complete; or come to an end.

What I intended by completed was the complete infinite series thought
of as a single set. I could have used a better expression I suppose.

This is exactly what you refuse to do. Mathematics views the entire,
infinitely long series as a single whole. I think it would be fair to view
a natural number generator as not a mathematical concept.

On Saturday, August 20, 2022 at 12:31:43 AM UTC-7, Skep Dick wrote:
> On Friday, 19 August 2022 at 20:48:02 UTC+2, dklei...@gmail.com wrote:
> > On Friday, August 19, 2022 at 4:46:10 AM UTC-7, Skep Dick wrote:
> > >
> > > Show me the number 0! Not the symbol representing it.
> > >
> > Most mathematicians would, given this context, take 0 to mean
> > the empty set. Then the successor of any number N would be N
> > plus the set whose only member is N.
> That's not really an answer. Show me the empty set. Not the syhmbols representing it - the empty set itself.
>
> This is a fundamental problem with representation systems. When you represent nothing does it become something or is it still nothing?
>
> Is nothing something; or is it just NO(thing)?

These, I have said, are problems for philosophers. Try to live
with the empty set. It's the best known of all the sets.

On Saturday, August 20, 2022 at 11:26:45 AM UTC-7, dklei...@gmail.com wrote:
> On Saturday, August 20, 2022 at 12:31:43 AM UTC-7, Skep Dick wrote:
> > On Friday, 19 August 2022 at 20:48:02 UTC+2, dklei...@gmail.com wrote:
> > > On Friday, August 19, 2022 at 4:46:10 AM UTC-7, Skep Dick wrote:
> > > >
> > > > Show me the number 0! Not the symbol representing it.
> > > >
> > > Most mathematicians would, given this context, take 0 to mean
> > > the empty set. Then the successor of any number N would be N
> > > plus the set whose only member is N.
> > That's not really an answer. Show me the empty set. Not the syhmbols representing it - the empty set itself.
> >
> > This is a fundamental problem with representation systems. When you represent nothing does it become something or is it still nothing?
> >
> > Is nothing something; or is it just NO(thing)?
> These, I have said, are problems for philosophers. Try to live
> with the empty set. It's the best known of all the sets.

"This is a computer science forum, not a set theory forum."

On Saturday, August 20, 2022 at 3:23:43 PM UTC-7, Jeffrey Rubard wrote:
> On Saturday, August 20, 2022 at 11:26:45 AM UTC-7, dklei...@gmail.com wrote:
> > On Saturday, August 20, 2022 at 12:31:43 AM UTC-7, Skep Dick wrote:
> > > On Friday, 19 August 2022 at 20:48:02 UTC+2, dklei...@gmail.com wrote:
> > > > On Friday, August 19, 2022 at 4:46:10 AM UTC-7, Skep Dick wrote:
> > > > >
> > > > > Show me the number 0! Not the symbol representing it.
> > > > >
> > > > Most mathematicians would, given this context, take 0 to mean
> > > > the empty set. Then the successor of any number N would be N
> > > > plus the set whose only member is N.
> > > That's not really an answer. Show me the empty set. Not the syhmbols representing it - the empty set itself.
> > >
> > > This is a fundamental problem with representation systems. When you represent nothing does it become something or is it still nothing?
> > >
> > > Is nothing something; or is it just NO(thing)?
> > These, I have said, are problems for philosophers. Try to live
> > with the empty set. It's the best known of all the sets.
> "This is a computer science forum, not a set theory forum."
>
The name of the forum - comp.theory - could expand to various
things. I read it "computation".

Set theory is a fundamental tool for a formal treatment of any
subject. Learn some of it or be forever ignorant,

On Saturday, 20 August 2022 at 14:57:40 UTC+2, richar...@gmail.com wrote:
> Which are just ways to create a representation of it.
Idiot. You don't even understand what a homoiconic language is.

Or a self-interpreting system.

> You just broke your own rules, maybe because you forgot what you first
> asked.
No I didn't. You are mis-interpreting my request as a violation of "my rules".

> Your logic seems to be inconsistent.
My logic is exists. In the exact sense humans use the word "exist.

Your logicis in yourhead. Like God.

> > Add an egg.
> The show me "Two" without the "Egg".
OK. Here it is ^^^^^^^^^. What does "Two" relate to!?!

> The "Twoness" is an abstract quality.
So is redness. What's your point? It represents a property.

What property does "zeroness" represent?

> So it depends on which system you are working in, and how you want to
> define a number.
I am not working in a number system. I am working in a representation system.

Shame. Is representation theory out of your depth?

> Natural Numbers have a very direct relation to counting things.
> Integers add some abstractions to allow for 0 or negative quantities,
> but are still basically counts but with an abstraction.
> We can then move to Reals, which move from what can be "counted" to what
> is Measured. We move from "How Many" to "How Much"
Cute. Numbers.

What type of symbol-manipulation systems are those?

On Saturday, 20 August 2022 at 15:18:37 UTC+2, richar...@gmail.com wrote:
> > https://en.wikipedia.org/wiki/Open_system_(systems_theory)
> But I am using it differently.
> An open system is a system that is open for others to use, change, to
> WORK IN.
> Linux is an Open System vs Windows is a Closed System, as we just get to
> see the "outside" of the system.
OOOOH! You mean an "open source" system!

OK! Show me the source code for the Real numbers already!!!!!

I've asked you 10+ times!

> Note, in my model we WORK IN a system because we adopt its rules are are
> partcipating in the behavior of the system. It allows us to actually
> understand and see the abstractions in it.
OK! Show me the source code for the rules!

Where is it ?!?

> Maybe your refusal to put yourself into the systems is the reason you
> can't understand the abstractions of the system.
Maybe your refusal to provide the source code is why I can't put myself "in" the system?

> This is just one of the lies you admit you do.
I haven't admitted to any lies. I only admited that I am a liar.

I lie about lying all the time!

> And only the ones that define it according to the established definition
> are aligned with the established system, and thus "right" in that system.
Ooooh. So you are in the "wrong" system when you re-defined "open system?

> > All of the above bindings are valid.
> Depends on what you want to call valid.
Any re-definition of terms is valid.

Just like you re-defined "open systems" to mean "open source system".

Valid!

> But we aren't computers so we don't actually need to "de-reference" a
> binding.
Of course we do! What are you talking about when you use the word "nothing" ?!?

What are you refering to?

> > Q.E.D you don't actually understand the difference between "rules of logic"; and "logic of rules".
> No, I think you do understand it.
Liar.

> >> For example, you were asking for a "Well-Defined Definition", but that
> >> ment you were IMPOSING A RULE about how to define things.
> > Nonsense. I am using the standard, socially accepted concept "well-defined" objects.

> > The color of this sentence is red. <--- Imagine that the font-color is the conventional meaning of red.
> > The color of this sentence is red. <--- Imagine that the font-color is the conventional meaning of green.
> > The color of this sentence is red. <--- Imagine that the font-color is the conventional meaning of blue.
> And, unless you have indicated you aren't in the standard meaning of the
> color words, only the first sentence is "correct"
Fucking idiot! They are ALL correct.

Because they are ALL valid definitions of the term "red".

All three sentences above are definitions. Cant you tell?

> Yes, if you escape out of conventional meaning, you can talk about being
> more abstract in your binding of meaning, but you need to be careful, or
> you lose all sense of meaning.
Really? What do you mean by "meaning"? Do you mean denotational semantics, or do you mean operational semantics?

> > Use it; or don't use it.
> And if you throw away all conventions, you have no base to start anything.
Truly spoken like a person who has never build a self-hosting compiler, or a self-interpreting language!

There is no base other than your own ability to exploit recursion!

> I don't need to, as it IS defined. Maybe not in your broken system, but
> it is in the one that you actually are living in, even if you reject it.
>
> From the dictionary:
> 1
> a : being in accordance with reason
> a reasonable theory
> b : not extreme or excessive
> reasonable requests
> 1a with perhaps a bit of 1b seems to fit.

HAHAHAHAHAHAHAHAHAHAHAHAH! That's an insufficient definition you clown.

So if it's with accordance with reason then it's reasonable.
And if it's not in accordance with reason then it's unreasonable.

So is it; or isn't it with accordance with reason? How do we decide?

> If you want more, then you run into the problem that you definition of
> "well-defined" isn't actually able to be "well-defined" because ALL
> definitions, when you expand them eventually become cirucular are refer
> to words that are only later defined. That is why we need to understand
> our First Principles, which form our base.
Nonsense! This is precisely why we need to understand meta-circular evaluation!

Self-interpretation. That is the "base"!

> What NULL-object, I don't directly work with object pointers, as that
> isn't my model of logic.
LIar! You openly admitted that the symbols point TO concepts.

0 points to "zeroness".
1 points to "oneness"
2 points to "twoness"

> > https://en.wikipedia.org/wiki/Futures_and_promises
> Whose says that I am using it in that meaning?
OH. So you admit that you aren't using the standard English/computational meaning of a promise?

> Its isn't even applicable, since I was talkinga about systems of LOGIC
> and that is about program execution. Thus, not applicable.
Of course it's applicable! When I promise something it means I will DO something later in time.

That's how humans use the concept of a "promise".
That's also how computers use promises. Asynchronous functions.

> YOU seem to be violating your own precepts. Your system is inconsistent.
> FAIL.
No it isn't! At worst my system is consistently inconsistent.

My system is consistent with reality. Beause my system is realizable.
If contradictions exist - then they exist. As real Mathematical objects and everything.

> > Modality.
> But if X is established, ~x is false.
Horseshit. X is a free variable. ~(x) is a computation.

> Truth IS established.
Nonsense. Truth is only relative to a particular model. Different models - different ruths.

> > I am honest about being dishonest, you shit-for-brains.
> Glad you admit it.
Glad you continue to admit your inability to navigate the liar's paradox.

> If you are dishonest, why should we listen to you.
Because I am honest.

> > The moment you try to bind me to your symbols your system blows
> SO nothing you say matters.
Your system just blew up.

> DEFINITION.
I gave you THREE definitions of "red". You couldn't even recognize them for what they were!

On Saturday, 20 August 2022 at 20:23:13 UTC+2, dklei...@gmail.com wrote:
> On Saturday, August 20, 2022 at 12:28:34 AM UTC-7, Skep Dick wrote:
> > On Friday, 19 August 2022 at 20:31:29 UTC+2, dklei...@gmail.com wrote:
> > > On Thursday, August 18, 2022 at 11:02:48 PM UTC-7, Skep Dick wrote:
> > > > On Friday, 19 August 2022 at 06:17:23 UTC+2, dklei...@gmail.com wrote:
> > > > > Still meaningless. There is no "last" digit.
> > > > There is a last digit to ANYONE who can look past completed infinities!
> > > >
> > > > That is you (according to you).
> > > >
> > > You don't like this but I say whether infinite objects are real or not is a
> > > matter for philosophers - not you or me.
> > No. This is not a philosophical issue. This is a Kolmogorov complexity issue.
> >
> > We know how to create finite representations/encodings of infinite objects.
> > Writing a generator for ALL the Natural numbers in any programming language is trivial.
> >
> > What is not trivial is getting the generator to "complete" the process of generating ALL Natural numbers.
> > > When I contemplate an infinite I see no last member. There are always
> > > more members. There are just as many more members as there are
> > > original members.
> > Then what did you mean when you said "completed" process/infinity?
> >
> > Because when I use that word I use its standard English meaning.
> >
> > Synonymous with entire; finished; having come to an end; entirely done.
> >
> > And I would never use that word to describe the natural number generator.
> > It's never done, It's never finished, complete; or come to an end.
> What I intended by completed was the complete infinite series thought
> of as a single set. I could have used a better expression I suppose.
Yeah... expressions. Evaluation of expressions turns out to be a hard problem (in computer science).

> This is exactly what you refuse to do. Mathematics views the entire,
> infinitely long series as a single whole.
That's a wee bit presumptious on the ability of Mathematicians, is it not?

I could also view Time as a sngle whole. But I sure as shit can't tell you what happens in the end.

>I think it would be fair to view a natural number generator as not a mathematical concept.
Why not?!? It's absolutely a Mathematical concept.

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

On Saturday, 20 August 2022 at 20:26:45 UTC+2, dklei...@gmail.com wrote:
> > This is a fundamental problem with representation systems. When you represent nothing does it become something or is it still nothing?
> >
> > Is nothing something; or is it just NO(thing)?
> These, I have said, are problems for philosophers. Try to live
> with the empty set. It's the best known of all the sets.

Au contraire. This is very much a problem for computer scientists. A choice exists. Between the existence and non-existence of the empty set.

Par for the course for non-deterministic programming! Afterall choice() IS the non-deterministic operator...

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

On Sunday, 21 August 2022 at 01:55:04 UTC+2, dklei...@gmail.com wrote:
> On Saturday, August 20, 2022 at 3:23:43 PM UTC-7, Jeffrey Rubard wrote:
> > On Saturday, August 20, 2022 at 11:26:45 AM UTC-7, dklei...@gmail.com wrote:
> > > On Saturday, August 20, 2022 at 12:31:43 AM UTC-7, Skep Dick wrote:
> > > > On Friday, 19 August 2022 at 20:48:02 UTC+2, dklei...@gmail.com wrote:
> > > > > On Friday, August 19, 2022 at 4:46:10 AM UTC-7, Skep Dick wrote:
> > > > > >
> > > > > > Show me the number 0! Not the symbol representing it.
> > > > > >
> > > > > Most mathematicians would, given this context, take 0 to mean
> > > > > the empty set. Then the successor of any number N would be N
> > > > > plus the set whose only member is N.
> > > > That's not really an answer. Show me the empty set. Not the syhmbols representing it - the empty set itself.
> > > >
> > > > This is a fundamental problem with representation systems. When you represent nothing does it become something or is it still nothing?
> > > >
> > > > Is nothing something; or is it just NO(thing)?
> > > These, I have said, are problems for philosophers. Try to live
> > > with the empty set. It's the best known of all the sets.
> > "This is a computer science forum, not a set theory forum."
> >
> The name of the forum - comp.theory - could expand to various
> things. I read it "computation".
>
> Set theory is a fundamental tool for a formal treatment of any
> subject. Learn some of it or be forever ignorant,

I think we have a fundamentally divergent understanding of computation.

Computation is conceptually prior to set theory.
Computation is prior to any theory - even a theory of computation!

The act of constructing a formal theory (such as set theory, or theory of computation) is what I call "programming".

Of course, I can't take much credit for this view. This is Peter Naur. Programming is theory-building.

https://pages.cs.wisc.edu/~remzi/Naur.pdf

On 8/21/22 5:08 AM, Skep Dick wrote:
> On Sunday, 21 August 2022 at 01:55:04 UTC+2, dklei...@gmail.com wrote:
>> On Saturday, August 20, 2022 at 3:23:43 PM UTC-7, Jeffrey Rubard wrote:
>>> On Saturday, August 20, 2022 at 11:26:45 AM UTC-7, dklei...@gmail.com wrote:
>>>> On Saturday, August 20, 2022 at 12:31:43 AM UTC-7, Skep Dick wrote:
>>>>> On Friday, 19 August 2022 at 20:48:02 UTC+2, dklei...@gmail.com wrote:
>>>>>> On Friday, August 19, 2022 at 4:46:10 AM UTC-7, Skep Dick wrote:
>>>>>>>
>>>>>>> Show me the number 0! Not the symbol representing it.
>>>>>>>
>>>>>> Most mathematicians would, given this context, take 0 to mean
>>>>>> the empty set. Then the successor of any number N would be N
>>>>>> plus the set whose only member is N.
>>>>> That's not really an answer. Show me the empty set. Not the syhmbols representing it - the empty set itself.
>>>>>
>>>>> This is a fundamental problem with representation systems. When you represent nothing does it become something or is it still nothing?
>>>>>
>>>>> Is nothing something; or is it just NO(thing)?
>>>> These, I have said, are problems for philosophers. Try to live
>>>> with the empty set. It's the best known of all the sets.
>>> "This is a computer science forum, not a set theory forum."
>>>
>> The name of the forum - comp.theory - could expand to various
>> things. I read it "computation".
>>
>> Set theory is a fundamental tool for a formal treatment of any
>> subject. Learn some of it or be forever ignorant,
>
> I think we have a fundamentally divergent understanding of computation.
>
> Computation is conceptually prior to set theory.
> Computation is prior to any theory - even a theory of computation!
>
> The act of constructing a formal theory (such as set theory, or theory of computation) is what I call "programming".

So, you are just admititng you are using the wrong words for things.

>
> Of course, I can't take much credit for this view. This is Peter Naur. Programming is theory-building.
>
> https://pages.cs.wisc.edu/~remzi/Naur.pdf
>

Which seems to be largely about redefining language to related but
different meanings.

I also note that he talks about being ABLE to build a theory in the
programming model, not tha it MUST be done that way.

So, you are just incorrect that computation MUST be prior to any theory.

You are just showing that you live in an anti-social framework.

On Sunday, 21 August 2022 at 08:14:09 UTC+1, Skep Dick wrote:
>
> 0 points to "zeroness".
> 1 points to "oneness"
> 2 points to "twoness"
>
A computer just sees symbols. It doesn't "know" that a circle with a stroke through it
represents zeroness.
However if you have a finite set of symbols, but an unbounded set of numbers you
want to represent, then you have to have rules which are more sophisticated than
a one to one mapping.
Now I'm no mathematician, so I couldn't tell you if there is an infinite supply of such rules,
all working on different principles, or a limited set, maybe with a unbounded number
of accidental variations which don't change the underlying system (e.g. we can say that
the decimal point separates the units from the fractions, or we can write the order
of magnitude and put the decimal point after the most significant digit, or do lots of
variations on that, but we haven't changed the underlying system).

On 8/21/22 7:31 AM, Malcolm McLean wrote:
> On Sunday, 21 August 2022 at 08:14:09 UTC+1, Skep Dick wrote:
>>
>> 0 points to "zeroness".
>> 1 points to "oneness"
>> 2 points to "twoness"
>>
> A computer just sees symbols. It doesn't "know" that a circle with a stroke through it
> represents zeroness.
> However if you have a finite set of symbols, but an unbounded set of numbers you
> want to represent, then you have to have rules which are more sophisticated than
> a one to one mapping.
> Now I'm no mathematician, so I couldn't tell you if there is an infinite supply of such rules,
> all working on different principles, or a limited set, maybe with a unbounded number
> of accidental variations which don't change the underlying system (e.g. we can say that
> the decimal point separates the units from the fractions, or we can write the order
> of magnitude and put the decimal point after the most significant digit, or do lots of
> variations on that, but we haven't changed the underlying system).

The number of Provable Theorems in the real number system is, I beleive,
infinte (not sure if it is a countable or an uncountable infinity, I
think countable).

The key is that the number of required axioms that we start from is
finite, and the number of steps to get to any provable rule is finite.

Note, with the Induction process, we can generate a countable infinite
number of properties from a finite number of base properties. This makes
the list of properties be an uncomputable set, since you can only
compute a finite set.

Richard Damon <Richard@Damon-Family.org> writes:

> The key is that the number of required axioms that we start from is
> finite, and the number of steps to get to any provable rule is finite.

A large number of interesting theories can not be finitely axiomatized.

> Note, with the Induction process, we can generate a countable infinite
> number of properties from a finite number of base properties. This
> makes the list of properties be an uncomputable set, since you can
> only compute a finite set.

Are you talking about formal theories here because I don't recognise the
terms you use? Induction (in formal theories) is an axiom schema and
not a process. And what are properties? And what is a computable set?

--
Ben.

On Sunday, 21 August 2022 at 20:19:01 UTC+8, richar...@gmail.com wrote:
> On 8/21/22 7:31 AM, Malcolm McLean wrote:
> > On Sunday, 21 August 2022 at 08:14:09 UTC+1, Skep Dick wrote:
> >>
> >> 0 points to "zeroness".
> >> 1 points to "oneness"
> >> 2 points to "twoness"
> >>
> > A computer just sees symbols. It doesn't "know" that a circle with a stroke through it
> > represents zeroness.
> > However if you have a finite set of symbols, but an unbounded set of numbers you
> > want to represent, then you have to have rules which are more sophisticated than
> > a one to one mapping.
> > Now I'm no mathematician, so I couldn't tell you if there is an infinite supply of such rules,
> > all working on different principles, or a limited set, maybe with a unbounded number
> > of accidental variations which don't change the underlying system (e.g. we can say that
> > the decimal point separates the units from the fractions, or we can write the order
> > of magnitude and put the decimal point after the most significant digit, or do lots of
> > variations on that, but we haven't changed the underlying system).
> The number of Provable Theorems in the real number system is, I beleive,
> infinte (not sure if it is a countable or an uncountable infinity, I
> think countable).

What is 'Provable Theorems', definition man!

> The key is that the number of required axioms that we start from is
> finite, and the number of steps to get to any provable rule is finite.

Anything new?

> Note, with the Induction process, we can generate a countable infinite
> number of properties from a finite number of base properties.

Prove it.

>This makes the list of properties be an uncomputable set, since you can only
> compute a finite set.

Prove it.

wij <wyniijj2@gmail.com> writes:

> On Sunday, 21 August 2022 at 20:19:01 UTC+8, richar...@gmail.com wrote:

>> The number of Provable Theorems in the real number system is, I beleive,
>> infinte (not sure if it is a countable or an uncountable infinity, I
>> think countable).
>
> What is 'Provable Theorems', definition man!

As usual I'm curious about the meta question... Why would you ask this?
Do you think that people who study formal theories have not defined what
a provable theorem is? And if you know that they have, but have some
issue with that definition, why not ask about what's bothering you about
it? Are you asking for RD to copy and paste two chapters from a
textbook like Shoenfield's, Mendelson's or Kleene's?

--
Ben.

On 8/21/2022 9:32 AM, Ben Bacarisse wrote:
> wij <wyniijj2@gmail.com> writes:
>
>> On Sunday, 21 August 2022 at 20:19:01 UTC+8, richar...@gmail.com wrote:
>
>>> The number of Provable Theorems in the real number system is, I beleive,
>>> infinte (not sure if it is a countable or an uncountable infinity, I
>>> think countable).
>>
>> What is 'Provable Theorems', definition man!
>
> As usual I'm curious about the meta question... Why would you ask this?
> Do you think that people who study formal theories have not defined what
> a provable theorem is? And if you know that they have, but have some
> issue with that definition, why not ask about what's bothering you about
> it? Are you asking for RD to copy and paste two chapters from a
> textbook like Shoenfield's, Mendelson's or Kleene's?
>

If {provable} is not defined as applying truth preserving operations to
a set of premises to derive a conclusion that necessarily follows from
these premises then {provable} is defined incoherently.

--
Copyright 2022 Pete Olcott

"Talent hits a target no one else can hit;
Genius hits a target no one else can see."
Arthur Schopenhauer