On Friday, 12 August 2022 at 23:30:22 UTC+2, Mr Flibble wrote:
> 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.
Regurgitating definitions doesn't seem to amount to any understanding on your behalf.

> Not when dealing with infinity it isn't.
Infinity is not exempt from change - that's just a sacred cow.

> >
> >
> > > 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.
I know, you idiot.

Do you actually know what a performative contradiction is?

You SAY that infinity cannot be assigned to a variable in a formula or an equation.... and THEN you assign it to a variable in a formula/equation.

The expression "infinity = infinity + 1" means the exact same thing as the expression "x = x + 1" (with infinity being assigned to the variable x)
The expression "infinity = infinity - 1" means the exact same thing as the expression "x = x - 1" (with infinity being assigned to the variable x)
The expression "infinity = infinity * 2" means the exact same thing as the expression "x = x * 1" (with infinity being assigned to the variable x)
The expression "infinity = infinity /2" means the exact same thing as the expression "x = x / 1" (with infinity being assigned to the variable x)

> You are the one over simplifying things, so that would be a projection,
> dear.
Yes, well. This is very much like explaining colors to the colourblind.

On 8/12/22 9:50 AM, Skep Dick wrote:
> On Friday, 12 August 2022 at 13:41:32 UTC+2, richar...@gmail.com wrote:
>>> Use another system.
>> The actually USE the other system, but you need to specify it.
>
> I am USING the other system. And no - I don't have to fucking specify it.
> I'll USE whichever damn system I want to use.
>
> As long as it works.

But be WORNG because without specifying it, your statement is put into
another system that it doesn't work in.

Failure to specify the domain of a statement, unless the domain is the
domain that is assumed by the conventions, is an error.

You are just proving that you aren't going to work with others.

>
>> If you don't define the system you are in, your symbols are meaningless.
>> That seems to be where you are stuck,
> Ooooh! Are you sure you want to play that game?
>
> If you don't define "Truth" then "Truth" is meaningless.
> If you don't define "define" then "define" is meaningless.
> If you don't define "meaningless" then "meaningless" is meaningless.

Nope, since there IS a convention of definitions that apply unless
stated otherwise, you can build on the conventions without needed to
explicitly respecify those definitions.

That is why you need to specifiy if you are using something else,
otherwise you DO need to fully specify EVERYTHING from the beginning
every time.

>
>> Who needs mind-reading. That is YORU false assumption.
> My assumption is neither true, nor false - it's just a fact.
>
> It's a fact THAT I can't read your mind.
> It's a fact THAT you failed to communicate which system you are using.

No, as I said, you don't need to be a mind-reader, just know the
socially established conventions and follow them, so be clear that you
are deviating from them, and how.

>
>> And that is your problem, you should be using them in the way that makes
>> sense to the people you are talking about by being clear about the
>> system you are working in.
> So when are you going to make clear which system of Truth you are working in?
>
>> You are just proving your EGO problem.
> In so far as one of us has an EGO problem. It's the guy who always has to be right...

It is the guy who says *I* have to be right, instead of *WE* are right.

>
>>> I have no ego. Which is why I am pointing out THAT Mathematics is relative.
>> So you are just ignorant.
> Ahhh. The irony!
>
> IF Mathematics is relative and you don't know that. Which one of us is ignorant?
>
> Remind me again whether the truth of 0.999...= 1 is absolute; or relative.

0.999... = 1 IN THE DEFUALT NUMBER SYSTEM OF THE REAL NUMBER SYSTEM, is
a ABSOLUTE truth.

>
>
>> Incorrect.
> You are incorrect about me being incorrect 😂😂😂😂
>
>> Yes, a system can define what it will treat as correct, but
>> there are fundamental rules that must be followed or the system is just
>> broken (and thus "incorrect")
> Shame. We have a fundamentalist on our hands.
>
>>> But who created the system and why? Does their creation suit my purpose?
>>>
>> That is one of the big questions.
> So you don't actually know the answer, but you blindly follow the rules?
>
> Good computer!

I am not a Computer, I am a person. I am not bound by the limitation of
a computational device, as I have Free-Will.

Maybe you should learn about that.

On Friday, 12 August 2022 at 23:34:26 UTC+2, richar...@gmail.com wrote:
> Nope. Trans-finite math DOES seem strange to some, as some common
> properties get lost, like x + 1 > x
I am doing Transfinite math!

Without losing the most important property of all - common sense.

Seems you sold yours.

> 2 + 3 + 4 + 5 + 6 + ... = Infinity
> and
> 1 + 2 + 3 + 4 + 5 + 6 + ... = Infinity.
Which infinity? There are so many of them!

> but the first + 1 equals the second, so Infinity + 1 = Infinity.
Only in systems lacking common sense.

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

Almost as if I don't have to treat infinities as if they are special.

On Fri, 12 Aug 2022 14:42:54 -0700 (PDT)
Skep Dick <skepdick22@gmail.com> wrote:

> On Friday, 12 August 2022 at 23:30:22 UTC+2, Mr Flibble wrote:
> > 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.
> Regurgitating definitions doesn't seem to amount to any understanding
> on your behalf.
>
> > Not when dealing with infinity it isn't.
> Infinity is not exempt from change - that's just a sacred cow.
>
> > >
> > >
> > > > 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.
> I know, you idiot.
>
> Do you actually know what a performative contradiction is?
>
> You SAY that infinity cannot be assigned to a variable in a formula
> or an equation.... and THEN you assign it to a variable in a
> formula/equation.
>
> The expression "infinity = infinity + 1" means the exact same thing
> as the expression "x = x + 1" (with infinity being assigned to the
> variable x) The expression "infinity = infinity - 1" means the exact
> same thing as the expression "x = x - 1" (with infinity being
> assigned to the variable x) The expression "infinity = infinity * 2"
> means the exact same thing as the expression "x = x * 1" (with
> infinity being assigned to the variable x) The expression "infinity =
> infinity /2" means the exact same thing as the expression "x = x /
> 1" (with infinity being assigned to the variable x)

No, no, no and no. "infinity" is a symbol representing a concept it is
NOT equivalent to a variable, x.

>
> > You are the one over simplifying things, so that would be a
> > projection, dear.
> Yes, well. This is very much like explaining colors to the
> colourblind.

/Flibble

On Friday, 12 August 2022 at 23:44:17 UTC+2, richar...@gmail.com wrote:
> But be WORNG because without specifying it, your statement is put into
> another system that it doesn't work in.
What are you 5 year old? Is everything about right and wrong about you?

Wait... Never mind. That's a rhetorical question.

> Failure to specify the domain of a statement, unless the domain is the
> domain that is assumed by the conventions, is an error.
Oh, ok. Then I am wrong.

But you are still much wronger than me.

> You are just proving that you aren't going to work with others.
I don't like working with people who are much wronger than me.

> Nope, since there IS a convention of definitions that apply unless
> stated otherwise, you can build on the conventions without needed to
> explicitly respecify those definitions.
That's called an bandwagon fallacy. I thought you said you care about logic?

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

> That is why you need to specifiy if you are using something else,
> otherwise you DO need to fully specify EVERYTHING from the beginning
> every time.
Or I can just ignore idiots who can't keep up with the times?

Planck was right you know... A new scientific truth does not triumph by convincing its opponents and making them see the light, but rather because its opponents eventually die and a new generation grows up that is familiar with it ...

> No, as I said, you don't need to be a mind-reader, just know the
> socially established conventions and follow them
At which point did I give you the impression that I care about convention?

>so be clear that you are deviating from them, and how.
I wouldn't know that I am deviating from "social convention" now, would I?

Since I don't follow conventions.

> It is the guy who says *I* have to be right, instead of *WE* are right.
In both cases - you are the only one in this conversation who is talking about being right...

I just want better tools. I have better tools.

> 0.999... = 1 IN THE DEFUALT NUMBER SYSTEM OF THE REAL NUMBER SYSTEM, is
> a ABSOLUTE truth.
If your truth is ABSOLUTE truth, then my truth is more ABSOLUTE than yours.

infinity + 1 > infinity

> I am not a Computer, I am a person. I am not bound by the limitation of
> a computational device, as I have Free-Will.
I haven't seen any free will. You just follow rules. Exactly like a computer.
> Maybe you should learn about that.
I have learned about that. I have free will.

That's why I can tell you don't.

I have freely chosen to give up my belief in R and accept R* as a better theory.

You haven't - the Real Numbers are "absolute truth" to you - they are your God. Your sacred cow.

On Friday, 12 August 2022 at 23:48:07 UTC+2, Mr Flibble wrote:
> No, no, no and no. "infinity" is a symbol representing a concept it is
> NOT equivalent to a variable, x.
Golly gosh. You don't even understand how bound and unbound variable work.

Start there. Infinity is a bit above your praygrade.

On Fri, 12 Aug 2022 14:59:07 -0700 (PDT)
Skep Dick <skepdick22@gmail.com> wrote:

> On Friday, 12 August 2022 at 23:48:07 UTC+2, Mr Flibble wrote:
> > No, no, no and no. "infinity" is a symbol representing a concept it
> > is NOT equivalent to a variable, x.
> Golly gosh. You don't even understand how bound and unbound variable
> work.
>
> Start there. Infinity is a bit above your praygrade.

Infinity is *not* a variable.

/Flibble

On 8/12/22 5:45 PM, Skep Dick wrote:
> On Friday, 12 August 2022 at 23:34:26 UTC+2, richar...@gmail.com wrote:
>> Nope. Trans-finite math DOES seem strange to some, as some common
>> properties get lost, like x + 1 > x
> I am doing Transfinite math!
>
> Without losing the most important property of all - common sense.
>
> Seems you sold yours.
>
>> 2 + 3 + 4 + 5 + 6 + ... = Infinity
>> and
>> 1 + 2 + 3 + 4 + 5 + 6 + ... = Infinity.
> Which infinity? There are so many of them!
>
>> but the first + 1 equals the second, so Infinity + 1 = Infinity.
> Only in systems lacking common sense.
>
>> And "x + 1 > x" as an always true statement doesn't hold for many
>> systems that have the value of infinity in them.
> And yet it holds in mine.
>
> Almost as if I don't have to treat infinities as if they are special.

And you get that:

> 1+2+3+4+5... = -1/8

So, it shows how useful your system is.

On 8/12/22 5:58 PM, Skep Dick wrote:
> On Friday, 12 August 2022 at 23:44:17 UTC+2, richar...@gmail.com wrote:
>> But be WORNG because without specifying it, your statement is put into
>> another system that it doesn't work in.
> What are you 5 year old? Is everything about right and wrong about you?
>
> Wait... Never mind. That's a rhetorical question.
>
>> Failure to specify the domain of a statement, unless the domain is the
>> domain that is assumed by the conventions, is an error.
> Oh, ok. Then I am wrong.
>
> But you are still much wronger than me.
>
>> You are just proving that you aren't going to work with others.
> I don't like working with people who are much wronger than me.
>
>> Nope, since there IS a convention of definitions that apply unless
>> stated otherwise, you can build on the conventions without needed to
>> explicitly respecify those definitions.
> That's called an bandwagon fallacy. I thought you said you care about logic?
>
> https://en.wikipedia.org/wiki/Argumentum_ad_populum

That isn't what I said, so you are wrong.
>
>
>> That is why you need to specifiy if you are using something else,
>> otherwise you DO need to fully specify EVERYTHING from the beginning
>> every time.
> Or I can just ignore idiots who can't keep up with the times?
>
> Planck was right you know... A new scientific truth does not triumph by convincing its opponents and making them see the light, but rather because its opponents eventually die and a new generation grows up that is familiar with it ...

Yes, a new system CAN become the accepted default,

>
>> No, as I said, you don't need to be a mind-reader, just know the
>> socially established conventions and follow them
> At which point did I give you the impression that I care about convention?
>
>> so be clear that you are deviating from them, and how.
> I wouldn't know that I am deviating from "social convention" now, would I?
>
> Since I don't follow conventions.

And thus are anti-social (by definition)?

When entering a group, your first responsibility is to learn there
conventions.

>
>
>> It is the guy who says *I* have to be right, instead of *WE* are right.
> In both cases - you are the only one in this conversation who is talking about being right...

No, you keep on saying that you are right because you have chosen to be.

>
> I just want better tools. I have better tools.
>
>> 0.999... = 1 IN THE DEFUALT NUMBER SYSTEM OF THE REAL NUMBER SYSTEM, is
>> a ABSOLUTE truth.
> If your truth is ABSOLUTE truth, then my truth is more ABSOLUTE than yours.
>
> infinity + 1 > infinity

Which gets you that 1 + 2 + 3 + 4 + 5 = infinity = -1/8

>
>
>> I am not a Computer, I am a person. I am not bound by the limitation of
>> a computational device, as I have Free-Will.
> I haven't seen any free will. You just follow rules. Exactly like a computer.
>
>> Maybe you should learn about that.
> I have learned about that. I have free will.
>
> That's why I can tell you don't.
>
> I have freely chosen to give up my belief in R and accept R* as a better theory.
>
> You haven't - the Real Numbers are "absolute truth" to you - they are your God. Your sacred cow.

I never said you can't beleive in *R as better, just that unless you are
talking in a group that HAS also accepted that as the default, it is an
error to assume it is the default.

You are just proving you are anti-social.

You confuse free-will with license.

WHen we have free-will, we CHOOSE to limit ourselves to that which
actually is benificial, and works with the group.

Otherwise, we are shown to be controlled by our EGO.

On Saturday, 13 August 2022 at 00:08:38 UTC+2, richar...@gmail.com wrote:
> On 8/12/22 5:45 PM, Skep Dick wrote:
> > On Friday, 12 August 2022 at 23:34:26 UTC+2, richar...@gmail.com wrote:
> >> Nope. Trans-finite math DOES seem strange to some, as some common
> >> properties get lost, like x + 1 > x
> > I am doing Transfinite math!
> >
> > Without losing the most important property of all - common sense.
> >
> > Seems you sold yours.
> >
> >> 2 + 3 + 4 + 5 + 6 + ... = Infinity
> >> and

> >> 1 + 2 + 3 + 4 + 5 + 6 + ... = Infinity.
> > Which infinity? There are so many of them!
> >
> >> but the first + 1 equals the second, so Infinity + 1 = Infinity.
> > Only in systems lacking common sense.
> >
> >> And "x + 1 > x" as an always true statement doesn't hold for many
> >> systems that have the value of infinity in them.
> > And yet it holds in mine.
> >
> > Almost as if I don't have to treat infinities as if they are special.
> And you get that:
>
> > 1+2+3+4+5... = -1/8
>
> So, it shows how useful your system is.
You don’t even understand sarcasm, do you?

Speaking of utility… how useful is a system in which x + 1 = x -1; and x / 2 = x * 2 ?

On Saturday, 13 August 2022 at 00:17:19 UTC+2, richar...@gmail.com wrote:
> >> That is why you need to specifiy if you are using something else,
> >> otherwise you DO need to fully specify EVERYTHING from the beginning
> >> every time.
> > Or I can just ignore idiots who can't keep up with the times?
> >
> > Planck was right you know... A new scientific truth does not triumph by convincing its opponents and making them see the light, but rather because its opponents eventually die and a new generation grows up that is familiar with it ...
> Yes, a new system CAN become the accepted default

I know! It has become my default. When will the rest of society catch up? I don’t care…

> >> No, as I said, you don't need to be a mind-reader, just know the
> >> socially established conventions and follow them
> > At which point did I give you the impression that I care about convention?
> >
> >> so be clear that you are deviating from them, and how.
> > I wouldn't know that I am deviating from "social convention" now, would I?
> >
> > Since I don't follow conventions.
> And thus are anti-social (by definition)?

I will be social just as soon as the convention catches up to me.

> When entering a group, your first responsibility is to learn there
> conventions.
Who is entering what group? I don’t give a shit about your conventions.

> No, you keep on saying that you are right because you have chosen to be.
Is that you you are understanding my words?

That sure sounds like your vocabulary.

I am anti-social, remember? Being right doesn’t get me any social status.

> Which gets you that 1 + 2 + 3 + 4 + 5 = infinity = -1/8
Can’t take a joke, eh?

But it is funny how your don’t think the proof for 0.999… = 0 isn’t as stupid as the proof for 1 + 2 + 3 + 4 + 5 … = -1/8

> WHen we have free-will, we CHOOSE to limit ourselves to that which
> actually is benificial, and works with the group.
And what is it that you think I am doing when I choose to use a system in which x +1 > x ?

I am working with the group of humans who find them to be their default intuition about how stuff works.
Mind you, I am absolutely working AGAINST the group of ivory tower Mathematicians who have mistaken themselves as being representative of the group’s intellectuals.

I am just kicking then high Priests of Mathematics out of the temple.

> Otherwise, we are shown to be controlled by our EGO.
An egoist is not mentally equipped to tell that others aren’t like them.

On 8/12/22 6:17 PM, Skep Dick wrote:
> On Saturday, 13 August 2022 at 00:08:38 UTC+2, richar...@gmail.com wrote:
>> On 8/12/22 5:45 PM, Skep Dick wrote:
>>> On Friday, 12 August 2022 at 23:34:26 UTC+2, richar...@gmail.com wrote:
>>>> Nope. Trans-finite math DOES seem strange to some, as some common
>>>> properties get lost, like x + 1 > x
>>> I am doing Transfinite math!
>>>
>>> Without losing the most important property of all - common sense.
>>>
>>> Seems you sold yours.
>>>
>>>> 2 + 3 + 4 + 5 + 6 + ... = Infinity
>>>> and
>
>
>>>> 1 + 2 + 3 + 4 + 5 + 6 + ... = Infinity.
>>> Which infinity? There are so many of them!
>>>
>>>> but the first + 1 equals the second, so Infinity + 1 = Infinity.
>>> Only in systems lacking common sense.
>>>
>>>> And "x + 1 > x" as an always true statement doesn't hold for many
>>>> systems that have the value of infinity in them.
>>> And yet it holds in mine.
>>>
>>> Almost as if I don't have to treat infinities as if they are special.
>> And you get that:
>>
>>> 1+2+3+4+5... = -1/8
>>
>> So, it shows how useful your system is.
> You don’t even understand sarcasm, do you?
>
> Speaking of utility… how useful is a system in which x + 1 = x -1; and x / 2 = x * 2 ?

Depends what you are using it for.

Note, that many of these system you can assert that x+1 > x for a
significant subset of the system, you just need to keep track of which
types of numbers things are.

You get the ability to talk about infinities, at the cost of losing some
common properties unless you know that in THIS instance you aren't
talking about infinities, because they DO behave differently.

If you know the rules, and are clear about them, you can do a lot.

Sort of like division has this problem with 0, but as long as we watch
out for it, it is important.

So, if we have that x*y == x*z, IF we know that x isn't 0, and we are
working in the Reals, then we can say that y == z,

We can then progress to the notion that if we have x*y == x*z that
either x == 0 or y == z (or possibly both, that or is inclusive).

On 8/12/22 6:31 PM, Skep Dick wrote:
> On Saturday, 13 August 2022 at 00:17:19 UTC+2, richar...@gmail.com wrote:
>>>> That is why you need to specifiy if you are using something else,
>>>> otherwise you DO need to fully specify EVERYTHING from the beginning
>>>> every time.
>>> Or I can just ignore idiots who can't keep up with the times?
>>>
>>> Planck was right you know... A new scientific truth does not triumph by convincing its opponents and making them see the light, but rather because its opponents eventually die and a new generation grows up that is familiar with it ...
>> Yes, a new system CAN become the accepted default
>
> I know! It has become my default. When will the rest of society catch up? I don’t care…
>
>>>> No, as I said, you don't need to be a mind-reader, just know the
>>>> socially established conventions and follow them
>>> At which point did I give you the impression that I care about convention?
>>>
>>>> so be clear that you are deviating from them, and how.
>>> I wouldn't know that I am deviating from "social convention" now, would I?
>>>
>>> Since I don't follow conventions.
>> And thus are anti-social (by definition)?
>
> I will be social just as soon as the convention catches up to me.
>
>> When entering a group, your first responsibility is to learn there
>> conventions.
> Who is entering what group? I don’t give a shit about your conventions.
>
>> No, you keep on saying that you are right because you have chosen to be.
> Is that you you are understanding my words?
>
> That sure sounds like your vocabulary.
>
> I am anti-social, remember? Being right doesn’t get me any social status.
>
>
>> Which gets you that 1 + 2 + 3 + 4 + 5 = infinity = -1/8
> Can’t take a joke, eh?
>
> But it is funny how your don’t think the proof for 0.999… = 0 isn’t as stupid as the proof for 1 + 2 + 3 + 4 + 5 … = -1/8
>
>

maybe because the proof that 0.9999... == 1 is corret (if we are in a
system like the Reals), and gives us a nice consistant system.

The system that shows that 1 + 2 + 3 + 4 + 5 + ... == -1/8 doesn't

>
>> WHen we have free-will, we CHOOSE to limit ourselves to that which
>> actually is benificial, and works with the group.
> And what is it that you think I am doing when I choose to use a system in which x +1 > x ?
>
> I am working with the group of humans who find them to be their default intuition about how stuff works.
> Mind you, I am absolutely working AGAINST the group of ivory tower Mathematicians who have mistaken themselves as being representative of the group’s intellectuals.
>
> I am just kicking then high Priests of Mathematics out of the temple.

Then talk with them in the places where they are,

All you are showing is you don't know where you are.

>
>> Otherwise, we are shown to be controlled by our EGO.
> An egoist is not mentally equipped to tell that others aren’t like them.
>
>

As you are proving.

On Tuesday, August 9, 2022 at 10:42:50 AM UTC-7, wyni...@gmail.com wrote:
>
> Rational number means the ratio of two integer numbers p/q.
>
Not quite. Rational numbers are the set of all ordered pairs of two
signed integers modulo the equivalence {two pairs [a,b] and [c,d]
are equivalent if and only if a*d = b*c}.

On Friday, 12 August 2022 at 23:30:15 UTC+2, malcolm.ar...@gmail.com wrote:
> 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
Are you SURE you are you are using ℝ? Are you sure sure?

Because if dx^2 = 0 then dx = 0. There is no quantity in ℝ such that x^2 = 0

if dx = 0 => dy = 2x*dx => dy = 2x * 0 => dy = 0

On Friday, 12 August 2022 at 23:30:15 UTC+2, malcolm.ar...@gmail.com wrote:
> 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.

That right there tells me everything I need to know. You are actually using *ℝ, but you think you are using ℝ.

The quantity you are speaking about is the infinitesimal ε such that 0 <= ε, ε^2 = 0

On Saturday, 13 August 2022 at 00:01:38 UTC+2, Mr Flibble wrote:
> On Fri, 12 Aug 2022 14:59:07 -0700 (PDT)
> Skep Dick <skepd...@gmail.com> wrote:
>
> > On Friday, 12 August 2022 at 23:48:07 UTC+2, Mr Flibble wrote:
> > > No, no, no and no. "infinity" is a symbol representing a concept it
> > > is NOT equivalent to a variable, x.
> > Golly gosh. You don't even understand how bound and unbound variable
> > work.
> >
> > Start there. Infinity is a bit above your praygrade.
> Infinity is *not* a variable.

Imbecille. Nobody is saying that x is a variable.

Lets start with simple things, because infinity is definitely swimming in the deep end for you.

5 is not a variable either. 5 is ASSINGED to the variable.
Once you ASSIGN 5 to x you can use x and 5 interchangeably.

>>> x
Traceback (most recent call last):
File "<stdin>", line 1, in <module>
NameError: name 'x' is not defined
>>> x = 5
>>> x + 1
6 >>>5+1
6 >>>5+1 == x + 1
True

On Sat, 13 Aug 2022 01:16:00 -0700 (PDT)
Skep Dick <skepdick22@gmail.com> wrote:

> On Saturday, 13 August 2022 at 00:01:38 UTC+2, Mr Flibble wrote:
> > On Fri, 12 Aug 2022 14:59:07 -0700 (PDT)
> > Skep Dick <skepd...@gmail.com> wrote:
> >
> > > On Friday, 12 August 2022 at 23:48:07 UTC+2, Mr Flibble wrote:
> > > > No, no, no and no. "infinity" is a symbol representing a
> > > > concept it is NOT equivalent to a variable, x.
> > > Golly gosh. You don't even understand how bound and unbound
> > > variable work.
> > >
> > > Start there. Infinity is a bit above your praygrade.
> > Infinity is *not* a variable.
>
> Imbecille. Nobody is saying that x is a variable.

Imbecille? Of course x is a variable, stupid.

>
> Lets start with simple things, because infinity is definitely
> swimming in the deep end for you.
>
> 5 is not a variable either. 5 is ASSINGED to the variable.
> Once you ASSIGN 5 to x you can use x and 5 interchangeably.

Ergo x is a variable, stupid.

Infinity cannot be assigned to a variable in the same way as 5 can
because unlike 5 infinity is NOT a number.

/Flibble

On Saturday, 13 August 2022 at 13:38:12 UTC+2, Mr Flibble wrote:
> > Imbecille. Nobody is saying that x is a variable.
> Imbecille? Of course x is a variable, stupid.
**sigh** You uncharitable imbecille. Let me fix it for you (since it seems your brains's error correction algorithm is faulty)

Nobody is saying that ̶x̶ infinity is a variable.

> Infinity cannot be assigned to a variable in the same way as 5 can because unlike 5 infinity is NOT a number.
I know, you imbcecille. Which is preciesly why I am pointing out that YOU are violating your own rule. I am charging you with hyporcisy.

When you bind ∞ to x in ANY equation YOU are treating ∞ as a number! This contradicts your own rule.

IF ∞ cannot be assigned to x (a variable)
THEN you cannot replace x for ∞ in the expression "x = x"
THEREFORE the expression "∞ = ∞" is meaningless!

IF ∞ cannot be assigned to x (a variable)
THEN you cannot replace x for ∞ in the expression "x + 1 = x"
THEREFORE the expression "∞ + 1 = ∞" is meaningless!

IF ∞ cannot be assigned to x (a variable)
THEN you cannot replace x for ∞ in the expression "x - 1 = x"
THEREFORE the expression "∞ - 1 = ∞" is meaningless!

IF ∞ cannot be assigned to x (a variable)
THEN you cannot replace x for ∞ in the expression "x / 2 = x"
THEREFORE the expression "∞ /2 = ∞" is meaningless!

IF ∞ cannot be assigned to x (a variable)
THEN you cannot replace x for ∞ in the expression "x * 2 = x"
THEREFORE the expression "∞ * 2 = ∞" is meaningless!

On Sat, 13 Aug 2022 05:01:41 -0700 (PDT)
Skep Dick <skepdick22@gmail.com> wrote:

> On Saturday, 13 August 2022 at 13:38:12 UTC+2, Mr Flibble wrote:
> > > Imbecille. Nobody is saying that x is a variable.
> > Imbecille? Of course x is a variable, stupid.
> **sigh** You uncharitable imbecille. Let me fix it for you (since it
> seems your brains's error correction algorithm is faulty)
>
> Nobody is saying that ̶x̶ infinity is a variable.
>
> > Infinity cannot be assigned to a variable in the same way as 5 can
> > because unlike 5 infinity is NOT a number.
> I know, you imbcecille. Which is preciesly why I am pointing out
> that YOU are violating your own rule. I am charging you with
> hyporcisy.
>
> When you bind ∞ to x in ANY equation YOU are treating ∞ as a number!
> This contradicts your own rule.
>
> IF ∞ cannot be assigned to x (a variable)
> THEN you cannot replace x for ∞ in the expression "x = x"
> THEREFORE the expression "∞ = ∞" is meaningless!
>
> IF ∞ cannot be assigned to x (a variable)
> THEN you cannot replace x for ∞ in the expression "x + 1 = x"
> THEREFORE the expression "∞ + 1 = ∞" is meaningless!
>
> IF ∞ cannot be assigned to x (a variable)
> THEN you cannot replace x for ∞ in the expression "x - 1 = x"
> THEREFORE the expression "∞ - 1 = ∞" is meaningless!
>
> IF ∞ cannot be assigned to x (a variable)
> THEN you cannot replace x for ∞ in the expression "x / 2 = x"
> THEREFORE the expression "∞ /2 = ∞" is meaningless!
>
> IF ∞ cannot be assigned to x (a variable)
> THEN you cannot replace x for ∞ in the expression "x * 2 = x"
> THEREFORE the expression "∞ * 2 = ∞" is meaningless!

No, no, no, no and no. Infinity can be used in any formula but it is
NOT acting as a variable in the formula just as a constant is not
acting as a variable in the formula.

/Flibble

On Saturday, 13 August 2022 at 14:09:50 UTC+2, Mr Flibble wrote:
> No, no, no, no and no. Infinity can be used in any formula but it is
> NOT acting as a variable in the formula just as a constant is not
> acting as a variable in the formula.

Imbecile. When 5 is assigned to x then x also acts as a constant in the equation "1 + x = 6"

On Sat, 13 Aug 2022 05:14:51 -0700 (PDT)
Skep Dick <skepdick22@gmail.com> wrote:

> On Saturday, 13 August 2022 at 14:09:50 UTC+2, Mr Flibble wrote:
> > No, no, no, no and no. Infinity can be used in any formula but it
> > is NOT acting as a variable in the formula just as a constant is
> > not acting as a variable in the formula.
>
> Imbecile. When 5 is assigned to x then x also acts as a constant in
> the equation "1 + x = 6"

You must have skipped math lessons at school. x is NOT constant in "1 +
x = 6", it is a VARIABLE.

/Flibble

On Saturday, 13 August 2022 at 14:37:21 UTC+2, Mr Flibble wrote:o x then x also acts as a constant in
> > the equation "1 + x = 6"
> You must have skipped math lessons at school. x is NOT constant in "1 +
> x = 6", it is a VARIABLE.

I told you that you don't undrstand the difference between bound and unbound variables, but you didn't even understand what that means.

The x in "1 + x = 6" is a variable when x is unbound.
The x in "1 + x = 6" is NOT a variable when x is bound to 5

Similarly:

If you give the name x to the symbol ∞;
and you give the name y to the symbol 1

Then you can write the following expression:

(x + y = x) ≡ (∞ + 1 = ∞)

Name binding. You don't understand it.

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

On Sat, 13 Aug 2022 05:48:47 -0700 (PDT)
Skep Dick <skepdick22@gmail.com> wrote:

> On Saturday, 13 August 2022 at 14:37:21 UTC+2, Mr Flibble wrote:o x
> then x also acts as a constant in
> > > the equation "1 + x = 6"
> > You must have skipped math lessons at school. x is NOT constant in
> > "1 + x = 6", it is a VARIABLE.
>
> I told you that you don't undrstand the difference between bound and
> unbound variables, but you didn't even understand what that means.
>
> The x in "1 + x = 6" is a variable when x is unbound.
> The x in "1 + x = 6" is NOT a variable when x is bound to 5
>
> Similarly:
>
> If you give the name x to the symbol ∞;
> and you give the name y to the symbol 1
>
> Then you can write the following expression:
>
> (x + y = x) ≡ (∞ + 1 = ∞)
>
> Name binding. You don't understand it.
>
> https://en.wikipedia.org/wiki/Name_binding

Now you are confusing/conflating mathematics with programming
languages. You really are hopeless.

/Flibble

On Saturday, 13 August 2022 at 14:56:40 UTC+2, Mr Flibble wrote:
> On Sat, 13 Aug 2022 05:48:47 -0700 (PDT)
> Skep Dick <skepd...@gmail.com> wrote:
>
> > On Saturday, 13 August 2022 at 14:37:21 UTC+2, Mr Flibble wrote:o x
> > then x also acts as a constant in
> > > > the equation "1 + x = 6"
> > > You must have skipped math lessons at school. x is NOT constant in
> > > "1 + x = 6", it is a VARIABLE.
> >
> > I told you that you don't undrstand the difference between bound and
> > unbound variables, but you didn't even understand what that means.
> >
> > The x in "1 + x = 6" is a variable when x is unbound.
> > The x in "1 + x = 6" is NOT a variable when x is bound to 5
> >
> > Similarly:
> >
> > If you give the name x to the symbol ∞;
> > and you give the name y to the symbol 1
> >
> > Then you can write the following expression:
> >
> > (x + y = x) ≡ (∞ + 1 = ∞)
> >
> > Name binding. You don't understand it.
> >
> > https://en.wikipedia.org/wiki/Name_binding
> Now you are confusing/conflating mathematics with programming
> languages. You really are hopeless.

If I am hopeless then you are way worse. I understand exactly what Programming and Mathematics is all about.

In [1]: expression="1 + x == 6" # 1 + x = 6 is a Mathematical expression.

In [2]: eval(expression) # The expression cannot be evaluated if x is undefined. Obviously!
---------------------------------------------------------------------------
NameError Traceback (most recent call last)
Input In [2], in <cell line: 1>()
----> 1 eval(expression)
File <string>:1, in <module>
NameError: name 'x' is not defined

In [3]: x = 5 # As soon as we define x...

In [4]: eval(expression) # the expression evaluates to True (as expected)
Out[4]: True

In [5]: x = 9 # ... and with x=9

In [6]: eval(expression) # it evaluates to False (as expected)
Out[6]: False