On 8/18/22 8:29 PM, Skep Dick wrote:
> On Friday, 19 August 2022 at 01:59:18 UTC+2, richar...@gmail.com wrote:
>> -1 and -2 are NOT Natural Numbers
> Idiot.!1 is a natural number. 2 is a natural number.
>
> Every time you see "-X" just remember it's just a shorthand for (0 - (X))
>
>> And All the Natural Numbers, and the Integers are part of the Real
>> Numbers, so they are Real Numbers too.
> Which has what to do with comparing infinite-precision Real numbers?
>
>>> You can't traverse infinitely many digits in finite time.
>> No real number is infinitely close to zero. Those are the infinitesimals
>> which are NOT part of the Reals.
> Yep! You are a fucking idiot!
>
> The reals are smooth ( https://en.wikipedia.org/wiki/Smoothness )
> If if there is no Real number infinitely close to any other Real number then there are gaps in the continuum.
>
> Ooops?
>
>> All Real Numbers are Finite.
> Soo the Diagonalization argument doesn't mean anything to you?
>
>>> This applies to any x < y ! because you can just re-write it to 0 < y - x
>> And that is a Finite number. Remember, you keep saying we are talking
>> about R, which is a well defined set.
> OK well. You are as dumb as Olcott.
>>>
>>>> So x > y doesn't tell us anything about which number is closer to 0.
>>> Maybe! If the numbers are computable.
>> Which number in my example wasn't computable.
> Your example is not R. Your example is a tiny subset of R.
>
>>> It only becomes a "fact" (or a negation of a fact) if the proof terminates.
>>>
>> No, it can be a restriction.
> It can be. It isn't.
>
>> In the limit definition we talk about something needing to be true for
>> all x > X, so that statement is a restriction on what x's we need to
>> look at.
> The > in the limit statement is as undecidable as the > in x > y.
>
> Because > is undecidable for the Reals.

Why do you say that?

Given any two Real Numbers, there is a finite difference between them,
so you can determine that in finite time.

>
>> It says the statement that followed doesn't need to hold for ALL x in R,
>> just all those x in R that are greater than X.
> And "greater than X" is undecidable in the Reals. Because for any pair x,y it's possible that (x > y) OR (x == y) OR (x < y)
>
> It's your algorithm's job to CHOOSE the correct theorem.
>
>

Note, In one sense you are correct, because Classical Computation Theory
doesn't work on Real Numbers because real numbers can not be all
computed in finite time, but not all Mathematics needs be based on
Computations.

That is one of the issues with trying to computerize proofs, is that
some domains are just beyond computations.

Trying to EMPERICALLY prove that a value is pi can be undecidable.

On 8/18/22 8:44 PM, Skep Dick wrote:
> On Friday, 19 August 2022 at 02:07:13 UTC+2, richar...@gmail.com wrote:
>>>> A limit exists only if the value it approach is a finite value, i.e a
>>>> actual Real Number.
>>> So if it approaches pi? Does that limit exist or ?
>> Pi is a Finite Number.
> No it isn't. The are finite computable representations of PI.
>
> Dumb luck!

Nope, the VALUE of pi is finite, because we can bound it by known finite
numbers.

>
>> Finite Number doesn't mean it has a finite representation
> All the worse for you! What do you mean by "finite number" if NOT. "finite representation" ?

That its magnatude is finite, i.e. it isn't infintesimal or infinite.

>
> Are you meaning the numbersystem with base pi in which 1 means pi?

Nope. Pi can be bounded, so is finite.

3 < pi < 4, therefore pi is finite.

>
>>> How would you tell if it approaches Pi or a number very close to pi?
>> Is the limit - Pi zero, or a non-zero number.
> You don't even know if the limit exists.

Well, if the limit doesn't exist, then it isn't a number, not even just
very close to pi.

>
>>> It means SyntaxError. "+" is a binary function.
>> Right, just like a lim operation without an expresion to take the limit of.
> So you don't understand how functors; or currying works? Gotcha!

No, I do, but that isn't what you were asking.

You could try to define an L(x)(y) where L(x) created a function that
takes in the lim(x->y) part of lim(x->y) f(x), but that part ISN'T just
"lim(x->y)", you need to transform that into something else.

>
>> If you mean the limit of x, say the limit of x.
> I do mean the limit of x ! Where x is a free variable.

THen why didn't you say that to begin with, instead of writing a syntax
error.

>
> EXACTLY like I mean "g = + 1 x"
>
> g 5 = 6
>
> # let plus x y = x + y;;
> val plus : int -> int -> int = <fun>
> # let g = plus 1;;
> val g : int -> int = <fun>
> # g 5;;
> - : int = 6
>

On 8/18/22 4:37 PM, Skep Dick wrote:
> On Thursday, 18 August 2022 at 22:18:54 UTC+2, Ben Bacarisse wrote:
>> Alan Mackenzie <a...@muc.de> writes:
>>> Skep Dick <skepd...@gmail.com> wrote:
>>
>>>> That's one way to defend your religion from critique.
>>>
>>> I'd hardly characterise the content of your last few posts as
>>> critique.
>> It's odd. Mr/Ms Dick comes across as a teenager[1]. In the old days,
>> young people would come a troll like this on Usenet every now and then,
>> but I'd be very surprised if Skep really is a teenager. If I'm wrong
>> he/she is the only one to have posted on Usenet since the early 90s.
>>
>> [1] I'll admit I remember playing the "nothing means anything" game when
>> I was 13, but that was before the Internet so I could only annoy the
>> other lads in my gang. And, anyway, they played it as well (we were,
>> unsurprisingly, what later became know as nerds).
> You think I am playing the "nothing means anything game? Hahahahahaha! idiot!
>
> I am literally pointing out arbitrary choices in your systems! The implication of arbitrary choices being that had you made a different set of choices - your system, and your symbols would take on a different meaning!
> I am pointing out that axioms are an attempt to impose constraints on meaning (of which there is infinite supply).
>
> Pretty much ALL operators in Mathematics are polymorphic - they have multiple meanings!
> The expression "x = x" can take on an infinite number of meanings in ANY infinitary logic!
>
> Idiot++
>
> I am playing the "Symbols mean what they are INTERPRETED to mean" game. It's a game about constructing self-interpreting systems.
>
> http://compilers.cs.ucla.edu/popl16/popl16-full.pdf
>

The problem is that in polite society we make it clear what game we are
playing at the start, not just make up rule as we go like in Fizzbin.

When we do that, we pull in the definition of the symbols, so we know
what we are doing.

Yes, systems are based on what could be called "arbitrary" decisions,
but many of those decision are NOT just arbitrary, but have been
carefully honed so as to build a system that turns out very useful for
the sort of things we normally want to do.

Ignoring the reasoning behind the "arbitrary" decisions gives you a very
good chance of creating a system that just collapses in inconsistency,
or creates results that can't be interpreted.

Yes, at times, the deliberate challenging of specific decisions can lead
things in new and useful directions, but to do that really needs someone
who has a very good grasp of why things were done the way they were.

When people who don't understand the reasoning do it, we get things like
Peter Olcott and Skep Dick, who just show how much they don't actually
understand things by the nonsense that their ideas produce.

Maybe you have something behind your ideas, but you put so much crap
into you discussion, you have probably poisoned them from being looked
at by someone who might be able to help you polish them into something
better than just a turd.

It appears that you have entered into a Gun Fight, but only brought a
blow up hammer to bop people with.

On Thursday, August 18, 2022 at 4:23:47 PM UTC-7, Skep Dick wrote:
> On Friday, 19 August 2022 at 01:06:53 UTC+2, dklei...@gmail.com wrote:
> > Once upon a time people really believed that but only
> > a few years of work with real digital devices have
> > convinced people they are not the same. This, it
> > seems, is a question for the philosophers.
> It's not a philosophical question. It's a pragmatic one.
>
> https://en.wikipedia.org/wiki/Curry%E2%80%93Howard_correspondence
> > To me the test is whether or not there are any variable.
> > A variable being a symbol that had more than one value
> > during the course of its use. Mathematics has no
> > variables (in this sense).
> Of course it does. They are called free variables.
>
> Every expression in Mathematics has a free variable - its truth-value!
> > > Why can't you tell me the last digit of pi?
> > Meaningless. One does not (cannot?) calculate the
> > digits of pi by applying some process to the first
> > K digits to get the K+1 digit.
> Of course we can! We have algorithms to generate ALL the digits of pi.
>
> Its just that for every extra digit - you need extra time.
> >One uses some other
> > iterative process that continues forever and therefore
> > has no last step.
> Yeah! So what? These are your exact words "What mathematics does with process is work with the completed process as a single whole."
>
> If the process for generating the digits of pi is "completed" then tell me the last digit!
>
Still meaningless. There is no "last" digit.

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).

On Thursday, 18 August 2022 at 12:36:19 UTC+8, wij wrote:
> On Thursday, 18 August 2022 at 09:31:16 UTC+8, richar...@gmail.com wrote:
> > On 8/17/22 8:25 AM, wij wrote:
> > > On Wednesday, 17 August 2022 at 20:17:44 UTC+8, richar...@gmail.com wrote:
> > >> On 8/17/22 2:34 AM, wij wrote:
> > >>>> ...
> > >>> It already mentioned: Your math. cannot say "x+1 is closer than x to infinity".
> > >>> You often say infinity is a (your?) "concept", what kind of concept?
> > >>> Where is your books say infinity is a Special "vaue"?
> > >>> Where in your books Infinity/Closer/Approaching is defined?
> > >>>
> > >>> You cannot use "-∞ <------ 0 ------> +∞" to debate anything.
> > >>> You keep dream talking.
> > >> I am just following the standard model of the Real Numbers.
> > >>
> > >> I don't have the time to teach you that.
> > >
> > > I know, DEFINITION man. The problem is that you don't really know what the
> > > standard model and the Real Numbers and DEFINITION you are talking about.
> > > It is time to stop dream-talk and accept my proposal.
> > The problem is that once you try to define that "infinity - x"
> > represents a number, you open the system to contradictions.
> >
> > It has been shown that trying to make "infinity" act like a number
> > REQUIRES the remove of some other "standard" rule of the Real Number
> > system that we like to be able to assume.
> >
> > Thus, there is a sharp line between the Real Number System that doesn't
> > include "Infinity" as a number, and the various Trans-Finite system that
> > do allow "Infinity" to be treated as a "Normal" member of the system.
> >
> > One of the big problems is that there are many ways to get to "infinity"
> > and if you try to make it work as a normal value, and let "infinity" ==
> > "infinity" be true.
> >
> > For instancd, the sum of the odd Natural numbers is infinity, as is the
> > sum of the even Natural numbers, as is the sum of the Natual numbers.
> >
> > But clearly the sum of the Natural Numbers is the sum of the odd Natural
> > Numbers + the Sum of the Even Natural Numbers so
> >
> > Infinity = Infinity + Infinity.
> >
> > Subtract an Infinity from both sides and you get:
> >
> >
> > 0 = Infinity.
> >
> > Which seems crazy. This is what happens when you try to treat "Infinity"
> > as just a normal number. You need to remove certain operations, at least
> > when some of the operands are an infinite.
> It depends. The root reason is your notion of infinity is fuzzy.
> That leads to your infinity sometimes means unbounded large, sometimes a normal
> value, sometimes not, sometimes just an indication word. When really arguing,
> infinity does not exist. Like infinitesimal, at the beginning it is unbounded
> small non-zero VALUE, In the end, it is zero VALUE. When arguing, infinitesimal
> does not exist. What is the difference with POO Halt !!!
>
> How can we arguing this for a definite answer? No, we cannot.
> If we want a definite answer or a number containing infinity/infinitesimal in
> its expression definite, make the meaning unique first as I did.

Let's say "-∞ <------ 0 ------> +∞" denotes the x-axis in textbooks.
The message the schematic conveys should be: -∞<0<+∞ (note that '∞' is now
'legitimately' decorated with signs).
Assume "-∞<0<+∞" is accepted [note1]. And, to express the notion of 'close' or
'arbitrarily approaching to', we assume there are special rules that '∞'
interacts with normal numbers. To express "x+1 closer than x to ∞":

1) ∞-(x+1) < ∞-x
2) ∞-x-1 < ∞-x
3) ∞-1 < ∞
4) ∞ < ∞+1

Whatever the idea of '∞' is, as long as its meaning is unique, the notion of '∞'
must lead to the notion "∞ < ∞+1" being true (Is not x+1 closer than x by one
to infinity?).

[note1] You can refute "-∞<0<∞", but you would need to establish a 'theory' to
explain this assumed intermediate step. You need to explain lots more than simple
denial, explain enough to replace what is in the textbooks. Note that,
whatever you do is likely your own, not what the textbooks mean to say.
[note2] What does "arbitrarily close to" mean? Note the word 'distance' in
https://en.wikipedia.org/wiki/Limit_(mathematics)
Where is the approaching value of x from? Is it not the density property
guarantee you "For any two different numbers there exists a DIFFERENT
number", so you can find another x in between? What is wrong if we use
rational number x to approach like ancient Pythagorean did? Is the
result still valid by the limit argument? Why in the final, 'approach'
becomes 'equal', the x EQUALS to c, f(c)=L, the density property is
abandoned?
The limit theory has no concept of equality in its premise, it cannot
logically deduce the equality conclusion, except limit defines equality.
[note3] All decimals are real number, including infinitely long decimals. This is
general recognition, not any standard. Finite number of symbols cannot
define all of them. Actually, lots (technically almost all) of real numbers
are each not definable. What the Dedekind-cut like theory claims is false
(I don't need to look inside deep, circular arguments/definition should exist).

On Friday, 19 August 2022 at 04:22:47 UTC+2, richar...@gmail.com wrote:
> Nope, the VALUE of pi is finite, because we can bound it by known finite
> numbers.
> That its magnatude is finite, i.e. it isn't infintesimal or infinite.
> Nope. Pi can be bounded, so is finite.
> 3 < pi < 4, therefore pi is finite.
That's a circular definition, you clown!

You are claiming THAT pi is bounded by "Finite numbers".
ergo you are claiming that 3 is "finite"; and that 4 is "finite".

Which property of 3 and 4 is their "finiteness" ?!?! You still haven't provided the proof! The decision procedure which returns True for Finite(3).
So if I ask you "Why is 3 finite?" You are going to give me the exact same drivel!
It's bounded by 2 < 3 < 4. Why is 2 finite... ? Without loss of generality! you are betting on this axiom: FORALL: n -1 < n < n + 1

And without skipping a heartbeat! ω must be a finite number also!

Why? By YOUR EXACT LOGIC! Because it's bounded by ω-1 < ω < w + 1

> > You don't even know if the limit exists.
> Well, if the limit doesn't exist, then it isn't a number, not even just
> very close to pi.
Just as well! Please provide the decider for x ∈ Number

> > So you don't understand how functors; or currying works? Gotcha!
> No, I do, but that isn't what you were asking.
It's PRECISELY what I was asking. I splled it out for you even by giving you an arbitrary binding for x being the identity type.

> You could try to define an L(x)(y) where L(x) created a function that
> takes in the lim(x->y) part of lim(x->y) f(x), but that part ISN'T just
> "lim(x->y)", you need to transform that into something else.
You do understand that lim(x->y) z. means EXACTLY THE SAME THING as lim(x->y) f(x), right?!?!? Because you can bind z = f(x)

You say you "understand" partial application. But then you don't understand lim(x->y) z where x,y and z are partial variables !?!?

> > I do mean the limit of x ! Where x is a free variable.
> THen why didn't you say that to begin with, instead of writing a syntax
> error.
I did! In multiple posts. At multiple times I wrote any variation of "lim(x->y) z" (the unbound version), and "lim(x->y) f(x)" (the version bound to an anonumous functon).

You don't seem so good at understanding!

On Friday, 19 August 2022 at 04:46:52 UTC+2, richar...@gmail.com wrote:
> The problem is that in polite society we make it clear what game we are
> playing at the start, not just make up rule as we go like in Fizzbin.
So be polite already and make it clear! YOU are playing the game you call "Mathematics". YOU insist that it has A foundation.

Whar are the rules?

I have been transparent from the get-go! There are NO rules!
You constantly shift perspectives to accommodate your own contradictions!

You use Sum types in one second. Product types the next second. Limit types the third.
In one instant you are pretending the Real number line is continuous/smooth and in the very next instance you have discontinuities everywhere.
You contradict every single thing you say towards your (UNSTATED!) pragmatic goals and you keep pretending you are "consistent"!

Mean while you absolutely cannot tell me WHEN you use which rule and WHY. Laregely because the WHY question is theorem-dependent.
>
> When we do that, we pull in the definition of the symbols, so we know
> what we are doing.
Bullshit. You have NO idea what the definitions of half your symbols are!

And at times - you have more than one definition for the same thing - so you keep using whichever one suits you.

Without explaininng the choice.

> Yes, systems are based on what could be called "arbitrary" decisions,
> but many of those decision are NOT just arbitrary, but have been
> carefully honed so as to build a system that turns out very useful for
> the sort of things we normally want to do.
Well isn't that's a vague statement for a Mathematician! What sort of things do we "normally want to do" with Mathematics ?!?

> Ignoring the reasoning behind the "arbitrary" decisions gives you a very
> good chance of creating a system that just collapses in inconsistency,
> or creates results that can't be interpreted.
You mean like a system which can reference NULL-types and cause Null-pointer exceptions ?!?

> Yes, at times, the deliberate challenging of specific decisions can lead
> things in new and useful directions, but to do that really needs someone
> who has a very good grasp of why things were done the way they were.
There is NO such person! If Mathematics is to be pragmatic - WHY things were done in a particular way depends on your GOALS.

Dfferent goals - different Mathematics!

> When people who don't understand the reasoning do it, we get things like
> Peter Olcott and Skep Dick, who just show how much they don't actually
> understand things by the nonsense that their ideas produce.
Idiot! Every single thing you've said is nonse!

Every single claim/argument you've made relies on arbitrary adjectives (judgments) about the semantic properties of the objects you are working with.
Semantic properties which you can't encode in a DECIDABLE proof!

The semantic property of boundedness, finiteness, arbitrary-closeness.

How are you DOING arithmetic on the Reals with undecidable operators?!?

Only YOU know. But you can't tell me.

> Maybe you have something behind your ideas, but you put so much crap
> into you discussion, you have probably poisoned them from being looked
> at by someone who might be able to help you polish them into something
> better than just a turd.
Fucktard. Do I look like I want my ideas polished? Do I strike you as somebody who seeks social validation?

I am pointing out THAT everything you are DOING fits into the category-theoretic perspective of Mathematics.
In which there are no such things as "numbers".

Absolutely everything you are DOING can be re-interpreted from the lens of homotopy type theory/Univalent foundations.

Without the need to cling onto the self-deception about your system being "consistent".

> It appears that you have entered into a Gun Fight, but only brought a
> blow up hammer to bop people with.
You keep framing everything as a fight. That's why you are a loser.

This is how knowledge-synchronization works. But what would you know about synchrnoization in Mathematics!

On Friday, 19 August 2022 at 04:22:47 UTC+2, richar...@gmail.com wrote:
> >>> How would you tell if it approaches Pi or a number very close to pi?
> >> Is the limit - Pi zero, or a non-zero number.
> > You don't even know if the limit exists.
> Well, if the limit doesn't exist, then it isn't a number, not even just
> very close to pi.
So can I apply this EXACT logic to 0 ?!?!

If 0 can't be bounded, if the limit doesn't exist on the continuum then 0 is NOT a number.

-∞ <-----------------> +∞

OOOPS!!!!

On Friday, 19 August 2022 at 04:12:54 UTC+2, richar...@gmail.com wrote:
> > Because > is undecidable for the Reals.
> Why do you say that?
I am saying it because it's true.

The Real numberline is compact. The cardinality of (0,1) and (0, ∞) is the same - Every Real number exists between (0, 1) so your "bounding" principle fails.

> Given any two Real Numbers, there is a finite difference between them, so you can determine that in finite time.
Bullshit. Have you seen how subtraction works? You start with the least significant digit. Which digit is that in an infinite sequence?

Subtraction is undecidable too! ALL arithmetic on the reals is undecidable
Addition? Undecidable!

> >
> Note, In one sense you are correct, because Classical Computation Theory
> doesn't work on Real Numbers because real numbers can not be all
> computed in finite time, but not all Mathematics needs be based on
> Computations.
Look, sophist. This is not a theoretical limit! This is the limit of how humans DO subtraction, addition and multiplication.

We start with the most significant digit. Which is the right-most digit and we "borrow" from the digits on the left.

This is why a choice exists in Digital computers on whether to use little or big endian encoding . it saves times on computations.

> That is one of the issues with trying to computerize proofs, is that
> some domains are just beyond computations.
That's neither here nor there. You can always do symbolic computation.

But at some point the rubber has to hit the road! At some point you need to turn the abstractions into something concrete.

Otherwise they are useless in practice.

> Trying to EMPERICALLY prove that a value is pi can be undecidable.
"empirical proof" is an oxymoron. There are no proofs outside the formal sciences.

pi is a Mathematical (ideal/transcendental) construct. It doesn't exist in the empirical.

If you are refering to numerical methods (like Montecarlo simulations) - yeah! That's what we use quantum computers for. Fast, concurrent approximations.

On 19/08/2022 01:30, Ben Bacarisse wrote:
>>> If RL(LR) = 1/3, why is R(L) not 0?
>> Because, viewed as a Hackenbush string, the player of R wins with
>> or without the first move, so R(L) is > 0. It's a surreal number, but not
>> a real number.
> Right (I happen to know this) but 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! As you know, there
are whole books written on this general topic, so I was hoping rather
to give readers some sort of flavour and to intrigue them. There have
been other hints dropped in the thread about where it all goes.

> The only information you gave about the number represented by a string
> was based on summing the digit values. And this included an example of
> what /looks/ like an infinite sum:
> RL(LR) = 1 - 1/2 - 1/4 + 1/8 - 1/16 + 1/32 ... = 1/3.
> And yet,
> R(L) = 1 - 1/2 - 1/4 - 1/8 ... =/= 0.
> Again, I know why, by how could anyone else work out that from the
> rules?

I didn't give "the rules", apart from "left as an exercise";
so only by reading about the relationships between numbers and games.
An infinite sum is different from a limit of such a sum is different
from games played with representations of that sum.

> Calling this "balanced binary" also somewhat loaded the dice. It
> strongly suggested that summing digit values (even in limit cases) is
> what gives a digit string its denoted value.
Yes, but limits are so Real .... "Balanced binary", as such,
is simply a different form of binary, just as balanced ternary, using
"digits" 0, 1 and -1, is a different form of ternary, more symmetric
between positive and negative but less familiar for other arithmetic.
But once you've taken that step, the notations are suggestive; because
balanced binary has no digit 0, some arithmetic looks quite different.

[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.]

--
Andy Walker, Nottingham.
Andy's music pages: www.cuboid.me.uk/andy/Music
Composer of the day: www.cuboid.me.uk/andy/Music/Composers/Bach

On 8/19/22 3:48 AM, Skep Dick wrote:
> On Friday, 19 August 2022 at 04:12:54 UTC+2, richar...@gmail.com wrote:
>>> Because > is undecidable for the Reals.
>> Why do you say that?
> I am saying it because it's true.
>
> The Real numberline is compact. The cardinality of (0,1) and (0, ∞) is the same - Every Real number exists between (0, 1) so your "bounding" principle fails.

Nope. You are just using wrong definition to get your wrong answer.

You use the wrong definition because you refuse to define what system
you are in.

If you don't know where you are, you can't know how to get to anywhere.

See: https://en.wikipedia.org/wiki/Finite_number

>
>> Given any two Real Numbers, there is a finite difference between them, so you can determine that in finite time.
> Bullshit. Have you seen how subtraction works? You start with the least significant digit. Which digit is that in an infinite sequence?

You are confusing the representation of the number with the number.

You fail to understand the concept of what the number actually is.

>
> Subtraction is undecidable too! ALL arithmetic on the reals is undecidable
> Addition? Undecidable!

Yes, the Reals are not "Computable" by finite automation. That doesn't
mean they don't exist and have actual properties, and that the
operations like addition and subtracttion aren't actually definied for them.

Just says that no computer (or computation per a finite computaiton
theory) can actually deal with them.

That shows that not everything can be a computation, computable, or a
program.

>
>>>
>> Note, In one sense you are correct, because Classical Computation Theory
>> doesn't work on Real Numbers because real numbers can not be all
>> computed in finite time, but not all Mathematics needs be based on
>> Computations.
> Look, sophist. This is not a theoretical limit! This is the limit of how humans DO subtraction, addition and multiplication.

Nope, it is how humans do things when they are working in the concrete.
I guess your mind can't switch to abstract computation mode, becuase
that processor is broken in yours.

>
> We start with the most significant digit. Which is the right-most digit and we "borrow" from the digits on the left.

Only when in concrete mode. In abstract mode we do things like start on
the line at the location of the first number and move back a distance
specified by the second.

>
> This is why a choice exists in Digital computers on whether to use little or big endian encoding . it saves times on computations.

Which has nothing to do with the Real Numbers.

And most don't give you a choice, but it was how they were built.

>
>> That is one of the issues with trying to computerize proofs, is that
>> some domains are just beyond computations.
> That's neither here nor there. You can always do symbolic computation.
>
> But at some point the rubber has to hit the road! At some point you need to turn the abstractions into something concrete.

Nope.

>
> Otherwise they are useless in practice.

Nope. You can do useful stuff and stay in the abstract

>
>> Trying to EMPERICALLY prove that a value is pi can be undecidable.
> "empirical proof" is an oxymoron. There are no proofs outside the formal sciences.

Depends on your definitions.

>
> pi is a Mathematical (ideal/transcendental) construct. It doesn't exist in the empirical.
>
> If you are refering to numerical methods (like Montecarlo simulations) - yeah! That's what we use quantum computers for. Fast, concurrent approximations.

On 8/19/22 2:20 AM, Skep Dick wrote:
> On Friday, 19 August 2022 at 04:22:47 UTC+2, richar...@gmail.com wrote:
>> Nope, the VALUE of pi is finite, because we can bound it by known finite
>> numbers.
>> That its magnatude is finite, i.e. it isn't infintesimal or infinite.
>> Nope. Pi can be bounded, so is finite.
>> 3 < pi < 4, therefore pi is finite.
> That's a circular definition, you clown!

All definitions eventually get to a circular definition, as the first
definition needs something to define it.

>
> You are claiming THAT pi is bounded by "Finite numbers".
> ergo you are claiming that 3 is "finite"; and that 4 is "finite".

Yep.

>
> Which property of 3 and 4 is their "finiteness" ?!?! You still haven't provided the proof! The decision procedure which returns True for Finite(3).
> So if I ask you "Why is 3 finite?" You are going to give me the exact same drivel!
> It's bounded by 2 < 3 < 4. Why is 2 finite... ? Without loss of generality! you are betting on this axiom: FORALL: n -1 < n < n + 1

The NATURAL numbers, are defined to be finite. ω is NOT a natural
number, you can't get to it by simple counting.

>
> And without skipping a heartbeat! ω must be a finite number also!

Nope. It is in a different series.

>
> Why? By YOUR EXACT LOGIC! Because it's bounded by ω-1 < ω < w + 1

but ω-1 didn't exist until ω did, so you can't use that number to prove
ω is finite

>
>>> You don't even know if the limit exists.
>> Well, if the limit doesn't exist, then it isn't a number, not even just
>> very close to pi.
> Just as well! Please provide the decider for x ∈ Number

Who said that the operation was decidable by a finite computation? Only
you, and that is where you go wrong.

You "model" can't handle the Real Numbers.

>
>>> So you don't understand how functors; or currying works? Gotcha!
>> No, I do, but that isn't what you were asking.
> It's PRECISELY what I was asking. I splled it out for you even by giving you an arbitrary binding for x being the identity type.

And when you added the identity transform, you filled in the missing piece.

>
>> You could try to define an L(x)(y) where L(x) created a function that
>> takes in the lim(x->y) part of lim(x->y) f(x), but that part ISN'T just
>> "lim(x->y)", you need to transform that into something else.
> You do understand that lim(x->y) z. means EXACTLY THE SAME THING as lim(x->y) f(x), right?!?!? Because you can bind z = f(x)

Yes, but it doesn't mean the same thing as "lim(x->y)" as that is
missing the token, and you can't bind to the non-existent token.

>
> You say you "understand" partial application. But then you don't understand lim(x->y) z where x,y and z are partial variables !?!?

But you question wasn't "lim(x->y) z", it was "lim(x->y)", the missing
symbol is important.

Maybe you mind just has run out of storage and you forget where you were
wrong.

>
>
>>> I do mean the limit of x ! Where x is a free variable.
>> THen why didn't you say that to begin with, instead of writing a syntax
>> error.
> I did! In multiple posts. At multiple times I wrote any variation of "lim(x->y) z" (the unbound version), and "lim(x->y) f(x)" (the version bound to an anonumous functon).
>
> You don't seem so good at understanding!
>

I think your memory system has been dropping bits.

Go back and check what you actually wrote at the beginning.

On 8/19/22 3:05 AM, Skep Dick wrote:
> On Friday, 19 August 2022 at 04:22:47 UTC+2, richar...@gmail.com wrote:
>>>>> How would you tell if it approaches Pi or a number very close to pi?
>>>> Is the limit - Pi zero, or a non-zero number.
>>> You don't even know if the limit exists.
>> Well, if the limit doesn't exist, then it isn't a number, not even just
>> very close to pi.
> So can I apply this EXACT logic to 0 ?!?!
>
> If 0 can't be bounded, if the limit doesn't exist on the continuum then 0 is NOT a number.
>
> -∞ <-----------------> +∞
>
> OOOPS!!!!
>
>
>
>

And 0 is bounded, so not a problem.

On 8/19/22 2:02 AM, 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).

Then what is it?

On Friday, 19 August 2022 at 13:11:36 UTC+2, richar...@gmail.com wrote:
> Nope. You are just using wrong definition to get your wrong answer.
>
> You use the wrong definition because you refuse to define what system
> you are in.
I don't know in what language I must say this to you! I am not IN the system. I am OUTSIDE of the system.

Do you actually understand the difference between the internal and external languages of a theory?

I am using Operational Semantics.
I am NOT using denotational semantics!

Do you actually grok the difference?!?

There is no such thing as a "wrong" definition, you numbskull! I define this color as green: 🔴

> If you don't know where you are, you can't know how to get to anywhere.
I know precisely where I am. That can't be said about you. Standing at the 0 of the Real number line.

> You are confusing the representation of the number with the number.
No, I am not.

YOU-the-human are never operating with the numbers.
YOU-the-human are ALWAYS operating with the representations.

Show me the number 0! Not the symbol representing it.

> You fail to understand the concept of what the number actually is.
OK! So teach me. Tell me something about the number 0.

> Yes, the Reals are not "Computable" by finite automation. That doesn't
> mean they don't exist and have actual properties, and that the
> operations like addition and subtracttion aren't actually definied for them.
Oooooh! Is that how it works. Well i can DEFINE division by zero also!

Look! It type-checks and everything!

# let divide_by_0 x = x /. 0.;;
val divide_by_0 : float -> float = <fun>

But can i APPLY the operation to any numerator? Well look at here! I can apply it also!
On a finite automation!

# divide_by_0 10.0 ;;
- : float = infinity

> Just says that no computer (or computation per a finite computaiton
> theory) can actually deal with them.
Mine just did. Is your computer broken?

> That shows that not everything can be a computation, computable, or a
> program.
Sophist. Computation is symbol manipulation.

Every manipulation you can do with pen/paper - the computer can do also.

> > Look, sophist. This is not a theoretical limit! This is the limit of how humans DO subtraction, addition and multiplication.
> Nope, it is how humans do things when they are working in the concrete.
Uhuh. So you are not working with concrete numbers?!? What are you working with then?

> I guess your mind can't switch to abstract computation mode, becuase
> that processor is broken in yours.
You keep lying about that.

> > We start with the most significant digit. Which is the right-most digit and we "borrow" from the digits on the left.
> Only when in concrete mode. In abstract mode we do things like start on
> the line at the location of the first number and move back a distance
> specified by the second.
Fucking idiot! x > y is abstract mode. The proposition "x > y" translates PRECISELY into English as "Is X to the right of Y?"

Maybe yes -∞<----------y-------x----------> +∞
Maybe no: -∞<----------x-------y----------> +∞

> > Otherwise they are useless in practice.
> Nope. You can do useful stuff and stay in the abstract
Oh can you?!? OK show me!

Given the proposition x>y (N.B NOT the theorem!)

which is the "correct" representation of the continuum?

-∞<----------y-------x----------> +∞ OR -∞<----------x-------y----------> +∞

> > "empirical proof" is an oxymoron. There are no proofs outside the formal sciences.
> Depends on your definitions.
I am using the standard definition of "proof" from "proof theory" as accepted by the general Mathematical community!

I guess you were lying about using the standard model. Asshole.

On Friday, 19 August 2022 at 13:22:46 UTC+2, richar...@gmail.com wrote:
> >
> And 0 is bounded, so not a problem.

By what ?!? When constructing R the first number you identify is 0.

What is it bounded by? -1 and 1?! That doesn't count. Those aren't bounded either!

On Friday, 19 August 2022 at 13:23:47 UTC+2, richar...@gmail.com wrote:
> > That is you (according to you).
> Then what is it?
I have NO fucking idea.

I don't have access to ordinal time! It's just an abstract model.

Can't you work with abstractions, man?

On 8/19/22 2:58 AM, Skep Dick wrote:
> On Friday, 19 August 2022 at 04:46:52 UTC+2, richar...@gmail.com wrote:
>> The problem is that in polite society we make it clear what game we are
>> playing at the start, not just make up rule as we go like in Fizzbin.
> So be polite already and make it clear! YOU are playing the game you call "Mathematics". YOU insist that it has A foundation.
>
> Whar are the rules?
>
> I have been transparent from the get-go! There are NO rules!
> You constantly shift perspectives to accommodate your own contradictions!
>
> You use Sum types in one second. Product types the next second. Limit types the third.
> In one instant you are pretending the Real number line is continuous/smooth and in the very next instance you have discontinuities everywhere.
> You contradict every single thing you say towards your (UNSTATED!) pragmatic goals and you keep pretending you are "consistent"!
>
> Mean while you absolutely cannot tell me WHEN you use which rule and WHY. Laregely because the WHY question is theorem-dependent.
>>
>> When we do that, we pull in the definition of the symbols, so we know
>> what we are doing.
> Bullshit. You have NO idea what the definitions of half your symbols are!
>
> And at times - you have more than one definition for the same thing - so you keep using whichever one suits you.
>
> Without explaininng the choice.

Then you aren't communicating. You need to use the one that is
applicable, as would be agreed upon.

You are just proving you are anti-social and unable to effectively work
with others.

>
>
>> Yes, systems are based on what could be called "arbitrary" decisions,
>> but many of those decision are NOT just arbitrary, but have been
>> carefully honed so as to build a system that turns out very useful for
>> the sort of things we normally want to do.
> Well isn't that's a vague statement for a Mathematician! What sort of things do we "normally want to do" with Mathematics ?!?
>
>> Ignoring the reasoning behind the "arbitrary" decisions gives you a very
>> good chance of creating a system that just collapses in inconsistency,
>> or creates results that can't be interpreted.
> You mean like a system which can reference NULL-types and cause Null-pointer exceptions ?!?
>
>
>> Yes, at times, the deliberate challenging of specific decisions can lead
>> things in new and useful directions, but to do that really needs someone
>> who has a very good grasp of why things were done the way they were.
> There is NO such person! If Mathematics is to be pragmatic - WHY things were done in a particular way depends on your GOALS.
>
> Dfferent goals - different Mathematics!
>

Yes, but a GIVEN Mathematics is GIVEN.

Thus things like "The Real Numbers" have precise definitions.

Thus, we need to be clear WHICH Mathematics we are talking in, and why
there are "defaults" when not specified.

>> When people who don't understand the reasoning do it, we get things like
>> Peter Olcott and Skep Dick, who just show how much they don't actually
>> understand things by the nonsense that their ideas produce.
> Idiot! Every single thing you've said is nonse!
>
> Every single claim/argument you've made relies on arbitrary adjectives (judgments) about the semantic properties of the objects you are working with.
> Semantic properties which you can't encode in a DECIDABLE proof!
>
> The semantic property of boundedness, finiteness, arbitrary-closeness.
>
> How are you DOING arithmetic on the Reals with undecidable operators?!?
>
> Only YOU know. But you can't tell me.

Because it has been well defined for a long time but you can't seem to
understand it.

>
>> Maybe you have something behind your ideas, but you put so much crap
>> into you discussion, you have probably poisoned them from being looked
>> at by someone who might be able to help you polish them into something
>> better than just a turd.
> Fucktard. Do I look like I want my ideas polished? Do I strike you as somebody who seeks social validation?

The go into your hole and DIE.

>
> I am pointing out THAT everything you are DOING fits into the category-theoretic perspective of Mathematics.
> In which there are no such things as "numbers".

And that is where you are wrong. "Numbers" exist, they have been defined

>
> Absolutely everything you are DOING can be re-interpreted from the lens of homotopy type theory/Univalent foundations.

Apparently not, since you seem to be unable to handle some of the concepts.

>
> Without the need to cling onto the self-deception about your system being "consistent".

We assume consistentcy until proven wrong (but accept that it is a
possibility)

Can you prove it isn't? NOTE, the proof needs to follow the rules of
the system or it isn't applicable, and so far it seems that is beyond
your mental ability.

>
>> It appears that you have entered into a Gun Fight, but only brought a
>> blow up hammer to bop people with.
> You keep framing everything as a fight. That's why you are a loser.
>
> This is how knowledge-synchronization works. But what would you know about synchrnoization in Mathematics!

knowledge-synchronization is based on having inadequate tools for the Job?

Seems to be a poor concept then.

YOU are the one that made the fight, as you want to disagree with how
things are.

You seem to be doing a pretty good job at beating yourself up though, so
GOOD JOB. Keep it up and you will totally defeat yourself.

On 8/19/22 2:16 AM, wij wrote:
> On Thursday, 18 August 2022 at 12:36:19 UTC+8, wij wrote:
>> On Thursday, 18 August 2022 at 09:31:16 UTC+8, richar...@gmail.com wrote:
>>> On 8/17/22 8:25 AM, wij wrote:
>>>> On Wednesday, 17 August 2022 at 20:17:44 UTC+8, richar...@gmail.com wrote:
>>>>> On 8/17/22 2:34 AM, wij wrote:
>>>>>>> ...
>>>>>> It already mentioned: Your math. cannot say "x+1 is closer than x to infinity".
>>>>>> You often say infinity is a (your?) "concept", what kind of concept?
>>>>>> Where is your books say infinity is a Special "vaue"?
>>>>>> Where in your books Infinity/Closer/Approaching is defined?
>>>>>>
>>>>>> You cannot use "-∞ <------ 0 ------> +∞" to debate anything.
>>>>>> You keep dream talking.
>>>>> I am just following the standard model of the Real Numbers.
>>>>>
>>>>> I don't have the time to teach you that.
>>>>
>>>> I know, DEFINITION man. The problem is that you don't really know what the
>>>> standard model and the Real Numbers and DEFINITION you are talking about.
>>>> It is time to stop dream-talk and accept my proposal.
>>> The problem is that once you try to define that "infinity - x"
>>> represents a number, you open the system to contradictions.
>>>
>>> It has been shown that trying to make "infinity" act like a number
>>> REQUIRES the remove of some other "standard" rule of the Real Number
>>> system that we like to be able to assume.
>>>
>>> Thus, there is a sharp line between the Real Number System that doesn't
>>> include "Infinity" as a number, and the various Trans-Finite system that
>>> do allow "Infinity" to be treated as a "Normal" member of the system.
>>>
>>> One of the big problems is that there are many ways to get to "infinity"
>>> and if you try to make it work as a normal value, and let "infinity" ==
>>> "infinity" be true.
>>>
>>> For instancd, the sum of the odd Natural numbers is infinity, as is the
>>> sum of the even Natural numbers, as is the sum of the Natual numbers.
>>>
>>> But clearly the sum of the Natural Numbers is the sum of the odd Natural
>>> Numbers + the Sum of the Even Natural Numbers so
>>>
>>> Infinity = Infinity + Infinity.
>>>
>>> Subtract an Infinity from both sides and you get:
>>>
>>>
>>> 0 = Infinity.
>>>
>>> Which seems crazy. This is what happens when you try to treat "Infinity"
>>> as just a normal number. You need to remove certain operations, at least
>>> when some of the operands are an infinite.
>> It depends. The root reason is your notion of infinity is fuzzy.
>> That leads to your infinity sometimes means unbounded large, sometimes a normal
>> value, sometimes not, sometimes just an indication word. When really arguing,
>> infinity does not exist. Like infinitesimal, at the beginning it is unbounded
>> small non-zero VALUE, In the end, it is zero VALUE. When arguing, infinitesimal
>> does not exist. What is the difference with POO Halt !!!
>>
>> How can we arguing this for a definite answer? No, we cannot.
>> If we want a definite answer or a number containing infinity/infinitesimal in
>> its expression definite, make the meaning unique first as I did.
>
> Let's say "-∞ <------ 0 ------> +∞" denotes the x-axis in textbooks.
> The message the schematic conveys should be: -∞<0<+∞ (note that '∞' is now
> 'legitimately' decorated with signs).
> Assume "-∞<0<+∞" is accepted [note1]. And, to express the notion of 'close' or
> 'arbitrarily approaching to', we assume there are special rules that '∞'
> interacts with normal numbers. To express "x+1 closer than x to ∞":

But that step presumes that we are ALLOWED to mix ∞ with other numbers
in the mathematical operators.

Yes, we can define the "order" relationships on this "extended value" of
infinity, but that doesn't mean that it has fully been broght into the
family.

In fact, we find that we can't even say that ∞ == ∞, as that is enough
to cause problems. Infinities are ordered with the Reals, but only very
limited with each other. -∞ < ∞ but that is about all we can say.

>
> 1) ∞-(x+1) < ∞-x
> 2) ∞-x-1 < ∞-x
> 3) ∞-1 < ∞
> 4) ∞ < ∞+1
>
> Whatever the idea of '∞' is, as long as its meaning is unique, the notion of '∞'
> must lead to the notion "∞ < ∞+1" being true (Is not x+1 closer than x by one
> to infinity?).

And you stated part of the problem, in a real sense ∞ is NOT "unique",
there are MANY infinities that all have some common properties, but they
are not all the same.

>
> [note1] You can refute "-∞<0<∞", but you would need to establish a 'theory' to
> explain this assumed intermediate step. You need to explain lots more than simple
> denial, explain enough to replace what is in the textbooks. Note that,
> whatever you do is likely your own, not what the textbooks mean to say.
> [note2] What does "arbitrarily close to" mean? Note the word 'distance' in
> https://en.wikipedia.org/wiki/Limit_(mathematics)
> Where is the approaching value of x from? Is it not the density property
> guarantee you "For any two different numbers there exists a DIFFERENT
> number", so you can find another x in between? What is wrong if we use
> rational number x to approach like ancient Pythagorean did? Is the
> result still valid by the limit argument? Why in the final, 'approach'
> becomes 'equal', the x EQUALS to c, f(c)=L, the density property is
> abandoned?
> The limit theory has no concept of equality in its premise, it cannot
> logically deduce the equality conclusion, except limit defines equality.
> [note3] All decimals are real number, including infinitely long decimals. This is
> general recognition, not any standard. Finite number of symbols cannot
> define all of them. Actually, lots (technically almost all) of real numbers
> are each not definable. What the Dedekind-cut like theory claims is false
> (I don't need to look inside deep, circular arguments/definition should exist).

On Friday, 19 August 2022 at 13:50:47 UTC+2, richar...@gmail.com wrote:
> > Without explaininng the choice.
> Then you aren't communicating. You need to use the one that is
> applicable, as would be agreed upon.
Applicable to WHAT? There is zero context!

Definition/function APPLICATION is applied to concrete objects.
Not an abstract one.

> You are just proving you are anti-social and unable to effectively work
> with others.
What WORK, dickhead? There is no task on the table.

Do you even understand how synchronization works? You've made EVERY attempt to hinder communication/synchronization with your abstract sophistry.

https://en.wikipedia.org/wiki/Synchronization_(computer_science)

> Yes, but a GIVEN Mathematics is GIVEN.
So GIVE it! GIVE me the Mathematics for the Real numbers. Where is it ?!?!?!

ENCODE it.
TRANSMIT it.
COMMUNICATE it.

> Thus things like "The Real Numbers" have precise definitions.
You can't even precisely define "precise", you sophist!

> Thus, we need to be clear WHICH Mathematics we are talking in, and why
> there are "defaults" when not specified.
It has helped you NOTHING. You have made it abundantly clear that whatever numbers you are talking about, it can't possibly be the standard Real numbers.

> > Only YOU know. But you can't tell me.
> Because it has been well defined for a long time but you can't seem to
> understand it.
The standard definition is incomprehensible.

Maybe your understanding is much better. It's a shame you can't communicate it.

> And that is where you are wrong. "Numbers" exist, they have been defined
I don't see how that's possible. "define" is undefined.

I mean, I can define you out of existence, but you are still there...
You must be missing something about HOW definitions work.
> > Absolutely everything you are DOING can be re-interpreted from the lens of homotopy type theory/Univalent foundations.
> Apparently not, since you seem to be unable to handle some of the concepts.
Like you can't handle the concept of understanding understanding?

Yeah, function self-application is tricky to idiots who restrict comprehension.

> > Without the need to cling onto the self-deception about your system being "consistent".
> We assume consistentcy until proven wrong (but accept that it is a
> possibility)
It's an obvious fact to any software engineer. Your system represents, references and de-references NULL-types.

Any non-idiot knows that's a runtime error.

> Can you prove it isn't? NOTE, the proof needs to follow the rules of or it isn't applicable, and so far it seems that is beyond your mental ability.
> the system
Bullshit. There's the system and there's the meta-system.

Your foundations. The fact that your brain can't handle the null-pointer exceptions is just another clusterfuck in the system.

> knowledge-synchronization is based on having inadequate tools for the Job?
What Job? You haven't specified a task.
> YOU are the one that made the fight, as you want to disagree with how
> things are.
Bullshit. I am pointing out that your description/definition of the Real Numbers fails to capture how things are!

> You seem to be doing a pretty good job at beating yourself up though, so
> GOOD JOB. Keep it up and you will totally defeat yourself.
There's no such thing as self-defeat. Let me demonstrate.

This sentence defeats it self.

Look! It's still there. You've been confusing self-affirmation for self-defeat all along. You dumb Mathematician!

On 8/19/22 7:46 AM, Skep Dick wrote:
> On Friday, 19 August 2022 at 13:11:36 UTC+2, richar...@gmail.com wrote:
>> Nope. You are just using wrong definition to get your wrong answer.
>>
>> You use the wrong definition because you refuse to define what system
>> you are in.
> I don't know in what language I must say this to you! I am not IN the system. I am OUTSIDE of the system.

Then you can't talk about a system you are in if you aren't in one.

Note, operators are defined INSIDE systems, generally with abstract
propertied that hold across many systems, but they are only fully
defined in a given system.

If you aren't "In" a system, you have no fully defined operatiors to
work with.

>
> Do you actually understand the difference between the internal and external languages of a theory?
>
> I am using Operational Semantics.
> I am NOT using denotational semantics!

So you are talking about programming and not logic.

or maybe you aren't actually talking about Operational Semantics, since
you won't let yourself be defined.

>
> Do you actually grok the difference?!?
>
> There is no such thing as a "wrong" definition, you numbskull! I define this color as green: 🔴

>
>> If you don't know where you are, you can't know how to get to anywhere.
> I know precisely where I am. That can't be said about you. Standing at the 0 of the Real number line.

Nope, you THINK you know where you are, but you lost your landmarks as
you refuse to look at them.
>
>
>> You are confusing the representation of the number with the number.
> No, I am not.
>
> YOU-the-human are never operating with the numbers.
> YOU-the-human are ALWAYS operating with the representations.

>
> Show me the number 0! Not the symbol representing it.

"Show" is representational, so question is incorrect.

>
>> You fail to understand the concept of what the number actually is.
> OK! So teach me. Tell me something about the number 0.

You have shown yourself to be too dumb for that.

>
>
>> Yes, the Reals are not "Computable" by finite automation. That doesn't
>> mean they don't exist and have actual properties, and that the
>> operations like addition and subtracttion aren't actually definied for them.
> Oooooh! Is that how it works. Well i can DEFINE division by zero also!
>
> Look! It type-checks and everything!
>
> # let divide_by_0 x = x /. 0.;;
> val divide_by_0 : float -> float = <fun>
>
> But can i APPLY the operation to any numerator? Well look at here! I can apply it also!
> On a finite automation!
>
> # divide_by_0 10.0 ;;
> - : float = infinity

WHich says that you number system isn't the Real Number system.

>
>
>> Just says that no computer (or computation per a finite computaiton
>> theory) can actually deal with them.
> Mine just did. Is your computer broken?

Ok, does it know the exact value of pi?

>
>> That shows that not everything can be a computation, computable, or a
>> program.
> Sophist. Computation is symbol manipulation.

Right, but FINITE symbol mannipulation,

>
> Every manipulation you can do with pen/paper - the computer can do also.

Ok, but not every manipulation I can do in my mind.

>
>
>>> Look, sophist. This is not a theoretical limit! This is the limit of how humans DO subtraction, addition and multiplication.
>> Nope, it is how humans do things when they are working in the concrete.
> Uhuh. So you are not working with concrete numbers?!? What are you working with then?

Numbers, in their absract form.

>
>
>> I guess your mind can't switch to abstract computation mode, becuase
>> that processor is broken in yours.
> You keep lying about that.

How is it a lie, you seem totally unable to even imagine your mind
working in the abstract field.

>
>>> We start with the most significant digit. Which is the right-most digit and we "borrow" from the digits on the left.
>> Only when in concrete mode. In abstract mode we do things like start on
>> the line at the location of the first number and move back a distance
>> specified by the second.
> Fucking idiot! x > y is abstract mode. The proposition "x > y" translates PRECISELY into English as "Is X to the right of Y?"
>
> Maybe yes -∞<----------y-------x----------> +∞
> Maybe no: -∞<----------x-------y----------> +∞

So why did we switch form the value of x - y to is x > y?

>
>>> Otherwise they are useless in practice.
>> Nope. You can do useful stuff and stay in the abstract
> Oh can you?!? OK show me!
>
> Given the proposition x>y (N.B NOT the theorem!)
>
> which is the "correct" representation of the continuum?
>
> -∞<----------y-------x----------> +∞ OR -∞<----------x-------y----------> +∞
>
>>> "empirical proof" is an oxymoron. There are no proofs outside the formal sciences.
>> Depends on your definitions.
> I am using the standard definition of "proof" from "proof theory" as accepted by the general Mathematical community!
>
> I guess you were lying about using the standard model. Asshole.

I think you are looking at the definition of a Analytical Proof, which
admittedly is often just shortened to "Proof", but when you look at the
actual definitions and root down to the core concepts, Emperical Facts
are proven.

Note, only certain type of propositions CAN be emperically proven.

A "There exists" proposition can be proven by showing an example that fits.

A "For All" or "No" proposition needs to be shown "For All" and since
many sets are unbounded or infinite, that can't be just "demonstrated"
emperically.

On 8/19/22 7:47 AM, Skep Dick wrote:
> On Friday, 19 August 2022 at 13:22:46 UTC+2, richar...@gmail.com wrote:
>>>
>> And 0 is bounded, so not a problem.
>
> By what ?!? When constructing R the first number you identify is 0.
>
> What is it bounded by? -1 and 1?! That doesn't count. Those aren't bounded either!
>

But that just shows you don't understand the definition, Yes -1 and 1
are bounds.

One way starts with 0 DEFINED as bounded, as a First Principle.

Then we have the inductive principle that if N is bounded, then N+1 is
bounded, and that lets us bound all the Natural Numbers

This doesn't get you to w, as w-1 can't be shown to be bounded.

On 8/19/22 7:49 AM, Skep Dick wrote:
> On Friday, 19 August 2022 at 13:23:47 UTC+2, richar...@gmail.com wrote:
>>> That is you (according to you).
>> Then what is it?
> I have NO fucking idea.

Then why to you put down others that say it doesn't exist?

>
> I don't have access to ordinal time! It's just an abstract model.
>
> Can't you work with abstractions, man?
>
>
>
>
>

On Friday, 19 August 2022 at 14:23:53 UTC+2, richar...@gmail.com wrote:
> On 8/19/22 7:49 AM, Skep Dick wrote:
> > On Friday, 19 August 2022 at 13:23:47 UTC+2, richar...@gmail.com wrote:
> >>> That is you (according to you).
> >> Then what is it?
> > I have NO fucking idea.
> Then why to you put down others that say it doesn't exist?

Which part of ASKING are you misinterpreting as "put-down" you fucking cuntwaffle?

If you tellme that you can see "past the end of infinities" I believe you at face value! This is as charitable as I can possibly get about such claims!

It is precisely because YOU can see past the end of infinities and I can't is WHY I am asking YOU to tell me what the last digit of pi is!