Question: What’s the biggest integer you can precisely defined in n characters? (No references to Graham’s number)
Answer: The least integer that cannot be precisely defined in n character.

On Thursday, August 25, 2022 at 5:40:11 AM UTC-7, skepd...@gmail.com wrote:
> Question: What’s the biggest integer you can precisely defined in n characters?
> (No references to Graham’s number)
> Answer: The least integer that cannot be precisely defined in n character..
>
Not quite. The least ... is one more than the most ...

Assigning no particular meaning to "be precisely defined in n characters".
On the whole - meaningless. Integers do not have intrinsic characters.

On Thursday, 25 August 2022 at 22:18:25 UTC+2, dklei...@gmail.com wrote:
> On Thursday, August 25, 2022 at 5:40:11 AM UTC-7, skepd...@gmail.com wrote:
> > Question: What’s the biggest integer you can precisely defined in n characters?
> > (No references to Graham’s number)
> > Answer: The least integer that cannot be precisely defined in n character.
> >
> Not quite. The least ... is one more than the most ...
No it isn't. Your indexing schema is off by 1.

The least integer greater than 4 is the 0th integer greater than 4.
And "0th integer greater than 4" is just another way of saying "5".

> Assigning no particular meaning to "be precisely defined in n characters"..
> On the whole - meaningless. Integers do not have intrinsic characters.
Why? That is precisely the algorithmic meaning. Kolmogorov complexity.

On Thursday, 25 August 2022 at 22:18:25 UTC+2, dklei...@gmail.com wrote:
> On Thursday, August 25, 2022 at 5:40:11 AM UTC-7, skepd...@gmail.com wrote:
> > Question: What’s the biggest integer you can precisely defined in n characters?
> > (No references to Graham’s number)
> > Answer: The least integer that cannot be precisely defined in n character.
> >
> Not quite. The least ... is one more than the most ...
Let me try that again (after some more wine)...

It depends entirely on your indexing schema. 0-based or 1-based indexing for the language which talks about "ALL the integers greater than 4."

What's the 1st integer greater than 4? It's 5!
What's the 0th integer greater than 4? It's 4!

On Thursday, August 25, 2022 at 1:57:36 PM UTC-7, skepd...@gmail.com wrote:
>
> What's the 1st integer greater than 4? It's 5!
> What's the 0th integer greater than 4? It's 4!
>
I like that. It's the most monumental stupidity I've seen in years.

On Friday, 26 August 2022 at 01:44:10 UTC+2, dklei...@gmail.com wrote:
> On Thursday, August 25, 2022 at 1:57:36 PM UTC-7, skepd...@gmail.com wrote:
> >
> > What's the 1st integer greater than 4? It's 5!
> > What's the 0th integer greater than 4? It's 4!
> >
> I like that. It's the most monumental stupidity I've seen in years.
Well, that entirely depends on how you define "stupid".

If "stupid" is thinking that the cardinal numbers start at 0 then... 5 is the 1st integer greater than 4.
If "stupid" is thinking that the cardinal numbers start at 1 then... 5 is the 0th integer greater than 4.

On Friday, 26 August 2022 at 02:12:02 UTC+2, Skep Dick wrote:
> On Friday, 26 August 2022 at 01:44:10 UTC+2, dklei...@gmail.com wrote:
> > On Thursday, August 25, 2022 at 1:57:36 PM UTC-7, skepd...@gmail.com wrote:
> > >
> > > What's the 1st integer greater than 4? It's 5!
> > > What's the 0th integer greater than 4? It's 4!
> > >
> > I like that. It's the most monumental stupidity I've seen in years.
> Well, that entirely depends on how you define "stupid".
>
> If "stupid" is thinking that the cardinal numbers start at 0 then... 5 is the 1st integer greater than 4.
> If "stupid" is thinking that the cardinal numbers start at 1 then... 5 is the 0th integer greater than 4.

Ordinal, cardinal... got mixed with the wine.

If "stupid" is thinking that the ordinal numbers start at 0 then... 5 is the 1st integer greater than 4.
If "stupid" is thinking that the ordinal numbers start at 1 then... 5 is the 0th integer greater than 4.

On Thursday, August 25, 2022 at 5:14:36 PM UTC-7, skepd...@gmail.com wrote:
> On Friday, 26 August 2022 at 02:12:02 UTC+2, Skep Dick wrote:
> > On Friday, 26 August 2022 at 01:44:10 UTC+2, dklei...@gmail.com wrote:
> > > On Thursday, August 25, 2022 at 1:57:36 PM UTC-7, skepd...@gmail.com wrote:
> > > >
> > > > What's the 1st integer greater than 4? It's 5!
> > > > What's the 0th integer greater than 4? It's 4!
> > > >
> > > I like that. It's the most monumental stupidity I've seen in years.
> > Well, that entirely depends on how you define "stupid".
> >
> > If "stupid" is thinking that the cardinal numbers start at 0 then... 5 is the 1st integer greater than 4.
> > If "stupid" is thinking that the cardinal numbers start at 1 then... 5 is the 0th integer greater than 4.
> Ordinal, cardinal... got mixed with the wine.
>
> If "stupid" is thinking that the ordinal numbers start at 0 then... 5 is the 1st integer greater than 4.
> If "stupid" is thinking that the ordinal numbers start at 1 then... 5 is the 0th integer greater than 4.
>
What makes you funny is your nix of meta language and technical
language. "5 is the first integer greater than 4" should be a
statement in meta language. Actually it's the definition of
5' as the successor to '4'. Then you misread "first" as a technical
concept and pull in the isomorphism of the natural numbers
to a subset therof.

On Thursday, August 25, 2022 at 1:40:11 PM UTC+1, skepd...@gmail.com wrote:
> Question: What’s the biggest integer you can precisely defined in n characters? (No references to Graham’s number)
> Answer: The least integer that cannot be precisely defined in n character..

Surely, for n > 77, "The least integer that cannot be precisely defined in n characters, plus 1000" is bigger?

On Friday, 26 August 2022 at 04:33:21 UTC+2, dklei...@gmail.com wrote:
> What makes you funny is your nix of meta language and technical
> language.
What makes you even funnier is the non-sensical implication that the "meta language" is not technical; or that there is even a difference between the "meta" and "technical" languages.

It sounds like your "understanding" of Mathematics is stuck in the last century. Where nobody understood reflexive languages.

>"5 is the first integer greater than 4" should be a
> statement in meta language.
Nonsense! It's a statement in the language, and its a statement about the language.

Because that's how reflection works.

>Actually it's the definition of 5' as the successor to '4'.
Where is it specified that the successor function is a unary function? For somebody who draws strict distinctions between metalanguages and technical languages, you sure seem to have assumed some metalanguage.

succ(n, order) is a binary function which is eqivalent to the + operator.
succ(1, n) is equivalent to n + 1, It also reads as the "1st successor to n"
succ(3, n) is equivalent to n + 3. It reads as the "3rd successor to n".
succ(0, n) is requivalent to n + 0. It reads as "0th successor to n".

In this (reflexive) language every number is the 0th successor to itself.

>Then you misread "first" as a technical concept and pull in the isomorphism of the natural numbers to a subset therof.
Oh, so it's NOT a technical concept? OK... what's the first natural number? Is it 0 or 1?

On Friday, 26 August 2022 at 15:30:49 UTC+2, Paul N wrote:
> Surely, for n > 77, "The least integer that cannot be precisely defined in n characters, plus 1000" is bigger?
The expression "plus 1000" adds 9 characters to your definition.

Skep Dick <skepdick22@gmail.com> writes:

> Oh, so it's NOT a technical concept? OK... what's the first natural
> number? Is it 0 or 1?

Despite the snowstorm of distractions you've posted since, I think the
nonsense that got DK's attention was your assertion that 4 is greater
than 4:

"What's the 0th integer greater than 4? It's 4!"

--
Ben.

On Sunday, 28 August 2022 at 22:02:55 UTC+2, Ben Bacarisse wrote:
> Skep Dick <skepd...@gmail.com> writes:
> Despite the snowstorm of distractions you've posted since, I think the
> nonsense that got DK's attention was your assertion that 4 is greater
> than 4:
I have made no such assertion. Can you even read?

I have asserted THAT 4 is the 0th object greater than 4.
Which is not the same statement as 4 is greater than 4.

On Sunday, August 28, 2022 at 11:55:07 AM UTC-7, skepd...@gmail.com wrote:
> On Friday, 26 August 2022 at 04:33:21 UTC+2, dklei...@gmail.com wrote:
> > What makes you funny is your nix of meta language and technical
> > language.
> What makes you even funnier is the non-sensical implication that the "meta language" is not technical; or that there is even a difference between the "meta" and "technical" languages.
>
> It sounds like your "understanding" of Mathematics is stuck in the last century. Where nobody understood reflexive languages.
>
Reflexive language isn't even good linguistics. It has nothing to do with
mathematics.
>
> >"5 is the first integer greater than 4" should be a
> > statement in meta language.
> Nonsense! It's a statement in the language, and its a statement about the language.
>
> Because that's how reflection works.
> >Actually it's the definition of 5' as the successor to '4'.
>
You have that backwards. In the most natural definition of
natural numbers the first natural number is the empty set
and the successor (to any natural number) is the union of
the number and the set whose only member is the number.
>
> Where is it specified that the successor function is a unary function? For somebody who draws strict distinctions between metalanguages and technical languages, you sure seem to have assumed some metalanguage.
>
> succ(n, order) is a binary function which is eqivalent to the + operator.
> succ(1, n) is equivalent to n + 1, It also reads as the "1st successor to n"
> succ(3, n) is equivalent to n + 3. It reads as the "3rd successor to n".
> succ(0, n) is requivalent to n + 0. It reads as "0th successor to n".
>
> In this (reflexive) language every number is the 0th successor to itself.
> >Then you misread "first" as a technical concept and pull in the isomorphism of the natural numbers to a subset therof.
> Oh, so it's NOT a technical concept? OK... what's the first natural number? Is it 0 or 1?
>
Above I gave a meta-language definition of natural numbers..

Skep Dick <skepdick22@gmail.com> writes:

> On Sunday, 28 August 2022 at 22:02:55 UTC+2, Ben Bacarisse wrote:
>> Skep Dick <skepd...@gmail.com> writes:
>> Despite the snowstorm of distractions you've posted since, I think the
>> nonsense that got DK's attention was your assertion that 4 is greater
>> than 4:
> I have made no such assertion. Can you even read?
>
> I have asserted THAT 4 is the 0th object greater than 4.
> Which is not the same statement as 4 is greater than 4.

I think we'll just leave that for the world to marvel at!

(A bit more context: you were talking about indexing "ALL the integers
greater than 4".)

--
Ben.

On Monday, 29 August 2022 at 04:22:07 UTC+2, Ben Bacarisse wrote:
> I think we'll just leave that for the world to marvel at!
>
> (A bit more context: you were talking about indexing "ALL the integers
> greater than 4".)

Yes, let the world marvel at you bringing your baggage full of "usual definitions" to a question stated in English.
Let us all marvel at the fact that your indoctrinated brain doesn't even comprehend that in order for the English question to become Mathematically meaningful it requires translation into a formal query language with sutable semantics for "integer", "biggest", and "defined in n characters"
Oh wait, apparently you don't have the symbol "?" in Mathematics. Thou shall not question!
Let us keep marvelling at your ignorance.

zero is a number.
succ zero is a number.
succ succ zero is a number.
succ succ succ zero is a number.

Given the nth_successor_of_x(n,x) function

What's the first successor to zero? Is it "succ zero" or "succ succ zero" ? Formally: nth_successor_of_x(1, 0) = ???
What's the zeroth successor to zero? is it "zero" or "succ zero"? Formally: nth_successor_of_x(0, 0) = ???

Parametric polymorphism: you don't fucking understand it!

On Monday, 29 August 2022 at 02:08:12 UTC+2, dklei...@gmail.com wrote:
> Reflexive language isn't even good linguistics. It has nothing to do with
> mathematics.
I have no idea what you mean by "good linguistics", but I sure as hell understand what reflection in formal languages is and how it works.

Perhaps you want to insist that programming language theory is not Mathematics; or linguistics when it's actually both!

> You have that backwards. In the most natural definition
I think I have that quite forward, thank you. I am aware of multitude of definitions. I have no idea which your aesthetic sensibilities consider "most natural".

Maybe you want to formalize your "most natural" proposition?

> natural numbers the first natural number is the empty set
Oh, wow! So the 1st number is not even the number 1 itself!?! The "first" number is a set! An empty one at that.

There's nothing natural about your definition of "natural".

> and the successor (to any natural number) is the union of
> the number and the set whose only member is the number.
If some technical mumbo jumbo is your idea of "natural" then... the technical definition that is "most natural" to me is a +1 monoid with 1 as the identity element.

> Above I gave a meta-language definition of natural numbers.
No, you didn't. You gave a set-theoretic definition of the natural numbers.

But if set theory is just the "meta language" then what language are you using to DO mathematics in ?!?

Skep Dick <skepdick22@gmail.com> writes:

> On Monday, 29 August 2022 at 04:22:07 UTC+2, Ben Bacarisse wrote:

Oh, you cut what you said. It's important:

"What's the 0th integer greater than 4? It's 4!"

>> I think we'll just leave that for the world to marvel at!
>>
>> (A bit more context: you were talking about indexing "ALL the integers
>> greater than 4".)
>
> Yes, let the world marvel at you bringing your baggage full of "usual
> definitions" to a question stated in English.
> Let us all marvel at the fact that your indoctrinated brain doesn't
> even comprehend that in order for the English question to become
> Mathematically meaningful it requires translation into a formal query
> language with sutable semantics for "integer", "biggest", and "defined
> in n characters" Oh wait, apparently you don't have the symbol "?" in
> Mathematics. Thou shall not question!

"What's the 0th integer greater than 4? It's 4!"

> Let us keep marvelling at your ignorance.
>
> zero is a number.
> succ zero is a number.
> succ succ zero is a number.
> succ succ succ zero is a number.
>
> Given the nth_successor_of_x(n,x) function

"What's the 0th integer greater than 4? It's 4!"

> What's the first successor to zero? Is it "succ zero" or "succ succ
> zero" ? Formally: nth_successor_of_x(1, 0) = ???

Who cares when the 0th integer greater than 4 is 4 (apparently). (Nice
try erasing what you said by no longer talking explicitly about "greater
than".)

--
Ben.

On Monday, 29 August 2022 at 16:03:33 UTC+2, Ben Bacarisse wrote:
> Skep Dick <skepd...@gmail.com> writes:
> Who cares when the 0th integer greater than 4 is 4 (apparently). (Nice
> try erasing what you said by no longer talking explicitly about "greater
> than".)
Even better! You can keep pretending that you "explicitly" know what I am talking about better than I do. Can you actually read whole English sentences?
The difference between "greater than" and "nth greater than - It's important!

The difference between:
val greater than : Nat -> Nat -> Bool = <function>
and
val nth_greater_than : Nat -> Nat -> Nat = <function>

They mean different things, you know.

Skep Dick <skepdick22@gmail.com> writes:

> On Monday, 29 August 2022 at 16:03:33 UTC+2, Ben Bacarisse wrote:
>> Skep Dick <skepd...@gmail.com> writes:
>> Who cares when the 0th integer greater than 4 is 4 (apparently). (Nice
>> try erasing what you said by no longer talking explicitly about "greater
>> than".)

> Even better! You can keep pretending that you "explicitly" know what I
> am talking about better than I do. Can you actually read whole English
> sentences?

> The difference between "greater than" and "nth greater than - It's
> important!

So it seems. As you say the 0th integer greater than 4 is 4.
Apparently at least one of "ALL the integers greater than 4" is 4 --
specifically the one indexed by 0. Who knew that "ALL the integers
greater than 4" includes 4 as the 0th indexed element (other than you)?

--
Ben.

On Monday, 29 August 2022 at 17:27:06 UTC+2, Ben Bacarisse wrote:
> So it seems. As you say the 0th integer greater than 4 is 4.
> Apparently at least one of "ALL the integers greater than 4" is 4 --
> specifically the one indexed by 0.
> greater than 4" includes 4 as the 0th indexed element (other than you)?
So you STILL refuse to tell me whether you think the 1st successor to 0 is "succ zero" or "succ succ zero".
And you STILL refuse to tell me whether you think the 0th successor to 0 is "zero" or "succ zero".

I guess we'll never know whether **TO YOU** ALL the successors to zero includes, or excludes zero itself...

On Monday, 29 August 2022 at 17:27:06 UTC+2, Ben Bacarisse wrote:
> So it seems. As you say the 0th integer greater than 4 is 4.
> Apparently at least one of "ALL the integers greater than 4" is 4 --
> specifically the one indexed by 0. Who knew that "ALL the integers
> greater than 4" includes 4 as the 0th indexed element (other than you)?

Heyyy! While you are so "relaxed" about notation. check this out: for x,y∈ℝ, "x≤y” is equivalent to “x>y ⇒ x<y”

jstor.org/stable/43303679‌

Skep Dick <skepdick22@gmail.com> writes:

> On Monday, 29 August 2022 at 17:27:06 UTC+2, Ben Bacarisse wrote:
>> So it seems. As you say the 0th integer greater than 4 is 4.
>> Apparently at least one of "ALL the integers greater than 4" is 4 --
>> specifically the one indexed by 0.
>> greater than 4" includes 4 as the 0th indexed element (other than you)?

> So you STILL refuse to tell me whether you think the 1st successor to
> 0 is "succ zero" or "succ succ zero". And you STILL refuse to tell me
> whether you think the 0th successor to 0 is "zero" or "succ zero".
>
> I guess we'll never know whether **TO YOU** ALL the successors to zero
> includes, or excludes zero itself...

Nope, and I don't think that the 0th integer greater than 4 is 4 either!

--
Ben.

Skep Dick <skepdick22@gmail.com> writes:

> Even better! You can keep pretending that you "explicitly" know what I
> am talking about better than I do.

Sorry if I misled you. I don't claim to know what you were talking about
when you said

"What's the 0th integer greater than 4? It's 4!"

so I'll stick to quoting it exactly as you wrote it.

--
Ben.

On Monday, August 29, 2022 at 3:13:22 AM UTC-7, skepd...@gmail.com wrote:
> On Monday, 29 August 2022 at 02:08:12 UTC+2, dklei...@gmail.com wrote:
> > Reflexive language isn't even good linguistics. It has nothing to do with
> > mathematics.
> I have no idea what you mean by "good linguistics", but I sure as hell understand what reflection in formal languages is and how it works.
>
> Perhaps you want to insist that programming language theory is not
> Mathematics; or linguistics when it's actually both!
>
Well, a programming language theory is a mathematical possibility. I
have never seen one. Reference?
>
> > You have that backwards. In the most natural definition
> I think I have that quite forward, thank you. I am aware of
> multitude of definitions. I have no idea which your aesthetic
> sensibilities consider "most natural".
>
Like most mathematicians I use "natural" in the meta-language
in an Occam-like sense. Of two propositions the more natural
one is one involving the least machinery to define.
>
> Maybe you want to formalize your "most natural" proposition?
> > natural numbers the first natural number is the empty set
> Oh, wow! So the 1st number is not even the number 1 itself!?!
> The "first" number is a set! An empty one at that.
>
> There's nothing natural about your definition of "natural".
>
> Hard to imagine anything simpler.
>
> and the successor (to any natural number) is the union of
> > the number and the set whose only member is the number.
> If some technical mumbo jumbo is your idea of "natural"
> then... the technical definition that is "most natural" to me is
> a +1 monoid with 1 as the identity element.
>
After you have defined "monoid", "identity" and probably more
stuff. Lots more machinery.
>
> > Above I gave a meta-language definition of natural numbers.
>
> No, you didn't. You gave a set-theoretic definition of the natural
> numbers.
>
> I used set-theory in the meta-language.
>
> But if set theory is just the "meta language" then what language
> are you using to DO mathematics in ?!?
>
None. Mathematics is not bound to the language it is expressed
in. Many mathematicians, like myself, think mostly in pictures.
Computation is a small rarely visited corner of mathematics.