Alan Mackenzie <acm@muc.de> writes:
> Skep Dick <skepdick22@gmail.com> wrote:
>> On Wednesday, 17 August 2022 at 01:04:38 UTC+2, richar...@gmail.com wrote:
>>> Nope, a given Mathematics tends to be fairly absolute.
>> Really? Which property of a given Mathematics is its "absoluteness"?
>
> That 1 + 1 = 2, for example.

Not true for the group of integers modulo 2.

[...]

--
Keith Thompson (The_Other_Keith) Keith.S.Thompson+u@gmail.com
Working, but not speaking, for Philips
void Void(void) { Void(); } /* The recursive call of the void */

On Tuesday, August 16, 2022 at 4:25:28 PM UTC-7, Skep Dick wrote:
>
> You like your definitions so much lets drop ℝ altogether. Lets start with the continuum.
> ( -∞, ∞ )
>
> -∞ <-------------------------------------> +∞
>
> Give me an algorithm to find 0.
>
Any member of the continuum can be taken as 0. All such
selections are isomorphic.

Skep Dick <skepdick22@gmail.com> writes:

> On Tuesday, 16 August 2022 at 03:46:58 UTC+2, Ben Bacarisse wrote:
>> Why would you do that? Anyway, don't worry; I do like you saying it.
>> Say it again and again, please.
> At your service...
>
> The expression "lim(x -> 0)" means exactly the same thing as "lim(x-> ∞)"
> when 0 is bound to ∞

No it doesn't. Sources of wisdom are readily available.

--
Ben.

On 8/16/22 7:25 PM, Skep Dick wrote:
> On Wednesday, 17 August 2022 at 00:44:38 UTC+2, richar...@gmail.com wrote:
>> And 1, 2, 3, ... are bound to a value concept, and ∞ is bound to a
>> non-value concept.
> Distinction without a difference.

makes a big differene.

>
>> And they are pointers of objects of different types.
> You don't understand dependent types.

Maybe you don't, since the definition of limit IS different between a
Real Limit and an "infinite" limit.

Use the wrong definition, you get the wrong results

That seems to be a common problem for you, you don't understand that
context affect meaning.

Note, I think you just blew up your system.

>
>> Nope because ∞ isn't a Real Number, but the concept of Infinity.
> Distinction without a difference. It's a parameter to a function.
>
> It does some work. Like every other symbol does some work.

So, you think that type doesn't matter. Use the factorial function and
computer 1.5!

You find that the type of the input DOES matter.

>
>
>>>
>>> Here is your number line ℝ: 0 |-----------------------------------------> ∞
>>>
>>> Could you please draw me a line where a finite number in ℝ begins approaching ∞?
>> Here is the number line ℝ:
>> <-----------------| 0 |---------------->
>>
>> "∞" isn't ON the Real Number Line, since it isn't a Real Number
>>
>> I suppose you could also notate it as: ( -∞, ∞ )
>>
>> Since the open interval doesn't include the end points.
> Idiot. You forgot to address the actual question.

No, I did, you just don't understand the answer.

>
> Where on ℝ do the finite numbers begin approaching ∞?
> You know damn well I meant ℝ+ you twat. I even drew you a picture.

You said Reals, not Positive Reals. Maybe you should say what you man.

Just replace the lower bound with [0 then.

>
> But just as well as you want to play dumb - draw me two lines instead.
> Where on ℝ do the finite numbers begin approaching -∞ and +?

Meaningless question. WHere do numbers start to approach 2?

You could say that for the positive real numbers All number are starting
to approach infinity, since for some limit process, the limit inequality
might be true for all real numberss.

For instance, for the lim(x -> inf) sin(x) / (1 + x*x)

When the error e is > 1, then the bound is statisfied for ALL s, so all
x are "approaching infinity".

For an e less than one, we get a limited region that is "appraching
infinity",

>
>
>>> Bullshit. I don't care about the value of the limit.
>> Then why are you talking about it.
> I am talking about infinity. You said it's not a value.
>
> Have you changed your mind?
>
>> lim( x:ℝ -> ∞ ) F(x) means what number L, if it exists, statisfies the
>> property that for any positve number e, we can find a bound X such that
>> for ALL x > X, | f(x) - L | < e
> Why are you blabbering about stuff that nobody is asking you about?
>
> I asked you what "lim( x:ℝ -> ∞ )" means, not what "lim( x:ℝ -> ∞ ) F(x)" means.

It doesn't mean anything, as you need to take the limit of SOMETHING.
What does integral mean then without a function to integrate?

>
>>> if ALL numbers in ℝ are finite, and NO finite number is closer to infinity than any other then what the fuck does it mean for a real number to approach infinity?
>> We don't talk about NUMBERS approaching infinity, but of the parameter
>> to the function approaching infinity.
> Idiot. The parameter to the function is a number.
>
> "lim( x:ℝ -> ∞ )" means "as the parameter to the function approaches infinity".

What function?

>
> But ALL x in ℝ are finite. NO number in ℝ is any closer to infinity than any other number in ℝ.

Not quite. Larger numbers are "closer" but we can't measure how much closer.

Remember the bounding is for a given e we get the interval the function
satisfies is for x > X, so a large X requires the domain to be "closer"
to infinity.

>
>> That means you don't ACTUALLY know how to properly do things, because if
>> you don't know the rules, you don't know if you are obeying them.
> What rules? Show them to me already!
>
> You like your definitions so much lets drop ℝ altogether. Lets start with the continuum.
> ( -∞, ∞ )
>
> -∞ <-------------------------------------> +∞
>
> Give me an algorithm to find 0.
>
>
>
>
0
Its a defined point.

On 8/16/22 7:44 PM, Skep Dick wrote:
> On Wednesday, 17 August 2022 at 01:04:38 UTC+2, richar...@gmail.com wrote:
>> Nope, a given Mathematics tends to be fairly absolute.
> Really? Which property of a given Mathematics is its "absoluteness"?

In a given mathematics, what it the results of a defined operation.

It is the defined answer(s) and only that.

THat seems pretty absolute to me.

What makes it NOT absolute

>
>> You can chose different variations for some purposes, but a given
>> Mathematics is fairly rigid.
> It's no more or less "rigid" than the arbitrary choices made to construct it.

But once the rules ARE chosen, the results are determined.

>
>>> Anybody who thinks Mathematics pursues "truth" is a crank.
>> Why?
> Because Mathematics is invented and truth isn't.

Nope, just shows you don't actualy understand Mathematics.

>
>>> What an idiotic idea. What is it that they are studying?
>>> What did the first Mathematics graduate study?
>> Mathemmatics, and Truth.
> So how did the first mathematician study Mathematics when nobody had invented any Mathematics yet?

They investigated what it would do and saw what it defined?

From a few basic definitions, they DISCOVERED how things worked from
those rules.

>
>> No, yoru are disrespectful of Rules and the Tradiition of understanding.
> I am? It seems to me I have acquired far more understanding than you have without following the "Rules and Traditions".

Seems all you have found is a lack of order and chaos. Do you actualy
KNOW anything?

>
>> You forget where the stuff you think you know came from.
> It came from the people who invented it. There are no rules to invention.
>
>>> There is no truth in Mathematics. It's invented, not discovered.
>> Nope, much of Mathematics is actually discovered.
> Oh really? Where do you look for Mathematics?
>
>> You need to quite peddling your lies.
> You need to stop lying about me lying.
>
>> And the TRUE decision procedure says YOU are the crank.
> The TRUE decision procedure said that your decision procedure is broken.
>
>> Since YOU think everyone gets to decide on their own system, so do I,
>> and thus I get to decide what it the true system.
>>
>> You lose.
> I lose? You have literally conceded my point!
>
> Mathematics is relative! Made up. Constructed.
>
> Welcome to the science of Distributed Systems. Where the most important problems are consesus algorithms.
> https://en.wikipedia.org/wiki/Consensus_(computer_science)

On Wednesday, 17 August 2022 at 03:16:31 UTC+2, Ben Bacarisse wrote:
> Skep Dick <skepd...@gmail.com> writes:
>
> > On Tuesday, 16 August 2022 at 03:46:58 UTC+2, Ben Bacarisse wrote:
> >> Why would you do that? Anyway, don't worry; I do like you saying it.
> >> Say it again and again, please.
> > At your service...
> >
> > The expression "lim(x -> 0)" means exactly the same thing as "lim(x-> ∞)"
> > when 0 is bound to ∞
> No it doesn't. Sources of wisdom are readily available.
Yes. It does. It's just a symbol in your alphabet. It doesn't denote anything.

-0 <-------------------------> +0

Here's your continum.

On Wednesday, 17 August 2022 at 03:04:40 UTC+2, dklei...@gmail.com wrote:
> Any member of the continuum can be taken as 0. All such
> selections are isomorphic.
OK! So then...

-∞<----------------------0-> +∞

If all selections are isomorphic, I wonder what "x approaches infinity" could possibly mean!
Move left. Move right - you are always at zero.

On Wednesday, 17 August 2022 at 02:19:00 UTC+2, Alan Mackenzie wrote:
> That 1 + 1 = 2, for example.
That's not true. It depends on what + means.

> There is no such choice. If there were, there would be radically
> different mathematics in different cultures, much as there are radically
> differnt religions.
Which is precisely what you are observing. Have you bothered to read any history?

Base 2 mathematics for computer scientists.
Base 10 for the SI system.
Base 60 for the Babylonians.
Base 20 for the French

> Again, there is one system of maths and it is universal. If you were
> right, there would be several distinct systems.
There are several different systems!

Natural numbers.
Complex numbers.
Real numbers.
Surreal numbers.
p-addic numbers.

> The first mathematician likely grasped that 1 + 1 = 2 was an abstract
> truth. Or something like that.
It's just a notation/representation. The operator "+" could mean so many different things!

> Your mathematical understanding is at a low level. It is at such a low
> level, you have no concept of what it is you are ignorant of.
Oh, I don't know. I think it's beyond the grasp of Mathematics to understand what it means to understand.

> Yet, somehow, all the "inventors" of mathematics come up with the same
> thing.
They didn't. They all invented different things!

They can be USED for similar purposes sure. Because computation is universal, but the Mathematics is all made up.

> Reality, both concrete and abstract.
I've never seen a single symbol in reality outside those created by humans.

> I'm not convinced you're lying. Most likely you're just ignorant,
> _very_ ignorant.
All we need to figure out now is the inhabitant of this ignorant you-type.

Is it you; or is it me. A mystery!

> No, it is absolute, as demonstrated above. Bear in mind, I've studied
> it, you haven't.
You studied other people's invented notations.
I've invented notations that other people study.

As a creator of formal languages I think I understand it much better than you.

On Wednesday, 17 August 2022 at 03:37:16 UTC+2, richar...@gmail.com wrote:
> makes a big differene.
It makes absolutely none when you have to parametrize lim(x->y) and define its domain.

> > You don't understand dependent types.
> Maybe you don't, since the definition of limit IS different between a
> Real Limit and an "infinite" limit.
Yeah, non-sequitur.

A limit is a limit is a limit. It's a generic/polymorphic type.

> Use the wrong definition, you get the wrong results
We aren't talking about definitions. We are talking about TYPES.

What is the TYPE of lim(x -> y)f(x)

> That seems to be a common problem for you, you don't understand that
> context affect meaning.
Moron! That is PRECISELY what I am pointing at.

The context of a function is called its domain. It's encoded as a type signature.

> Note, I think you just blew up your system.

> So, you think that type doesn't matter. Use the factorial function and
> computer 1.5!

Idiot. The domain of the factorial function is the natural numbers.
Its type is N->N.

What's the type for lim(x->y) ?

> >> Since the open interval doesn't include the end points.
> > Idiot. You forgot to address the actual question.
> No, I did, you just don't understand the answer.
Obviously! I can't understand an answer that isn't there.

> You said Reals, not Positive Reals. Maybe you should say what you man.
Ahhh, I seee. Rules for me but not for thee. Asshole.

Maybe YOU should say what you mean?

Do you mean the countable; or the uncountable Reals?
Do you mean the Dedekind reals or the Cauchy reals?

There are so many reals!

> Just replace the lower bound with [0 then.
That's a bit of a problem you see. Does 0 belong to the nega

> > Where on ℝ do the finite numbers begin approaching -∞ and +?
> Meaningless question. WHere do numbers start to approach 2?
ANYWHERE!

Add any non-zero quantity to a number less than 2 and it approaches 2.
Subtract any non-zero quantity from a number greater than 2 - it approaches 2.

Exactly NOTHING like approaching infinity.

lim(x->2) is perfectly meaningful in R.
lim(x->∞) is meaningless in R.

> You could say that for the positive real numbers All number are starting
> to approach infinity, since for some limit process, the limit inequality
> might be true for all real numberss.
No. You can't say that at all!

Any real value moving away from 0 is not moving towards ∞
The distance ∞-x is constant, but the distance x-0 is increasing!

So is it that x is approaching infninty, or is it that 0 is moving away from x ?!?!

> For instance, for the lim(x -> inf) sin(x) / (1 + x*x)
> When the error e is > 1
What error?!? I thought you said Mathematics doesn't have errors if you follow the rules.

On Wednesday, 17 August 2022 at 03:42:00 UTC+2, richar...@gmail.com wrote:
> On 8/16/22 7:44 PM, Skep Dick wrote:
> > On Wednesday, 17 August 2022 at 01:04:38 UTC+2, richar...@gmail.com wrote:
> >> Nope, a given Mathematics tends to be fairly absolute.
> > Really? Which property of a given Mathematics is its "absoluteness"?
> In a given mathematics, what it the results of a defined operation.
> It is the defined answer(s) and only that.
> THat seems pretty absolute to me.
That is so pecular. You say "absolute" while carefuly detailing the relativity of Mathematics.

> What makes it NOT absolute
The fact that given Mathematics A has defined different answers to given Mathematics B.

> But once the rules ARE chosen, the results are determined.
So what? Rules can be unchosen and re-determined.

> > Because Mathematics is invented and truth isn't.
> Nope, just shows you don't actualy understand Mathematics.
It doesn't show anything like that, but obviously - it's all relative.

> They investigated what it would do and saw what it defined?
> From a few basic definitions, they DISCOVERED how things worked from
> those rules.
Can you try paraphrase this in English? I have no idea what you are saying.

> Seems all you have found is a lack of order and chaos.
Lack of order is not chaos. Why would you say that?

That's only the sort of nonsense authoritarians spew. Rule peddlers.

>Do you actualy KNOW anything?
I know that I don't have any knowledge.

And I know that you can't resolve that paradox.

On 8/16/22 11:03 PM, Skep Dick wrote:
> On Wednesday, 17 August 2022 at 03:37:16 UTC+2, richar...@gmail.com wrote:
>> makes a big differene.
> It makes absolutely none when you have to parametrize lim(x->y) and define its domain.

So I guess YOU need to define how you do it in your math.

>
>>> You don't understand dependent types.
>> Maybe you don't, since the definition of limit IS different between a
>> Real Limit and an "infinite" limit.
> Yeah, non-sequitur.
>
> A limit is a limit is a limit. It's a generic/polymorphic type.

But is defined DIFFERENTLY for a limit to a finite number and to infinity.

Its YOUR problem to figure out how to do it in YOUR mathematic system.

>
>> Use the wrong definition, you get the wrong results
> We aren't talking about definitions. We are talking about TYPES.
>
> What is the TYPE of lim(x -> y)f(x)

Maybe you need to define what you mean by "Type" here.

>
>> That seems to be a common problem for you, you don't understand that
>> context affect meaning.
> Moron! That is PRECISELY what I am pointing at.
>
> The context of a function is called its domain. It's encoded as a type signature.

And limit isn't a "function" in the normal sense, its imputs are a Limit
value, which can be either a finite value or an infinity, and a function
with a parameter with to domain of the reals.

I guess this says that the "Type" of the Limit operation is a function
of either a Real Number, or an Infinite, and a function of a real number.

>
>> Note, I think you just blew up your system.
>
>> So, you think that type doesn't matter. Use the factorial function and
>> computer 1.5!
>
> Idiot. The domain of the factorial function is the natural numbers.
> Its type is N->N.

Depends on the Mathemeatics you use. There are extensions of the
factorial function that apply to all element of C execpt for the
negatives of the Natural Numbers >= 0. (i.e., not defined at 0, -1, -2,
-3, -4)

If you can change number systems, so can I (to make a point).

>
> What's the type for lim(x->y) ?

Incomplete.

>
>>>> Since the open interval doesn't include the end points.
>>> Idiot. You forgot to address the actual question.
>> No, I did, you just don't understand the answer.
> Obviously! I can't understand an answer that isn't there.
>
>> You said Reals, not Positive Reals. Maybe you should say what you man.
> Ahhh, I seee. Rules for me but not for thee. Asshole.
>
> Maybe YOU should say what you mean?
>
> Do you mean the countable; or the uncountable Reals?

There is no "Countable Reals", the closest that I know of are the
Rationals, but that is a different number system.

> Do you mean the Dedekind reals or the Cauchy reals?

Doesn't matter. Those are alternate ways to GENERATE the real numbers,
but you get to the exact same set of numbers, provable by being able to
make a 1:1 mapping of the sets with no left overs, and the matching
items having the same properties.

>
> There are so many reals!

Nope, maybe multiple "programs" that can generate them, but the same
numbers result.

Your just stuck that they give different "symbols" that represent them,
but we can show that the representations give us the same numbers.
>

>> Just replace the lower bound with [0 then.
> That's a bit of a problem you see. Does 0 belong to the nega

WHy is that a problem.

Traditional Definition is:
Positive > 0
Non-Negative >= 0
Negative < 0
Non-Positive <= 0

>
>>> Where on ℝ do the finite numbers begin approaching -∞ and +?
>> Meaningless question. WHere do numbers start to approach 2?
> ANYWHERE!

So, as I said later, the begin to approach infinity anywhere.
>
> Add any non-zero quantity to a number less than 2 and it approaches 2.
> Subtract any non-zero quantity from a number greater than 2 - it approaches 2.
>
> Exactly NOTHING like approaching infinity.

No, Add a positve number to any number less than infinity (which are all
real numbers) and it is closer to infinity, as in it is include in more
bounding sets of limits then the original number was.

>
> lim(x->2) is perfectly meaningful in R.
> lim(x->∞) is meaningless in R.

Nope, I've given you the definition, if YOUR system can't handle it,
that's YOUR problem. I guess you broke it.

>
>> You could say that for the positive real numbers All number are starting
>> to approach infinity, since for some limit process, the limit inequality
>> might be true for all real numberss.
> No. You can't say that at all!
>
> Any real value moving away from 0 is not moving towards ∞
> The distance ∞-x is constant, but the distance x-0 is increasing!

Nope, you can't compute ∞-x, as ∞ isn't a number in the Reals, so -
isn't defined for it. It is a "Special" value witha "Special" definition
of "Closer" and "Approaching"

If you system has lost that distinction, that is YOUR problem.

>
> So is it that x is approaching infninty, or is it that 0 is moving away from x ?!?!

Your math is just broken.

>
>> For instance, for the lim(x -> inf) sin(x) / (1 + x*x)
>> When the error e is > 1
> What error?!? I thought you said Mathematics doesn't have errors if you follow the rules.

Did you not read the definition of a limit, it is based on the existance
of a bound of x for any allowed "error" in the value of the function
compared to the limit.

You seem to be slow on the pickup.

The Definition was:

Limit (x -> ∞) f(x) means find a value L such that for EVERY error e >
0, you can an X such that for all x > X, that |F(x) - L| < e

IF an L exists, it is the value of the limit.

On 8/16/2022 6:45 PM, Keith Thompson wrote:
> Alan Mackenzie <acm@muc.de> writes:
>> Skep Dick <skepdick22@gmail.com> wrote:
>>> On Wednesday, 17 August 2022 at 01:04:38 UTC+2,
>>> richar...@gmail.com wrote:
>>>> Nope, a given Mathematics tends to be fairly absolute.
>>> Really? Which property of a given Mathematics is its
>>> "absoluteness"?
>>
>> That 1 + 1 = 2, for example.
>
> Not true for the group of integers modulo 2.

Unfortunately, it is: 1 + 1 = 2 (mod 2). This is a question of
conventional use and meaning. If the group is meant to include only 1
and 0, then 2 could be undefined. However, it is conventional to define
2 as a synonym of 0.

In any event we assume a zero (0) and a successor function s - a plus
s(0) in the group. Then we say 1 = s(0) and either 2 = s(1) or 2 = s(0)
+ s(0), and assuming that "+" is the group operator we have no problem
showing that 1 + 1 = 2.

I think you know all of this and more. I think a troll has got you all
taking umbridge at each dumb dick diatribe.
--
Jeff Barnett

On 8/16/22 11:14 PM, Skep Dick wrote:
> On Wednesday, 17 August 2022 at 03:42:00 UTC+2, richar...@gmail.com wrote:
>> On 8/16/22 7:44 PM, Skep Dick wrote:
>>> On Wednesday, 17 August 2022 at 01:04:38 UTC+2, richar...@gmail.com wrote:
>>>> Nope, a given Mathematics tends to be fairly absolute.
>>> Really? Which property of a given Mathematics is its "absoluteness"?
>> In a given mathematics, what it the results of a defined operation.
>> It is the defined answer(s) and only that.
>> THat seems pretty absolute to me.
> That is so pecular. You say "absolute" while carefuly detailing the relativity of Mathematics.

Maybe that is our difference in definitions.

*A* Mathematics is absolute, and since you generally work a problem in
*A* Mathematics, you get absolute reuslt.

>
>> What makes it NOT absolute
> The fact that given Mathematics A has defined different answers to given Mathematics B.

And you are generally working in a specific mathematics.

I suppose the major execption is when you are comparing two mathematics.

>
>> But once the rules ARE chosen, the results are determined.
> So what? Rules can be unchosen and re-determined.

But not in a given system.

>
>>> Because Mathematics is invented and truth isn't.
>> Nope, just shows you don't actualy understand Mathematics.
> It doesn't show anything like that, but obviously - it's all relative.

Not in a given system.

If you don't fix your system, you can't know what you are allowed to do.

>
>> They investigated what it would do and saw what it defined?
>> From a few basic definitions, they DISCOVERED how things worked from
>> those rules.
> Can you try paraphrase this in English? I have no idea what you are saying.

By defining the basic operations and how they work, you have CREATED a
logical computation system.

Out of that, definite results occur.

For instance, when we DEFINE that two lines in a plane, perpedicular to
the same line are parrallel, and always keep the same distance apart,
(plus the other basic postulates) we create the universe of Plane
Geometry, and can DISCOVER the effect that happen as a result of that
definition.

Change that definition, and we can get Hyperbolic Geometry, which has
different properties that we can discover.

THere are still things we are trying to discoveer about even the Natural
Numbers that were simply defined, and much that we have alread discoved.

For instance, we have DISCOVERED (not invented, as it comes out of a
nature result of the basic definitions) formulas relating to the
approximate density of primes on the number line.

We are still trying to figure out if there is a "last" set of Twin
Primes, or it they keep on appearing. We have CONJETURES about this, but
we haven't discovered the answer.

>
>> Seems all you have found is a lack of order and chaos.
> Lack of order is not chaos. Why would you say that?

It is LITERALLY one of the definition of Chaos.

chaos: noun
A lack of order or regular arrangement:
clutter, confusedness, confusion, derangement, disarrangement, disarray,
disorder, disorderedness, disorderliness, disorganization, jumble, mess,
mix-up, muddle, muss, scramble, topsy-turviness, tumble.
Slang: snafu.

From The American Heritage® Roget's Thesaurus. Copyright © 2013, 2014
by Houghton Mifflin Harcourt Publishing Company. Published by Houghton
Mifflin Harcourt Publishing Company. All rights reserved.

>
> That's only the sort of nonsense authoritarians spew. Rule peddlers.
>
>> Do you actualy KNOW anything?
> I know that I don't have any knowledge.
>
> And I know that you can't resolve that paradox.

Then you think you are smarter than you are.

IF you actually HAD the knowledge that you didn't know, you might seek
to learn.

On Tuesday, August 16, 2022 at 7:14:11 PM UTC-7, Skep Dick wrote:
> On Wednesday, 17 August 2022 at 03:04:40 UTC+2, dklei...@gmail.com wrote:
> > Any member of the continuum can be taken as 0. All such
> > selections are isomorphic.
> OK! So then...
>
> -∞<----------------------0-> +∞
>
> If all selections are isomorphic, I wonder what "x approaches infinity" could possibly mean!
> Move left. Move right - you are always at zero.
>
I'll assume you are honestly in seek of an answer'

Once chosen 0 does not change and the isomorphism
stops being of interest. What "approaches infinity"
means is something else you have to define.

Jeff Barnett <jbb@notatt.com> writes:
> On 8/16/2022 6:45 PM, Keith Thompson wrote:
>> Alan Mackenzie <acm@muc.de> writes:
>>> Skep Dick <skepdick22@gmail.com> wrote:
>>>> On Wednesday, 17 August 2022 at 01:04:38 UTC+2,
>>>> richar...@gmail.com wrote:
>>>>> Nope, a given Mathematics tends to be fairly absolute.
>>>> Really? Which property of a given Mathematics is its
>>>> "absoluteness"?
>>> That 1 + 1 = 2, for example.
>> Not true for the group of integers modulo 2.
>
> Unfortunately, it is: 1 + 1 = 2 (mod 2). This is a question of
> conventional use and meaning. If the group is meant to include only 1
> and 0, then 2 could be undefined. However, it is conventional to
> define 2 as a synonym of 0.

That's not my understanding (the group by definition contains only the
members 0 and 1, and 2 does not exist), but it was a minor nitpick and
I'm not going to argue the point. I'll certainly agree that 1 + 1 = 2
whenever 1, +, =, and 2 have their usual meanings.

> In any event we assume a zero (0) and a successor function s - a plus
> s(0) in the group. Then we say 1 = s(0) and either 2 = s(1) or 2 =
> s(0) + s(0), and assuming that "+" is the group operator we have no
> problem showing that 1 + 1 = 2.
>
> I think you know all of this and more. I think a troll has got you all
> taking umbridge at each dumb dick diatribe.

--
Keith Thompson (The_Other_Keith) Keith.S.Thompson+u@gmail.com
Working, but not speaking, for Philips
void Void(void) { Void(); } /* The recursive call of the void */

> ...
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.

On Wednesday, 17 August 2022 at 14:34:47 UTC+8, 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.

Cut too many. I was responding to richar...@gmail.com

On Wednesday, 17 August 2022 at 06:16:49 UTC+2, Jeff Barnett wrote:
> In any event we assume a zero (0) and a successor function s - a plus
> s(0) in the group.
That's a cute sleight of hand...

You take the extensional view of s(0) when it suits you.
Mean while any intensional definition of s(x) is a recursively defined s(x) = x + 1
>assuming that "+" is the group operator we have no problem showing that 1 + 1 = 2.
So much assumption! Every child (before the usual indoctrination) understands that the "+" operator is polymorphic and its meaning is context-dependent!

Are you adding apples? 1+1 = 2.
Are you adding temperatures? 1+1= 1
Are you concatenating strings? 1+1=11

You bozos go through a lot of effort to undermine common-sense high-order intuitions.

On Wednesday, 17 August 2022 at 07:15:58 UTC+2, dklei...@gmail.com wrote:
> Once chosen 0 does not change and the isomorphism
> stops being of interest.
It stops being of interest ??!?!?!

-∞<----------------------0-> +∞
is isomorphic to
-∞<-0----------------------> +∞

It gang-rapes my intuition that the isomorphism is being preserved despite my moving the "0" left and right!

It is incredibly interesting to me that Mathematics is so unintuitive!

On Wednesday, 17 August 2022 at 06:12:41 UTC+2, richar...@gmail.com wrote:
> On 8/16/22 11:03 PM, Skep Dick wrote:
> > On Wednesday, 17 August 2022 at 03:37:16 UTC+2, richar...@gmail.com wrote:
> >> makes a big differene.
> > It makes absolutely none when you have to parametrize lim(x->y) and define its domain.
> So I guess YOU need to define how you do it in your math.
No! I am not going to. You are like a damn parrot.

Define it! Define it! Define it!

lim(x->y) is polymorphic/overloaded. Like all damn operators.

> > A limit is a limit is a limit. It's a generic/polymorphic type.
> But is defined DIFFERENTLY for a limit to a finite number and to infinity..
Which definition are you talking about? The intensional; or extensional one?

There is only ONE generic limit-type and its sub-types.
https://en.wikipedia.org/wiki/Subtyping

> Its YOUR problem to figure out how to do it in YOUR mathematic system.
My mathematic system is a superset of your mathematic system.

> > What is the TYPE of lim(x -> y)f(x)
> Maybe you need to define what you mean by "Type" here.
No! I am not going to bloody define it. I mean the conventional meaning of type from type theory.
Which type theory? Approximatelly ALL of them

> > The context of a function is called its domain. It's encoded as a type signature.
> And limit isn't a "function" in the normal sense, its imputs are a Limit
> value, which can be either a finite value or an infinity, and a function
> with a parameter with to domain of the reals.
If it has inputs, or outputs - it's a generic function!

If you are using it in more than onse sense - you are talking about sub-types.

> I guess this says that the "Type" of the Limit operation is a function
> of either a Real Number, or an Infinite, and a function of a real number.
So you don't know what generic types are.

f:: Any -> Any
> >> So, you think that type doesn't matter. Use the factorial function and
> >> computer 1.5!
> >
> > Idiot. The domain of the factorial function is the natural numbers.
> > Its type is N->N.
> Depends on the Mathemeatics you use. There are extensions of the
> factorial function that apply to all element of C execpt for the
> negatives of the Natural Numbers >= 0. (i.e., not defined at 0, -1, -2,
> -3, -4)
No, it doesn't depend on the Mathematics I use.

If Factorial(x) is a polymorphic function then there is only one generic type.
There may be sub-types for N, R and C, but the compiler can decide which implementation to use for Factorial(1.5).
> If you can change number systems, so can I (to make a point).
You aren't making a point. Because I am not "changing" number systems.

I have generic types which handle the necessary context switching.

> > What's the type for lim(x->y) ?
> Incomplete.
Obviously! Complete it. By giving me its type.

> > Do you mean the countable; or the uncountable Reals?
> There is no "Countable Reals"
Your ignorance is not an argument.

https://www.youtube.com/watch?v=4CBFUojXoq4

>the closest that I know of are the Rationals, but that is a different number system.
All Number systems are just instances of a Generic number-system type!

Polymorphism. Do you understand it?!?

> > Do you mean the Dedekind reals or the Cauchy reals?
> Doesn't matter. Those are alternate ways to GENERATE the real numbers.
GENERATE the real numbers? Hahahahaha!

So you finally acknowledge that numbers are invented not discovered?!?

Also, you are abusing the determiner "the". If there are TWO different ways to generate THE "Real numbers", then what do you mean by 'THE' Real numbers?
Which way of generating them is more Real?

> but you get to the exact same set of numbers, provable by being able to
> make a 1:1 mapping of the sets with no left overs, and the matching
> items having the same properties.
That's not true. You missed one property.

Countability.

> > There are so many reals!
> Nope, maybe multiple "programs" that can generate them, but the same
> numbers result.
Nothing to do with their number. It's to do with the semantic property of "countability".

> Your just stuck that they give different "symbols" that represent them,
> but we can show that the representations give us the same numbers.
Well that entirely depends on what you mean by "the same". There are so many different types of equality!

https://ncatlab.org/nlab/show/equality

> Traditional Definition is:
> Positive > 0
Sorry. This operation is undecidable for infinite precision real numbers.

> Non-Negative >= 0
Sorry. This operation is undecidable for infinite precision real numbers.

> Negative < 0
Sorry. This operation is undecidable for infinite precision real numbers.

> Non-Positive <= 0
Sorry. This operation is undecidable for infinite precision real numbers.

> >>> Where on ℝ do the finite numbers begin approaching -∞ and +?
> >> Meaningless question. WHere do numbers start to approach 2?
> > ANYWHERE!
> So, as I said later, the begin to approach infinity anywhere.
And you are lying.

The approach to a finite number begins anywhere. Because you can actually approach it.
The approach to infinity begins nowhere. Because you can't actually approach it.

Unless it's a number.

> > Exactly NOTHING like approaching infinity.
> No, Add a positve number to any number less than infinity (which are all
> real numbers).
So x < ∞ is decidable, but ∞ is not a number, but x <0 is undecidable? 😂😂😂😂😂😂😂😂

> and it is closer to infinity, as in it is include in more
> bounding sets of limits then the original number was.
GREAT! It sounds like you have a distance metric between real numbers and ∞!

So then... in English. The distance from (x+1) to infinity is smaller than the distance from x to infinity.
In symbols: ∞ - (x+1) < ∞ - x
By conventional wisdom that ∞ - any real number = ∞ it follows that 0 < 0

> > lim(x->2) is perfectly meaningful in R.
> > lim(x->∞) is meaningless in R.
> Nope, I've given you the definition, if YOUR system can't handle it,
> that's YOUR problem. I guess you broke it.
I think you are lying to yourself. My system can handle it.

It's YOUR system that can't. Except when you pretend it can.

> >> You could say that for the positive real numbers All number are starting
> >> to approach infinity, since for some limit process, the limit inequality
> >> might be true for all real numberss.
> > No. You can't say that at all!
> >
> > Any real value moving away from 0 is not moving towards ∞
> > The distance ∞-x is constant, but the distance x-0 is increasing!
> Nope, you can't compute ∞-x, as ∞ isn't a number in the Reals, so -
> isn't defined for it. It is a "Special" value witha "Special" definition
> of "Closer" and "Approaching"
Hahahahahaha. So your "standard system" needs "special definitions" to deal with intuitive notions such as distance!?!

The QUESTION "Is 2 closer to ∞ than 1?" is the exact same QUESTION (N.B! NOT a statement) as ∞ - 2 < ∞ - 1

> If you system has lost that distinction, that is YOUR problem.
My system can make more distinctions than yours it seems.

> > So is it that x is approaching infninty, or is it that 0 is moving away from x ?!?!
> Your math is just broken.
My math is broken!?! x > 0 is undecidable in your math for values abtrarily close to 0!

> >> For instance, for the lim(x -> inf) sin(x) / (1 + x*x)
> >> When the error e is > 1
> > What error?!? I thought you said Mathematics doesn't have errors if you follow the rules.
> Did you not read the definition of a limit, it is based on the existance
> of a bound of x for any allowed "error" in the value of the function
> compared to the limit.
Look, sophist. You can't calculate the error if you don't know the true value of a function!

> The Definition was:
>
> Limit (x -> ∞) f(x) means find a value L such that for EVERY error e >
> 0, you can an X such that for all x > X, that |F(x) - L| < e
HAHAHAHAHAHAHAH!!!!!!!! 😂😂😂😂😂😂😂😂

F(x) < e is undecidable for infinitely-precise values arbitrarily close to 0

On 8/17/22 3:08 AM, Skep Dick wrote:
> On Wednesday, 17 August 2022 at 07:15:58 UTC+2, dklei...@gmail.com wrote:
>> Once chosen 0 does not change and the isomorphism
>> stops being of interest.
> It stops being of interest ??!?!?!
>
> -∞<----------------------0-> +∞
> is isomorphic to
> -∞<-0----------------------> +∞
>
> It gang-rapes my intuition that the isomorphism is being preserved despite my moving the "0" left and right!
>
> It is incredibly interesting to me that Mathematics is so unintuitive!
>
>
>

Why is that a problem, many things that are True are unintuitive.

Especially when you throw things like infinity into the mix, as we have
trouble really understanding it.

Maybe the biggest part of the issue is you are thinking of infinity
being AT the > symbol, when actually that is telling you it isn't there
but off a REAL FAR DISTANCE in that direction.

On Wednesday, 17 August 2022 at 13:54:24 UTC+2, richar...@gmail.com wrote:
> Why is that a problem, many things that are True are unintuitive.
Because Truth in Mathematics is ALWAYS relative to a model!

And the model is semantic (intuition!) not syntactic (proofs).
> Especially when you throw things like infinity into the mix, as we have
> trouble really understanding it.
I mean... your first sign of trouble is the ∃ operator. Which one is true?

∃∞ or ¬∃∞ ?

And the answer is... whichever model you CHOOSE.
> Maybe the biggest part of the issue is you are thinking of infinity
> being AT the > symbol, when actually that is telling you it isn't there
> but off a REAL FAR DISTANCE in that direction.
Maybe your problem is that you think there is a DISTANCE metric to infinity?

On Wednesday, 17 August 2022 at 19:54:24 UTC+8, richar...@gmail.com wrote:
> On 8/17/22 3:08 AM, Skep Dick wrote:
> > On Wednesday, 17 August 2022 at 07:15:58 UTC+2, dklei...@gmail.com wrote:
> >> Once chosen 0 does not change and the isomorphism
> >> stops being of interest.
> > It stops being of interest ??!?!?!
> >
> > -∞<----------------------0-> +∞
> > is isomorphic to
> > -∞<-0----------------------> +∞
> >
> > It gang-rapes my intuition that the isomorphism is being preserved despite my moving the "0" left and right!
> >
> > It is incredibly interesting to me that Mathematics is so unintuitive!
> >
> >
> >
> Why is that a problem, many things that are True are unintuitive.
>
> Especially when you throw things like infinity into the mix, as we have
> trouble really understanding it.
>
> Maybe the biggest part of the issue is you are thinking of infinity
> being AT the > symbol, when actually that is telling you it isn't there
> but off a REAL FAR DISTANCE in that direction.

What direction? Explain why x+1 is CLOSER than x to infinity.

On 8/17/22 8:04 AM, Skep Dick wrote:
> On Wednesday, 17 August 2022 at 13:54:24 UTC+2, richar...@gmail.com wrote:
>> Why is that a problem, many things that are True are unintuitive.
> Because Truth in Mathematics is ALWAYS relative to a model!
>
> And the model is semantic (intuition!) not syntactic (proofs).
>
>> Especially when you throw things like infinity into the mix, as we have
>> trouble really understanding it.
> I mean... your first sign of trouble is the ∃ operator. Which one is true?
>
> ∃∞ or ¬∃∞ ?
>
> And the answer is... whichever model you CHOOSE.

And the model you choose affects what operations are defined on all values.

>
>> Maybe the biggest part of the issue is you are thinking of infinity
>> being AT the > symbol, when actually that is telling you it isn't there
>> but off a REAL FAR DISTANCE in that direction.
> Maybe your problem is that you think there is a DISTANCE metric to infinity?
>
>

Nope, that your problem, You can have a comparative order without a metric.

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.