On Friday, 12 August 2022 at 22:04:33 UTC+8, Mr Flibble wrote:
> On Fri, 12 Aug 2022 06:58:27 -0700 (PDT)
> Skep Dick <skepd...@gmail.com> wrote:
>
> > On Friday, 12 August 2022 at 15:47:51 UTC+2, Mr Flibble wrote:
> > > 0.999... = 1.0, proof:
> > >
> > > S = 0.999...
> > > S * 10 = 9.999...
> > > S * 10 - S = 9.0
> > > S * 9 = 9.0
> > > S = 1.0
> > > ergo 0.999... = 1.0 QED
> > >
> > > /Flibble
> > if 0.999.. is convergent then the proof is valid.
> > if 0.999... is divergent then the proof is invalid.
> >
> > Is 0.999... convergent or divergent?
> >
> > That's undecidable. Subject to choice.
> Bullshit. 0.999... = 1.0 as I have just shown.
>
> /Flibble

S = 0.999...
S * 10 = 9.999...

An assumption is hidden here (deliberate?)
10*S= 9+S
This line specifies what the property of THE "0.999..." you mean (remove "...").
This property is 'unknown', not a 'given'.

S * 10 - S = 9.0
S * 9 = 9.0
S = 1.0
ergo 0.999... = 1.0 QED

On Friday, 12 August 2022 at 22:11:39 UTC+8, Skep Dick wrote:
> On Friday, 12 August 2022 at 16:04:33 UTC+2, Mr Flibble wrote:
> > On Fri, 12 Aug 2022 06:58:27 -0700 (PDT)
> > Skep Dick <skepd...@gmail.com> wrote:
> >
> > > On Friday, 12 August 2022 at 15:47:51 UTC+2, Mr Flibble wrote:
> > > > 0.999... = 1.0, proof:
> > > >
> > > > S = 0.999...
> > > > S * 10 = 9.999...
> > > > S * 10 - S = 9.0
> > > > S * 9 = 9.0
> > > > S = 1.0
> > > > ergo 0.999... = 1.0 QED
> > > >
> > > > /Flibble
> > > if 0.999.. is convergent then the proof is valid.
> > > if 0.999... is divergent then the proof is invalid.
> > >
> > > Is 0.999... convergent or divergent?
> > >
> > > That's undecidable. Subject to choice.
> > Bullshit. 0.999... = 1.0 as I have just shown.
> OK, genius.
>
> S = 1 + 2 + 3 + 4...
> S = 1 + (2 + 3 + 4) + (5 + 6 + 7)...
> S = 1 + 9 + 18 + 27...
> S = 1 + 9(1 + 2 + 3 + 4...)
> S = 1 + 9S
> S = -1/8
>
> ergo 1 + 2 + 3 + 4... < 0

See my solution in previous post about infinite series. All (hope) are solved.
(It seems people didn't read my post? just talking about their beliefs and pretend
they are talking about fact and truth.)

On Friday, 12 August 2022 at 15:11:39 UTC+1, Skep Dick wrote:
> On Friday, 12 August 2022 at 16:04:33 UTC+2, Mr Flibble wrote:
> > On Fri, 12 Aug 2022 06:58:27 -0700 (PDT)
> > Skep Dick <skepd...@gmail.com> wrote:
> >
> > > On Friday, 12 August 2022 at 15:47:51 UTC+2, Mr Flibble wrote:
> > > > 0.999... = 1.0, proof:
> > > >
> > > > S = 0.999...
> > > > S * 10 = 9.999...
> > > > S * 10 - S = 9.0
> > > > S * 9 = 9.0
> > > > S = 1.0
> > > > ergo 0.999... = 1.0 QED
> > > >
> > > > /Flibble
> > > if 0.999.. is convergent then the proof is valid.
> > > if 0.999... is divergent then the proof is invalid.
> > >
> > > Is 0.999... convergent or divergent?
> > >
> > > That's undecidable. Subject to choice.
> > Bullshit. 0.999... = 1.0 as I have just shown.
> OK, genius.
>
> S = 1 + 2 + 3 + 4...
S = infinity
> S = 1 + (2 + 3 + 4) + (5 + 6 + 7)...
S = infinity
> S = 1 + 9 + 18 + 27...
S = infinity
> S = 1 + 9(1 + 2 + 3 + 4...)
S = 1 + 9 * infinity
> S = 1 + 9S
S (infinity) =1 + 9 * infinity
> S = -1/8
infinity = -1/8. That's the point at which you go wrong. infinity = 1 + infinity,
but we can't subtract infinity from both sides of the equation to obtain 1 = 0
then use that result to prove theorems about the natural numbers.
>
> ergo 1 + 2 + 3 + 4... < 0
>
As you are obviously well aware. The algebra is good as a high school sort
of joke demonstration, but it's just based on a sleight of hand.

On Friday, 12 August 2022 at 17:00:52 UTC+2, malcolm.ar...@gmail.com wrote:
> That's the point at which you go wrong. infinity = 1 + infinity,
That's not true in *R ! Infinitesimals (ε) and infinities (ω) exist.

1/ε = ω/1

> but we can't subtract infinity from both sides of the equation to obtain 1 = 0
In your number system! Not in mine.

1/ε + 1 < 1/ε
ω < ω + 1

This is obvious to children but not to over-educated idiot Mathematicians.

X + 1 is ALWAYS more than X !

> As you are obviously well aware. The algebra is good as a high school sort
> of joke demonstration, but it's just based on a sleight of hand.
You have been lied to all your life.

The sleight of hand is by the Establishment of Mathematics.

0.999... = 1 is false, and infinity + 1 > infinity in any system where x+1 > x

On Fri, 12 Aug 2022 08:09:52 -0700 (PDT)
Skep Dick <skepdick22@gmail.com> wrote:

> On Friday, 12 August 2022 at 17:00:52 UTC+2, malcolm.ar...@gmail.com
> wrote:
> > That's the point at which you go wrong. infinity = 1 + infinity,
> That's not true in *R ! Infinitesimals (ε) and infinities (ω) exist.
>
> 1/ε = ω/1
>
> > but we can't subtract infinity from both sides of the equation to
> > obtain 1 = 0
> In your number system! Not in mine.
>
> 1/ε + 1 < 1/ε
> ω < ω + 1
>
> This is obvious to children but not to over-educated idiot
> Mathematicians.
>
> X + 1 is ALWAYS more than X !
>
> > As you are obviously well aware. The algebra is good as a high
> > school sort of joke demonstration, but it's just based on a sleight
> > of hand.
> You have been lied to all your life.
>
> The sleight of hand is by the Establishment of Mathematics.
>
> 0.999... = 1 is false, and infinity + 1 > infinity in any system
> where x+1 > x
0.999... = 1.0 as I have shown and demonstrated, QED.

/Flibble

On Fri, 12 Aug 2022 08:09:52 -0700 (PDT)
Skep Dick <skepdick22@gmail.com> wrote:

> On Friday, 12 August 2022 at 17:00:52 UTC+2, malcolm.ar...@gmail.com
> wrote:
> > That's the point at which you go wrong. infinity = 1 + infinity,
> That's not true in *R ! Infinitesimals (ε) and infinities (ω) exist.
>
> 1/ε = ω/1
>
> > but we can't subtract infinity from both sides of the equation to
> > obtain 1 = 0
> In your number system! Not in mine.
>
> 1/ε + 1 < 1/ε
> ω < ω + 1
>
> This is obvious to children but not to over-educated idiot
> Mathematicians.
>
> X + 1 is ALWAYS more than X !
>
> > As you are obviously well aware. The algebra is good as a high
> > school sort of joke demonstration, but it's just based on a sleight
> > of hand.
> You have been lied to all your life.
>
> The sleight of hand is by the Establishment of Mathematics.
>
> 0.999... = 1 is false, and infinity + 1 > infinity in any system
> where x+1 > x

No.

infinity + 1 = infinity.

/Flibble

On Friday, 12 August 2022 at 17:25:16 UTC+2, Mr Flibble wrote:
> No.
>
> infinity + 1 = infinity.
>
> /Flibble
Fucking idiot.

∀x : x + 1 > x

On Friday, 12 August 2022 at 17:23:47 UTC+2, Mr Flibble wrote:
> On Fri, 12 Aug 2022 08:09:52 -0700 (PDT)
> Skep Dick <skepd...@gmail.com> wrote:
>
> > On Friday, 12 August 2022 at 17:00:52 UTC+2, malcolm.ar...@gmail.com
> > wrote:
> > > That's the point at which you go wrong. infinity = 1 + infinity,
> > That's not true in *R ! Infinitesimals (ε) and infinities (ω) exist.
> >
> > 1/ε = ω/1
> >
> > > but we can't subtract infinity from both sides of the equation to
> > > obtain 1 = 0
> > In your number system! Not in mine.
> >
> > 1/ε + 1 < 1/ε
> > ω < ω + 1
> >
> > This is obvious to children but not to over-educated idiot
> > Mathematicians.
> >
> > X + 1 is ALWAYS more than X !
> >
> > > As you are obviously well aware. The algebra is good as a high
> > > school sort of joke demonstration, but it's just based on a sleight
> > > of hand.
> > You have been lied to all your life.
> >
> > The sleight of hand is by the Establishment of Mathematics.
> >
> > 0.999... = 1 is false, and infinity + 1 > infinity in any system
> > where x+1 > x
> 0.999... = 1.0 as I have shown and demonstrated, QED.

You are wrong. As I have shown.

There goes your God.

Skep Dick wrote:
> On Friday, 12 August 2022 at 17:25:16 UTC+2, Mr Flibble wrote:
>> No.
>>
>> infinity + 1 = infinity.
>>
>> /Flibble
> Fucking idiot.
>
> ∀x : x + 1 > x

What non-standard system of numbers are you using?

On Friday, 12 August 2022 at 17:29:50 UTC+2, Python wrote:
> > ∀x : x + 1 > x
> What non-standard system of numbers are you using?

I am using the standard system!

Adding 1 to ANYTHING makes it more.

Any system that says otherwise is the bullshit system.

Skep Dick wrote:
> On Friday, 12 August 2022 at 17:29:50 UTC+2, Python wrote:
>>> ∀x : x + 1 > x
>> What non-standard system of numbers are you using?
>
> I am using the standard system!
>
> Adding 1 to ANYTHING makes it more.

There is no infinity in the standard system for real numbers,
so you cannot say you're using the standard system.

> Any system that says otherwise is the bullshit system.

Have you heard about transifinite cardinals (or ordinals)? In
such systems ∀x : x + 1 > x is wrong. And they are not
"bullshit systems".

On Friday, 12 August 2022 at 17:45:44 UTC+2, Python wrote:
> There is no infinity in the standard system for real numbers,
> so you cannot say you're using the standard system.
You confused about WHICH system we are talking about.

I am not talking about the standard system for real numbers.
I am talking about the standard system of Mathematics.

In the standard system of Mathematics : ∞ + 1 = ∞

Which is exactly the same thing as saying.
x + 1 = x when x is bound to ∞

But if infinity is not a number then how the hell are you binding it to a variable?!?!?

> Have you heard about transifinite cardinals (or ordinals)? In
> such systems ∀x : x + 1 > x is wrong. And they are not "bullshit systems".
They are bullshit systems.

The ω in "1/ε = ω/1" is Omega. Cantor's Ω - the Absolute Infinite!
https://en.wikipedia.org/wiki/Absolute_Infinite

∀x : x + 1 > x !!!!!!!!!!!!
let x = Ω

THEN Ω + 1 > Ω

Skep Dick wrote:
> On Friday, 12 August 2022 at 17:45:44 UTC+2, Python wrote:
>> There is no infinity in the standard system for real numbers,
>> so you cannot say you're using the standard system.
> You confused about WHICH system we are talking about.
>
> I am not talking about the standard system for real numbers.
> I am talking about the standard system of Mathematics.

"standard system of mathematics" means what? The usual number
system? There is no ∞ there. Something else, then WHAT?

> In the standard system of Mathematics : ∞ + 1 = ∞
>
> Which is exactly the same thing as saying.
> x + 1 = x when x is bound to ∞
>
> But if infinity is not a number then how the hell are you binding it to a variable?!?!?

So again, when dealing with ∞, what system do you conside ? What is
the definition of ∞ there?

>> Have you heard about transifinite cardinals (or ordinals)? In
>> such systems ∀x : x + 1 > x is wrong. And they are not "bullshit systems".
> They are bullshit systems.

No they are not. You just don't know them.

And now I know that you are a crank (not that I doubted much...)

> The ω in "1/ε = ω/1" is Omega. Cantor's Ω - the Absolute Infinite!
> https://en.wikipedia.org/wiki/Absolute_Infinite
>
> ∀x : x + 1 > x !!!!!!!!!!!!

Not necessarily. You say so, that's not a proof.

On Fri, 12 Aug 2022 09:03:08 -0700 (PDT)
Skep Dick <skepdick22@gmail.com> wrote:

> On Friday, 12 August 2022 at 17:45:44 UTC+2, Python wrote:
> > There is no infinity in the standard system for real numbers,
> > so you cannot say you're using the standard system.
> You confused about WHICH system we are talking about.
>
> I am not talking about the standard system for real numbers.
> I am talking about the standard system of Mathematics.
>
> In the standard system of Mathematics : ∞ + 1 = ∞
>
> Which is exactly the same thing as saying.
> x + 1 = x when x is bound to ∞
>
> But if infinity is not a number then how the hell are you binding it
> to a variable?!?!?

Well obviously that was your mistake, you cannot assign a value of
infinity to any variable in the standard system of Mathematics, so:

infinity + 1 = infinity

*and*

x + 1 > x

/Flibble

On Friday, 12 August 2022 at 18:20:12 UTC+2, Mr Flibble wrote:
> infinity + 1 = infinity
>
> *and*
>
> x + 1 > x
>
> /Flibble
Translation: x + 1 > x

EXCEPT when x = infinity

On Fri, 12 Aug 2022 09:22:27 -0700 (PDT)
Skep Dick <skepdick22@gmail.com> wrote:

> On Friday, 12 August 2022 at 18:20:12 UTC+2, Mr Flibble wrote:
> > infinity + 1 = infinity
> >
> > *and*
> >
> > x + 1 > x
> >
> > /Flibble
> Translation: x + 1 > x
>
> EXCEPT when x = infinity

Nope, x can never be infinity, only infinity can be infinity.

/Flibble

Mr Flibble wrote:
> On Fri, 12 Aug 2022 09:22:27 -0700 (PDT)
> Skep Dick <skepdick22@gmail.com> wrote:
>
>> On Friday, 12 August 2022 at 18:20:12 UTC+2, Mr Flibble wrote:
>>> infinity + 1 = infinity
>>>
>>> *and*
>>>
>>> x + 1 > x
>>>
>>> /Flibble
>> Translation: x + 1 > x
>>
>> EXCEPT when x = infinity
>
> Nope, x can never be infinity, only infinity can be infinity.

So you have infinity as an "object" in the system, but you cannot
bound it to a name. Weird.

> /Flibble

>>> x = float("inf")
>>> x + 1 > x
False

(nothing specific to Python here, this is IEE754)

also:

>>> x = float("nan")
>>> x is x
True
>>> x == x
False

On Fri, 12 Aug 2022 18:27:41 +0200
Python <python@example.invalid> wrote:

> Mr Flibble wrote:
> > On Fri, 12 Aug 2022 09:22:27 -0700 (PDT)
> > Skep Dick <skepdick22@gmail.com> wrote:
> >
> >> On Friday, 12 August 2022 at 18:20:12 UTC+2, Mr Flibble wrote:
> >>> infinity + 1 = infinity
> >>>
> >>> *and*
> >>>
> >>> x + 1 > x
> >>>
> >>> /Flibble
> >> Translation: x + 1 > x
> >>
> >> EXCEPT when x = infinity
> >
> > Nope, x can never be infinity, only infinity can be infinity.
>
> So you have infinity as an "object" in the system, but you cannot
> bound it to a name. Weird.
>
> > /Flibble
>
> >>> x = float("inf")
> >>> x + 1 > x
> False

This because for any sane definition of infinity adding 1 to it doesn't
change it from being infinity, i.e.

infinity = infinity + 1

*and*

infinity + 1 = infinity

Similarly,

infinity - 1 = infinity
infinity * 2 = infinity
infinity / 2 = infinity

It is a shame the amateurish troll "Skep Dick" doesn't get this as it
seems quite simple to me.

/Flibble

On Friday, 12 August 2022 at 18:11:16 UTC+2, Python wrote:
> So again, when dealing with ∞
We are not dealing with ∞. That symbol is colloquial. It's what lazy Mathematicians and the general public use to represent a bunch of different infinities.

I could ask the exact same question when you write stuff like: x = float("inf")
What's the definition of "inf"? It doesn't have one! It's just the identity functon

f(x) = x
float("inf") = inf

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

Further more... you said that infinity is not a number. OK!
(NaN == NaN) ⇔ False

In [1]: float("nan") == float("nan")
Out[1]: False

So then... if infinity is not a number then... float("inf") == float("inf") must be False!

Uh! Oh! Contradiction!

In [1]: float("inf") == float("inf")
Out[1]: True

>what syste do you conside ?
https://en.wikipedia.org/wiki/Hyperreal_number

>What is the definition of ∞ there?
It doesn't have one!

What is defined (axiomatically) is the identity 1/ε = ω/1
ε is infinitesimal
ω is infinity

In English: dividing 1 by really small quantity produces an really big quantity.

> No they are not. You just don't know them.
Whatever floats your boat.

> And now I know that you are a crank (not that I doubted much...)
And now I know that you are an indoctrinated conformist who has never had an original thought in their life (not that I doubted much...)

> Not necessarily. You say so, that's not a proof.
Who needs to say it in order for it become a proof?

On Friday, 12 August 2022 at 18:32:55 UTC+2, Mr Flibble wrote:
> This because for any sane definition of infinity adding 1 to it doesn't
> change it from being infinity, i.e.
Au contraire! I think it's totally insane. Batshit crazy. Intellectually tonedeaf and outright crazy to pretend that adding something (however small) to something else (howvery big) changes nothing whatsoever.

It's even crazier and infinitely stupid to pretend that doubling or halving something leaves it unchanged.

> infinity = infinity + 1
Translation: x = x + 1

> infinity - 1 = infinity
Translation: x - 1 = x

> infinity * 2 = infinity
Translation: x * 2 = x

> infinity / 2 = infinity
Translation: x / 2 = x

> It is a shame the amateurish troll "Skep Dick" doesn't get this as it
> seems quite simple to me.
Everything is simple to a simple mind.

On Monday, 8 August 2022 at 15:16:39 UTC+2, Ben Bacarisse wrote:
> wij <wyni...@gmail.com> writes:
>
> > If 0.999... is rational, then:
> > 0.999....= p/q (p,q∈ℕ)
> > <=> 0.999...*q=p
> Yes. For example 0.999... = 1/1.
> > If 0.999...∈ℕ, there exist q∈ℕ such that 0.999...*q∈ℕ
> > since 0.999... is defined as infinite repeating, and q is finite,
> > but 0.999...*q is never finite.
> 0.999...*q is finite for all q in N.
> > I am kind of reluctant to raise this issue again,
> Really? Where would we be without someone denying (or not knowing) that
> ... denotes a limit every few weeks?
>
> --
> Ben.

Yeah so it's worth repeating. Ben doesn't actually know what a limit is either.

Ask him to work out the derrivative of f(x) = x^2 and watch him make a fool out of himself by regurgitating all the nonsense he's been taught about dy and dx.

But he will feel vindicated that he has "knowledge" because the entire status quo is behind him.

On 8/12/22 9:38 AM, Skep Dick wrote:
> On Friday, 12 August 2022 at 13:36:36 UTC+2, richar...@gmail.com wrote:
>>> Or are we only counting my communication failures but not yours?
>> But I DID, by following the conventions.
> Precisely! You failed to communicate THAT you are following the convention.
>

But the conventions says it doesn't need to be stated.

>> IT isn't MY fault that you are ignorant of the standard
>> social-mathematical conventions.
> It is your fault. You failed to communicate which convention you are using. Not me.

Nope. Just shows that you failed to learn the established conventions.

Ignorance of the rules is not an excuse.

>
>> Note, earlier in the conversation, and in the topic of the message, that
>> domain was actually specifically mentioned.
>> By making a rational/irrational comment, the domain being the Real is
>> made clear, as that is the smplest system that has both of them.
>
> What does that have to do with the point that the truth of 0.999... = 1 depends on an arbitrary choice?

But an choice that HAS been made by the convention, that applies unless
explicitly stated to not be in force.

Are you going to say that EVERYTHING needs to be explicit?

Why didn't you say you were going to talk in English?
And before you say that, you need to say you are going to anounce you
definition of the lanuage you are going to use in English.

.....

Conventions establish the base rules we follow to allow us to work with
each other, and to establish how we indicate we are going off in
"non-standard" directions, but stating that.

>
> It's true if you want it to be true.
> It's false if you want it to be false.

Not if you want to work with other.

>
> What do you want it to be?
>
>>>> I gave you charity at first. You then showed that you didn't care, and
>>>> just turned abusive.
>>> I turned "abusive" and "stopped caring" the moment I realised you are uncharitable.
>> Nope, I pointed out that your statements were incorret in the impllied system.
> See! You are uncharitable.
>
> The statement is whatever we want it to be! You want it to be true. I want it to be false.

And you are thus wrong.

>
> That doesn't make me incorrect. It makes you an ass.

Nope.

By YOUR logic, I get to define what I mean, and you need to accept it.
Right? Isn't that what you are doing?

That just shows your logic fails the EGO check.

>
> Mathematics is relative!

Nope. It CAN be relative once you establish a reference point.

>
>> I didn't say they couldn't be right if you actually specified a
>> domain, giving you the option to correct you statement and include the
>> domain.
> Idiot. Which part of choice-dependent truth is lost upon you?

Truth is NOT choice-dependent.

>
>> IF you ARE Right about something, you are right.
> One more time - for the idiot in the classroom. There is no such thing as "right" or "wrong" in Mathematics!
>
> 0.999... = 1 is neither right nor wrong!
>
> If you want to MAKE it wrong you use *R.
> If you want to MAKE it right you use R.
>
>> So, you don't know that Truth is ABSOLUTE.
> Ahahahahahahahahahahahahahahahahaha!
> Ahahahahahahahahahahahahahahahahahahahahahahahahahahahahahahahahahahahahahahahahahaha!
> Ahahahahahahahahahahahahahahahahahahahahahahahahahahahahahahahahahahahahahahahahahahahahahahahahahahahahahahahahaha!
> Ahahahahahahahahahahahahahahahahahahahahahahahahahahahahahahahahahahahahahahahahahahahahahahahahahahahahahahahahahahahahahahahahahahahahahahahahahaha!
>
> Shame. Somebody doesn't understand Tarski's theorems.

>
> https://en.wikipedia.org/wiki/Tarski%27s_undefinability_theorem
>>> You are the one gatekeeping YOUR interpretation.
>> WRONG.
> There is no right and wrong in Mathematics.
>
>

Maybe YOU don't understand the meaning of that.

You can't define Truth within the system, because the actual meaning of
Truth is established before the system existed.

>>>> You have proved what sort of person you are, and thus have lost the
>>>> right to charity.
>>> You are equivocating "prove" you uncharitable twat!
>>>
>>> The "sort of person I am" is beyond the techniques of Mathematics.
>> You are just proving the sort of person you are,
> Q.E.D using the concept of "proof" outside of its applicable domain.
>
> Does that make you an idiot? I wonder.

No, it makes me smarter that you as I understand stuff you do not.

>
>>>> What clear notation needs to be used?
>>> So clarity in communication is no longer your goal? I thought so!
> Q.E.D Ucharitable twat.

Nope, charity is to be given to those that honestly need it, not those
who get themselves into trouble by their own devices. They should suffer
the consequences of their actions, until they see their need for actual
charity.

On Friday, 12 August 2022 at 21:43:28 UTC+1, Skep Dick wrote:
> On Monday, 8 August 2022 at 15:16:39 UTC+2, Ben Bacarisse wrote:
> > wij <wyni...@gmail.com> writes:
> >
> > > If 0.999... is rational, then:
> > > 0.999....= p/q (p,q∈ℕ)
> > > <=> 0.999...*q=p
> > Yes. For example 0.999... = 1/1.
> > > If 0.999...∈ℕ, there exist q∈ℕ such that 0.999...*q∈ℕ
> > > since 0.999... is defined as infinite repeating, and q is finite,
> > > but 0.999...*q is never finite.
> > 0.999...*q is finite for all q in N.
> > > I am kind of reluctant to raise this issue again,
> > Really? Where would we be without someone denying (or not knowing) that
> > ... denotes a limit every few weeks?
> >
> > --
> > Ben.
>
> Yeah so it's worth repeating. Ben doesn't actually know what a limit is either.
>
> Ask him to work out the derrivative of f(x) = x^2 and watch him make a fool out of himself by regurgitating all the nonsense he's been taught about dy and dx.
>
> But he will feel vindicated that he has "knowledge" because the entire status quo is behind him.
>
y = x^2

now when we add a tiny amount to x, which we call dx, y will change, so call that dy.

y + dy = (x + dx)^2

expand

y + dy = x^2 + 2x*dx + (dx)^2

by y = x^2, so subtract from both sides

dy = 2x*dx + (dx)^2.

Now all we've said is that dx is a tiny amount we add to x. Let's say that it's so small that, when
squared, we cannot measure it at all.

(dx^2) = 0 (or ignore)
dy = 2x*dx

dy/dx = 2x

Now you can ask, "what does it mean to have a slope at a point?" Surely a slope is a characteristic
of two points. So we don't say that dx goes to zero. We say it goes arbitrarily small, so small that we
cannot measure (dx)^2. You can say that dx is an infinitesimal, but that opens up whole questions
about what the infinitesimal means. We don't need to go there. It's just arbitrarily small.

On Fri, 12 Aug 2022 13:17:26 -0700 (PDT)
Skep Dick <skepdick22@gmail.com> wrote:

> On Friday, 12 August 2022 at 18:32:55 UTC+2, Mr Flibble wrote:
> > This because for any sane definition of infinity adding 1 to it
> > doesn't change it from being infinity, i.e.
> Au contraire! I think it's totally insane. Batshit crazy.
> Intellectually tonedeaf and outright crazy to pretend that adding
> something (however small) to something else (howvery big) changes
> nothing whatsoever.

You don't seem to understand what infinity actually is: infinity is a
concept not a number, it isn't "very big" as "very big" implies some
finite size and of course infinity isn't finite, by definition.

>
> It's even crazier and infinitely stupid to pretend that doubling or
> halving something leaves it unchanged.

Not when dealing with infinity it isn't.

>
>
> > infinity = infinity + 1
> Translation: x = x + 1
>
> > infinity - 1 = infinity
> Translation: x - 1 = x
>
> > infinity * 2 = infinity
> Translation: x * 2 = x
>
> > infinity / 2 = infinity
> Translation: x / 2 = x

No, no, no and no. Infinity cannot be assigned to a variable in a
formula or equation as infinity is not a number.

>
> > It is a shame the amateurish troll "Skep Dick" doesn't get this as
> > it seems quite simple to me.
> Everything is simple to a simple mind.

You are the one over simplifying things, so that would be a projection,
dear.

/Flibble

On 8/12/22 11:09 AM, Skep Dick wrote:
> On Friday, 12 August 2022 at 17:00:52 UTC+2, malcolm.ar...@gmail.com wrote:
>> That's the point at which you go wrong. infinity = 1 + infinity,
> That's not true in *R ! Infinitesimals (ε) and infinities (ω) exist.
>
> 1/ε = ω/1
>
>> but we can't subtract infinity from both sides of the equation to obtain 1 = 0
> In your number system! Not in mine.
>
> 1/ε + 1 < 1/ε
> ω < ω + 1
>
> This is obvious to children but not to over-educated idiot Mathematicians.
>
> X + 1 is ALWAYS more than X !

Nope. Trans-finite math DOES seem strange to some, as some common
properties get lost, like x + 1 > x.

After all:
2 + 3 + 4 + 5 + 6 + ... = Infinity
and
1 + 2 + 3 + 4 + 5 + 6 + ... = Infinity.

but the first + 1 equals the second, so Infinity + 1 = Infinity.

>
>> As you are obviously well aware. The algebra is good as a high school sort
>> of joke demonstration, but it's just based on a sleight of hand.
> You have been lied to all your life.
>
> The sleight of hand is by the Establishment of Mathematics.
>
> 0.999... = 1 is false, and infinity + 1 > infinity in any system where x+1 > x
>
>

And "x + 1 > x" as an always true statement doesn't hold for many
systems that have the value of infinity in them.