it behaves like zero but is not.
..999 repeating plus an infinitesimal
sums to the first integer.
All integers are the same...

Mitchell Raemsch

On Tuesday, August 15, 2023 at 12:29:26 PM UTC-7, mitchr...@gmail.com wrote:
> it behaves like zero but is not.
> .999 repeating plus an infinitesimal
> sums to the first integer.
> All integers are the same...
>
> Mitchell Raemsch

..999 repeating and one don't plot on top of each other
they are two separated points. they are different quantities.
Different by an infinitesimal.

On Tuesday, August 15, 2023 at 8:05:51 PM UTC-7, mitchr...@gmail.com wrote:
> On Tuesday, August 15, 2023 at 12:29:26 PM UTC-7, mitchr...@gmail..com wrote:
> > it behaves like zero but is not.
> > .999 repeating plus an infinitesimal
> > sums to the first integer.
> > All integers are the same...
> >
> > Mitchell Raemsch
> .999 repeating and one don't plot on top of each other
> they are two separated points. they are different quantities.
> Different by an infinitesimal.

There are lots of kinds of infinitesimals, just like there are lots of kinds
of infinities, about the "potential' and "actual" and "effective" and "scalar"
and "absolute" and so on.

So, infinitesimals have various kinds like the nilpotent and nilvalent and nilsquare,
there are notions that are extensions of the Archimedean field like halos of hyperreals,
there are infinitesimals that are sort of standard like an Aristotle's continuum, and most
people's view of the "grain" of things, there are infinitesimals to infinitesimals, or what's
Newton's "fleas that bite 'em, ad infinitum" bit, there are lots of mathematical constructs
that are infinitesimals, Peano has infinitesimals, Stolz and Veronese, Dodgson, Vitali makes
a sort of infinitesimals, where Vitali's have the real character of the doubling space
and Aristotle's have the real character of the Zeno's space.

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

Cantor for example specifically has "no infinitesimals", or calls them the "cholera bacillus
of mathematics", but, at the time, what today we call "real analysis" was called "infintesimal
analysis", because it considers the treatments of arbitrarily small changes in arbitrarily small
intervals, or, the instantaneous rate of change, as with respect to usually Leibniz' differential,
but also Newton's fluents and fluxions, which can be seen as, sort of, two kinds of calculus, in,
how methods of exhaustion were known long before but Newton and Leibniz publicized
quite a few.

It's similar with retro-finitists, by excluding the infinite or infinitesimal, it makes some simpler
things easier to close, what aren't, though, because, they're unbounded, and they would have
closed them.

But, today there are various notions of mathematical infinitesimals, including those with
real character, i.e. that in mensurability add up to measures of things (areas, also for example
the lengths of lines, about integration and differentiation, and including in the non-standard
about the quasi-invariant measure theory and so on, or Ramsey theory, or Ross' special functions,
the re-Vitali-ization of measure theory and so on.)

For the historical account, it should be made clear that for a long time, Aristotle's continuum
accompanied Zeno's paradoxes, and as a complement to the notion of limit or exhaustion,
provides a usual notion of a modular clock arithmetic of infinitesimal differences, and
analysis was called "infinitesimal analysis" because that's what it is. Then, providing that
a justification for formalists according to rigor and modern mathematics (axiomatic set
theory, regular), gets pretty involved and Ross Finlayson's slates are the modern touchstone
of the paleo-classical renaissance.

On Tuesday, August 15, 2023 at 10:29:26 PM UTC+3, mitchr...@gmail.com wrote:
> it behaves like zero but is not.
> .999 repeating plus an infinitesimal
> sums to the first integer.
> All integers are the same...
>
> Mitchell Raemsch
Below infinitum is only another infitusem & the game is quite endless in mathematics

As if you are asking what is largest natural number, of course it doesn't exist so like the least infitusem in your mind doesn't exist although (as simple as it is)

But in non-mathematics, people are free to chose whatever they like to fitful their tasks practically

For Instance, a skilled carpenter would make his Epsilon as one mm , so like einginers or scientists, but uttely like the mathematicians also ....despite the fact that mathematicians are not carpenter nor they are any successful einginers or scientists
Where the theme is that modern mathematics is made solely by einginers & scientists where mathematicians cannot comprehend such a subtle truth & hide always behind practically & usefulness as the others do exactly

Got it?

🔊 Bassam Karzeddin 🔊

On Tuesday, August 15, 2023 at 8:22:18 PM UTC-7, Ross Finlayson wrote:
> On Tuesday, August 15, 2023 at 8:05:51 PM UTC-7, mitchr...@gmail.com wrote:
> > On Tuesday, August 15, 2023 at 12:29:26 PM UTC-7, mitchr...@gmail.com wrote:
> > > it behaves like zero but is not.
> > > .999 repeating plus an infinitesimal
> > > sums to the first integer.
> > > All integers are the same...
> > >
> > > Mitchell Raemsch
> > .999 repeating and one don't plot on top of each other
> > they are two separated points. they are different quantities.
> > Different by an infinitesimal.
> There are lots of kinds of infinitesimals, just like there are lots of kinds
> of infinities, about the "potential' and "actual" and "effective" and "scalar"
> and "absolute" and so on.
>
> So, infinitesimals have various kinds like the nilpotent and nilvalent and nilsquare,
> there are notions that are extensions of the Archimedean field like halos of hyperreals,
> there are infinitesimals that are sort of standard like an Aristotle's continuum, and most
> people's view of the "grain" of things, there are infinitesimals to infinitesimals, or what's
> Newton's "fleas that bite 'em, ad infinitum" bit, there are lots of mathematical constructs
> that are infinitesimals, Peano has infinitesimals, Stolz and Veronese, Dodgson, Vitali makes
> a sort of infinitesimals, where Vitali's have the real character of the doubling space
> and Aristotle's have the real character of the Zeno's space.
>
> https://en.wikipedia.org/wiki/Ad_infinitum
>
> Cantor for example specifically has "no infinitesimals", or calls them the "cholera bacillus
> of mathematics", but, at the time, what today we call "real analysis" was called "infintesimal
> analysis", because it considers the treatments of arbitrarily small changes in arbitrarily small
> intervals, or, the instantaneous rate of change, as with respect to usually Leibniz' differential,
> but also Newton's fluents and fluxions, which can be seen as, sort of, two kinds of calculus, in,
> how methods of exhaustion were known long before but Newton and Leibniz publicized
> quite a few.
>
> It's similar with retro-finitists, by excluding the infinite or infinitesimal, it makes some simpler
> things easier to close, what aren't, though, because, they're unbounded, and they would have
> closed them.
>
> But, today there are various notions of mathematical infinitesimals, including those with
> real character, i.e. that in mensurability add up to measures of things (areas, also for example
> the lengths of lines, about integration and differentiation, and including in the non-standard
> about the quasi-invariant measure theory and so on, or Ramsey theory, or Ross' special functions,
> the re-Vitali-ization of measure theory and so on.)
>
>
> For the historical account, it should be made clear that for a long time, Aristotle's continuum
> accompanied Zeno's paradoxes, and as a complement to the notion of limit or exhaustion,
> provides a usual notion of a modular clock arithmetic of infinitesimal differences, and
> analysis was called "infinitesimal analysis" because that's what it is. Then, providing that
> a justification for formalists according to rigor and modern mathematics (axiomatic set
> theory, regular), gets pretty involved and Ross Finlayson's slates are the modern touchstone
> of the paleo-classical renaissance.

Infinitesimals are just sorts of reciprocals and complementary duals of infinities.
Subject to many same forms of argument for and against them, I suppose you
can make that they're "ghosts of vanished quantities" to us, but, then the
argument goes that that's all we are to infinity, or apeiron.

There's a journal called "Apeiron", it has some various approaches in the non-standard
and as modernly.

The "apeiron" is Greek and it's basically both concepts of "infinity: no" and "infinity: yes".
The Archimedean is non-Archimedean is Archimedean again, ....

Another word is "iota", usually enough "one iota" is an infinitesimal.

On Tuesday, August 15, 2023 at 10:01:43 PM UTC-7, Ross Finlayson wrote:
> On Tuesday, August 15, 2023 at 8:22:18 PM UTC-7, Ross Finlayson wrote:
> > On Tuesday, August 15, 2023 at 8:05:51 PM UTC-7, mitchr...@gmail.com wrote:
> > > On Tuesday, August 15, 2023 at 12:29:26 PM UTC-7, mitchr...@gmail.com wrote:
> > > > it behaves like zero but is not.
> > > > .999 repeating plus an infinitesimal
> > > > sums to the first integer.
> > > > All integers are the same...
> > > >
> > > > Mitchell Raemsch
> > > .999 repeating and one don't plot on top of each other
> > > they are two separated points. they are different quantities.
> > > Different by an infinitesimal.
> > There are lots of kinds of infinitesimals, just like there are lots of kinds
> > of infinities, about the "potential' and "actual" and "effective" and "scalar"
> > and "absolute" and so on.
> >
> > So, infinitesimals have various kinds like the nilpotent and nilvalent and nilsquare,
> > there are notions that are extensions of the Archimedean field like halos of hyperreals,
> > there are infinitesimals that are sort of standard like an Aristotle's continuum, and most
> > people's view of the "grain" of things, there are infinitesimals to infinitesimals, or what's
> > Newton's "fleas that bite 'em, ad infinitum" bit, there are lots of mathematical constructs
> > that are infinitesimals, Peano has infinitesimals, Stolz and Veronese, Dodgson, Vitali makes
> > a sort of infinitesimals, where Vitali's have the real character of the doubling space
> > and Aristotle's have the real character of the Zeno's space.
> >
> > https://en.wikipedia.org/wiki/Ad_infinitum
> >
> > Cantor for example specifically has "no infinitesimals", or calls them the "cholera bacillus
> > of mathematics", but, at the time, what today we call "real analysis" was called "infintesimal
> > analysis", because it considers the treatments of arbitrarily small changes in arbitrarily small
> > intervals, or, the instantaneous rate of change, as with respect to usually Leibniz' differential,
> > but also Newton's fluents and fluxions, which can be seen as, sort of, two kinds of calculus, in,
> > how methods of exhaustion were known long before but Newton and Leibniz publicized
> > quite a few.
> >
> > It's similar with retro-finitists, by excluding the infinite or infinitesimal, it makes some simpler
> > things easier to close, what aren't, though, because, they're unbounded, and they would have
> > closed them.
> >
> > But, today there are various notions of mathematical infinitesimals, including those with
> > real character, i.e. that in mensurability add up to measures of things (areas, also for example
> > the lengths of lines, about integration and differentiation, and including in the non-standard
> > about the quasi-invariant measure theory and so on, or Ramsey theory, or Ross' special functions,
> > the re-Vitali-ization of measure theory and so on.)
> >
> >
> > For the historical account, it should be made clear that for a long time, Aristotle's continuum
> > accompanied Zeno's paradoxes, and as a complement to the notion of limit or exhaustion,
> > provides a usual notion of a modular clock arithmetic of infinitesimal differences, and
> > analysis was called "infinitesimal analysis" because that's what it is. Then, providing that
> > a justification for formalists according to rigor and modern mathematics (axiomatic set
> > theory, regular), gets pretty involved and Ross Finlayson's slates are the modern touchstone
> > of the paleo-classical renaissance.
> Infinitesimals are just sorts of reciprocals and complementary duals of infinities.
> Subject to many same forms of argument for and against them, I suppose you
> can make that they're "ghosts of vanished quantities" to us, but, then the
> argument goes that that's all we are to infinity, or apeiron.
>
> There's a journal called "Apeiron", it has some various approaches in the non-standard
> and as modernly.
>
> The "apeiron" is Greek and it's basically both concepts of "infinity: no" and "infinity: yes".
> The Archimedean is non-Archimedean is Archimedean again, ....
>
> Another word is "iota", usually enough "one iota" is an infinitesimal.

Huh, I just noticed that Wikipedia's Talk:Infinitesimal page is totally trash-filled by a troll
whose very notion is "what I'm talking about doesn't exist". What a tragedy of the commons.

The "Infinitesimal" page though is even suggesting that ".999... is both a dual representation
and has dual representations, ...".

Then it says "in modern mathematics such are built in ultrapowers", and it's like,
well, Aristotle just draws a line, of points a line, while Vitali atomizes that and
notices it doubles.

This where the "Infinity" page was often Russell's fawning quote, where now it's
a more gustatory "Cantor widened the study". Of course, Russell can stay in his
paradise, if though there's a rotten apple (or, bitter as it were).

So, the very attitude of controversy in what opinions form as modern mathematics
and modern axiomatic descriptive set theory, are in change, while of course it's about
the simplest, most direct, and most explored modern formalism, and as equi-interpretable
as any other. It's refreshing to see these changes over time, while of course would-be
denialists or do-overs will be expected to be paint-canned and whisk-broomed.

I'm pretty psyched, I can basically download and print this.

On Wednesday, August 16, 2023 at 1:42:12 AM UTC-4, Ross Finlayson wrote:
> On Tuesday, August 15, 2023 at 10:01:43 PM UTC-7, Ross Finlayson wrote:
> > On Tuesday, August 15, 2023 at 8:22:18 PM UTC-7, Ross Finlayson wrote:
> > > On Tuesday, August 15, 2023 at 8:05:51 PM UTC-7, mitchr...@gmail.com wrote:
> > > > On Tuesday, August 15, 2023 at 12:29:26 PM UTC-7, mitchr...@gmail.com wrote:
> > > > > it behaves like zero but is not.
> > > > > .999 repeating plus an infinitesimal
> > > > > sums to the first integer.
> > > > > All integers are the same...
> > > > >
> > > > > Mitchell Raemsch
> > > > .999 repeating and one don't plot on top of each other
> > > > they are two separated points. they are different quantities.
> > > > Different by an infinitesimal.
> > > There are lots of kinds of infinitesimals, just like there are lots of kinds
> > > of infinities, about the "potential' and "actual" and "effective" and "scalar"
> > > and "absolute" and so on.
> > >
> > > So, infinitesimals have various kinds like the nilpotent and nilvalent and nilsquare,
> > > there are notions that are extensions of the Archimedean field like halos of hyperreals,
> > > there are infinitesimals that are sort of standard like an Aristotle's continuum, and most
> > > people's view of the "grain" of things, there are infinitesimals to infinitesimals, or what's
> > > Newton's "fleas that bite 'em, ad infinitum" bit, there are lots of mathematical constructs
> > > that are infinitesimals, Peano has infinitesimals, Stolz and Veronese, Dodgson, Vitali makes
> > > a sort of infinitesimals, where Vitali's have the real character of the doubling space
> > > and Aristotle's have the real character of the Zeno's space.
> > >
> > > https://en.wikipedia.org/wiki/Ad_infinitum
> > >
> > > Cantor for example specifically has "no infinitesimals", or calls them the "cholera bacillus
> > > of mathematics", but, at the time, what today we call "real analysis" was called "infintesimal
> > > analysis", because it considers the treatments of arbitrarily small changes in arbitrarily small
> > > intervals, or, the instantaneous rate of change, as with respect to usually Leibniz' differential,
> > > but also Newton's fluents and fluxions, which can be seen as, sort of, two kinds of calculus, in,
> > > how methods of exhaustion were known long before but Newton and Leibniz publicized
> > > quite a few.
> > >
> > > It's similar with retro-finitists, by excluding the infinite or infinitesimal, it makes some simpler
> > > things easier to close, what aren't, though, because, they're unbounded, and they would have
> > > closed them.
> > >
> > > But, today there are various notions of mathematical infinitesimals, including those with
> > > real character, i.e. that in mensurability add up to measures of things (areas, also for example
> > > the lengths of lines, about integration and differentiation, and including in the non-standard
> > > about the quasi-invariant measure theory and so on, or Ramsey theory, or Ross' special functions,
> > > the re-Vitali-ization of measure theory and so on.)
> > >
> > >
> > > For the historical account, it should be made clear that for a long time, Aristotle's continuum
> > > accompanied Zeno's paradoxes, and as a complement to the notion of limit or exhaustion,
> > > provides a usual notion of a modular clock arithmetic of infinitesimal differences, and
> > > analysis was called "infinitesimal analysis" because that's what it is. Then, providing that
> > > a justification for formalists according to rigor and modern mathematics (axiomatic set
> > > theory, regular), gets pretty involved and Ross Finlayson's slates are the modern touchstone
> > > of the paleo-classical renaissance.
> > Infinitesimals are just sorts of reciprocals and complementary duals of infinities.
> > Subject to many same forms of argument for and against them, I suppose you
> > can make that they're "ghosts of vanished quantities" to us, but, then the
> > argument goes that that's all we are to infinity, or apeiron.
> >
> > There's a journal called "Apeiron", it has some various approaches in the non-standard
> > and as modernly.
> >
> > The "apeiron" is Greek and it's basically both concepts of "infinity: no" and "infinity: yes".
> > The Archimedean is non-Archimedean is Archimedean again, ....
> >
> > Another word is "iota", usually enough "one iota" is an infinitesimal.
> Huh, I just noticed that Wikipedia's Talk:Infinitesimal page is totally trash-filled by a troll
> whose very notion is "what I'm talking about doesn't exist". What a tragedy of the commons.
>
> The "Infinitesimal" page though is even suggesting that ".999... is both a dual representation
> and has dual representations, ...".
>
> Then it says "in modern mathematics such are built in ultrapowers", and it's like,
> well, Aristotle just draws a line, of points a line, while Vitali atomizes that and
> notices it doubles.
>
> This where the "Infinity" page was often Russell's fawning quote, where now it's
> a more gustatory "Cantor widened the study". Of course, Russell can stay in his
> paradise, if though there's a rotten apple (or, bitter as it were).
>
> So, the very attitude of controversy in what opinions form as modern mathematics
> and modern axiomatic descriptive set theory, are in change, while of course it's about
> the simplest, most direct, and most explored modern formalism, and as equi-interpretable
> as any other. It's refreshing to see these changes over time, while of course would-be
> denialists or do-overs will be expected to be paint-canned and whisk-broomed.
>
> I'm pretty psyched, I can basically download and print this.

Let x = 1.000...0 - 0.999...9
x = 0.000...01
xx = 0.000...0.000...01
so the square of the infinitessimal is a rank-two infinitessimal, which carries twice as many digits. It is far smaller.
If you don't like it stop using repeating digits: they are a bit of a farce..
Inductively speaking, though, they can work.

On 8/15/2023 12:29 PM, mitchr...@gmail.com wrote:
> it behaves like zero but is not.
> .999 repeating plus an infinitesimal
> sums to the first integer.
> All integers are the same...

Why do you think that negative numbers do not exist?

A negative number is less than zero. Got it?

It happens that Chris M. Thomasson formulated :
> On 8/15/2023 12:29 PM, mitchr...@gmail.com wrote:
>> it behaves like zero but is not.
>> .999 repeating plus an infinitesimal
>> sums to the first integer.
>> All integers are the same...
>
> Why do you think that negative numbers do not exist?
>
> A negative number is less than zero. Got it?

If he is really meaning the integers, then he is tacitly accepting
negative numbers.

On Wednesday, August 16, 2023 at 12:32:49 PM UTC-7, Chris M. Thomasson wrote:
> On 8/15/2023 12:29 PM, mitchr...@gmail.com wrote:
> > it behaves like zero but is not.
> > .999 repeating plus an infinitesimal
> > sums to the first integer.
> > All integers are the same...
> Why do you think that negative numbers do not exist?
>
> A negative number is less than zero. Got it?

There is nothing less than zero.
Zero quantity math wins.

Mitchell Raemsch

On 8/16/2023 4:49 PM, mitchr...@gmail.com wrote:
> On Wednesday, August 16, 2023 at 12:32:49 PM UTC-7, Chris M. Thomasson wrote:
>> On 8/15/2023 12:29 PM, mitchr...@gmail.com wrote:
>>> it behaves like zero but is not.
>>> .999 repeating plus an infinitesimal
>>> sums to the first integer.
>>> All integers are the same...
>> Why do you think that negative numbers do not exist?
>>
>> A negative number is less than zero. Got it?
>
> There is nothing less than zero.

> Zero quantity math wins.

So you say 2 - 4 is not possible and any calculator that can compute it
is wrong?

On Wednesday, August 16, 2023 at 5:25:59 PM UTC-7, Chris M. Thomasson wrote:
> On 8/16/2023 4:49 PM, mitchr...@gmail.com wrote:
> > On Wednesday, August 16, 2023 at 12:32:49 PM UTC-7, Chris M. Thomasson wrote:
> >> On 8/15/2023 12:29 PM, mitchr...@gmail.com wrote:
> >>> it behaves like zero but is not.
> >>> .999 repeating plus an infinitesimal
> >>> sums to the first integer.
> >>> All integers are the same...
> >> Why do you think that negative numbers do not exist?
> >>
> >> A negative number is less than zero. Got it?
> >
> > There is nothing less than zero.
>
>
> > Zero quantity math wins.
> So you say 2 - 4 is not possible and any calculator that can compute it
> is wrong?

Yes. That is its mistaken subtraction that is overshooting.
Can you compute it and how do you know it is right?

On 8/16/2023 5:48 PM, mitchr...@gmail.com wrote:
> On Wednesday, August 16, 2023 at 5:25:59 PM UTC-7, Chris M. Thomasson wrote:
>> On 8/16/2023 4:49 PM, mitchr...@gmail.com wrote:
>>> On Wednesday, August 16, 2023 at 12:32:49 PM UTC-7, Chris M. Thomasson wrote:
>>>> On 8/15/2023 12:29 PM, mitchr...@gmail.com wrote:
>>>>> it behaves like zero but is not.
>>>>> .999 repeating plus an infinitesimal
>>>>> sums to the first integer.
>>>>> All integers are the same...
>>>> Why do you think that negative numbers do not exist?
>>>>
>>>> A negative number is less than zero. Got it?
>>>
>>> There is nothing less than zero.
>>
>>
>>> Zero quantity math wins.
>> So you say 2 - 4 is not possible and any calculator that can compute it
>> is wrong?
>
> Yes. That is its mistaken subtraction that is overshooting.
> Can you compute it and how do you know it is right?

Yes. 2 - 4 = -2 It is right because -2 + 4 = 2

Where did you totally seem to manage to skip negative numbers when you
went to school? Think of a number line with a zero in it. Left negative,
right positive, middle is the zero at origin.

On Wednesday, August 16, 2023 at 5:51:30 PM UTC-7, Chris M. Thomasson wrote:
> On 8/16/2023 5:48 PM, mitchr...@gmail.com wrote:
> > On Wednesday, August 16, 2023 at 5:25:59 PM UTC-7, Chris M. Thomasson wrote:
> >> On 8/16/2023 4:49 PM, mitchr...@gmail.com wrote:
> >>> On Wednesday, August 16, 2023 at 12:32:49 PM UTC-7, Chris M. Thomasson wrote:
> >>>> On 8/15/2023 12:29 PM, mitchr...@gmail.com wrote:
> >>>>> it behaves like zero but is not.
> >>>>> .999 repeating plus an infinitesimal
> >>>>> sums to the first integer.
> >>>>> All integers are the same...
> >>>> Why do you think that negative numbers do not exist?
> >>>>
> >>>> A negative number is less than zero. Got it?
> >>>
> >>> There is nothing less than zero.
> >>
> >>
> >>> Zero quantity math wins.
> >> So you say 2 - 4 is not possible and any calculator that can compute it
> >> is wrong?
> >
> > Yes. That is its mistaken subtraction that is overshooting.
> > Can you compute it and how do you know it is right?
> Yes. 2 - 4 = -2 It is right because -2 + 4 = 2

There is no negative 2. That is a subtraction in your equation instead.

>
> Where did you totally seem to manage to skip negative numbers when you
> went to school? Think of a number line with a zero in it. Left negative,
> right positive, middle is the zero at origin.

On 8/16/2023 6:58 PM, mitchr...@gmail.com wrote:
> On Wednesday, August 16, 2023 at 5:51:30 PM UTC-7, Chris M. Thomasson wrote:
>> On 8/16/2023 5:48 PM, mitchr...@gmail.com wrote:
>>> On Wednesday, August 16, 2023 at 5:25:59 PM UTC-7, Chris M. Thomasson wrote:
>>>> On 8/16/2023 4:49 PM, mitchr...@gmail.com wrote:
>>>>> On Wednesday, August 16, 2023 at 12:32:49 PM UTC-7, Chris M. Thomasson wrote:
>>>>>> On 8/15/2023 12:29 PM, mitchr...@gmail.com wrote:
>>>>>>> it behaves like zero but is not.
>>>>>>> .999 repeating plus an infinitesimal
>>>>>>> sums to the first integer.
>>>>>>> All integers are the same...
>>>>>> Why do you think that negative numbers do not exist?
>>>>>>
>>>>>> A negative number is less than zero. Got it?
>>>>>
>>>>> There is nothing less than zero.
>>>>
>>>>
>>>>> Zero quantity math wins.
>>>> So you say 2 - 4 is not possible and any calculator that can compute it
>>>> is wrong?
>>>
>>> Yes. That is its mistaken subtraction that is overshooting.
>>> Can you compute it and how do you know it is right?
>> Yes. 2 - 4 = -2 It is right because -2 + 4 = 2
>
> There is no negative 2. That is a subtraction in your equation instead.

Four subtracted from two is negative two.

>
>>
>> Where did you totally seem to manage to skip negative numbers when you
>> went to school? Think of a number line with a zero in it. Left negative,
>> right positive, middle is the zero at origin.

On Wednesday, August 16, 2023 at 8:15:30 PM UTC-7, Chris M. Thomasson wrote:
> On 8/16/2023 6:58 PM, mitchr...@gmail.com wrote:
> > On Wednesday, August 16, 2023 at 5:51:30 PM UTC-7, Chris M. Thomasson wrote:
> >> On 8/16/2023 5:48 PM, mitchr...@gmail.com wrote:
> >>> On Wednesday, August 16, 2023 at 5:25:59 PM UTC-7, Chris M. Thomasson wrote:
> >>>> On 8/16/2023 4:49 PM, mitchr...@gmail.com wrote:
> >>>>> On Wednesday, August 16, 2023 at 12:32:49 PM UTC-7, Chris M.. Thomasson wrote:
> >>>>>> On 8/15/2023 12:29 PM, mitchr...@gmail.com wrote:
> >>>>>>> it behaves like zero but is not.
> >>>>>>> .999 repeating plus an infinitesimal
> >>>>>>> sums to the first integer.
> >>>>>>> All integers are the same...
> >>>>>> Why do you think that negative numbers do not exist?
> >>>>>>
> >>>>>> A negative number is less than zero. Got it?
> >>>>>
> >>>>> There is nothing less than zero.
> >>>>
> >>>>
> >>>>> Zero quantity math wins.
> >>>> So you say 2 - 4 is not possible and any calculator that can compute it
> >>>> is wrong?
> >>>
> >>> Yes. That is its mistaken subtraction that is overshooting.
> >>> Can you compute it and how do you know it is right?
> >> Yes. 2 - 4 = -2 It is right because -2 + 4 = 2
> >
> > There is no negative 2. That is a subtraction in your equation instead.
> Four subtracted from two is negative two.
> >
> >>
> >> Where did you totally seem to manage to skip negative numbers when you
> >> went to school? Think of a number line with a zero in it. Left negative,
> >> right positive, middle is the zero at origin.

It's a sort of variety of sock-puppet trollery, basically that the mental construct
it's provided is given various definitions or decisions in what are multiplicities,
then that it's able to maintain a simple strong consistency on the one side,
while the other is entirely etrangee, thus resulting that in very limited resources,
it's able to maintain a mental model of a limited domain, fully or as well-explored,
in limited resources.

That there are, "generalized inverses", or, "complementary duals", is a pretty usual
thing, then about though whether that leads to decision paralysis, or hysteresis,
that otherwise though it's required for (wider) thoroughness and completeness.

Then for things like infinitesimals, for example:

there's no smallest
vis-a-vis
there's an arbtrarily small that's indistinguishable from increment but is non-zero,

and it's similar for infinities, about framing things in relations like orderings or
inequalities, and noticing the carriage of the inverse, that what's true or factual
about the given setting like delta-epsilonics makes things, is sort of similarly
when simply reversing all the orderings and inequalities and whether that
results a converse, these kinds of things, in generalized inverses (of, for
exampled, generalized products like inner, central, and outer products),
and complementary duals (what fulfill being inverses in operations and such,
including where filling in the completions of each other what are incomplete
either way).

So, a stubborn adherence to a sort of the counter factual, or propositional,
it's sort of easy to understand why it could be so, though, still, there are
many ways why it could be so, and multiple ways, and it will vary from person
to person.

This is that "singularity theory" is really a branch of "multiplicity theory",
and, vice-versa.

Then, these kinds of exercises in reasoning can help in accommodation of
usual critical analysis and as from both sides and so on, argument the logical,
and rhetoric besides.

On Wednesday, August 16, 2023 at 9:20:52 PM UTC-7, Ross Finlayson wrote:
> On Wednesday, August 16, 2023 at 8:15:30 PM UTC-7, Chris M. Thomasson wrote:
> > On 8/16/2023 6:58 PM, mitchr...@gmail.com wrote:
> > > On Wednesday, August 16, 2023 at 5:51:30 PM UTC-7, Chris M. Thomasson wrote:
> > >> On 8/16/2023 5:48 PM, mitchr...@gmail.com wrote:
> > >>> On Wednesday, August 16, 2023 at 5:25:59 PM UTC-7, Chris M. Thomasson wrote:
> > >>>> On 8/16/2023 4:49 PM, mitchr...@gmail.com wrote:
> > >>>>> On Wednesday, August 16, 2023 at 12:32:49 PM UTC-7, Chris M. Thomasson wrote:
> > >>>>>> On 8/15/2023 12:29 PM, mitchr...@gmail.com wrote:
> > >>>>>>> it behaves like zero but is not.
> > >>>>>>> .999 repeating plus an infinitesimal
> > >>>>>>> sums to the first integer.
> > >>>>>>> All integers are the same...
> > >>>>>> Why do you think that negative numbers do not exist?
> > >>>>>>
> > >>>>>> A negative number is less than zero. Got it?
> > >>>>>
> > >>>>> There is nothing less than zero.
> > >>>>
> > >>>>
> > >>>>> Zero quantity math wins.
> > >>>> So you say 2 - 4 is not possible and any calculator that can compute it
> > >>>> is wrong?
> > >>>
> > >>> Yes. That is its mistaken subtraction that is overshooting.
> > >>> Can you compute it and how do you know it is right?
> > >> Yes. 2 - 4 = -2 It is right because -2 + 4 = 2
> > >
> > > There is no negative 2. That is a subtraction in your equation instead.
> > Four subtracted from two is negative two.
> > >
> > >>
> > >> Where did you totally seem to manage to skip negative numbers when you
> > >> went to school? Think of a number line with a zero in it. Left negative,
> > >> right positive, middle is the zero at origin.
> It's a sort of variety of sock-puppet trollery, basically that the mental construct
> it's provided is given various definitions or decisions in what are multiplicities,
> then that it's able to maintain a simple strong consistency on the one side,
> while the other is entirely etrangee, thus resulting that in very limited resources,
> it's able to maintain a mental model of a limited domain, fully or as well-explored,
> in limited resources.
>
> That there are, "generalized inverses", or, "complementary duals", is a pretty usual
> thing, then about though whether that leads to decision paralysis, or hysteresis,
> that otherwise though it's required for (wider) thoroughness and completeness.
>
> Then for things like infinitesimals, for example:
>
> there's no smallest
> vis-a-vis
> there's an arbtrarily small that's indistinguishable from increment but is non-zero,
>
> and it's similar for infinities, about framing things in relations like orderings or
> inequalities, and noticing the carriage of the inverse, that what's true or factual
> about the given setting like delta-epsilonics makes things, is sort of similarly
> when simply reversing all the orderings and inequalities and whether that
> results a converse, these kinds of things, in generalized inverses (of, for
> exampled, generalized products like inner, central, and outer products),
> and complementary duals (what fulfill being inverses in operations and such,
> including where filling in the completions of each other what are incomplete
> either way).
>
> So, a stubborn adherence to a sort of the counter factual, or propositional,
> it's sort of easy to understand why it could be so, though, still, there are
> many ways why it could be so, and multiple ways, and it will vary from person
> to person.
>
>
> This is that "singularity theory" is really a branch of "multiplicity theory",
> and, vice-versa.
>
>
> Then, these kinds of exercises in reasoning can help in accommodation of
> usual critical analysis and as from both sides and so on, argument the logical,
> and rhetoric besides.

The law or axiom of the inverse, is one of the first in a theory, like the
old "what goes up must come down", while, "some things go up".

On Wednesday, August 16, 2023 at 8:15:30 PM UTC-7, Chris M. Thomasson wrote:
> On 8/16/2023 6:58 PM, mitchr...@gmail.com wrote:
> > On Wednesday, August 16, 2023 at 5:51:30 PM UTC-7, Chris M. Thomasson wrote:
> >> On 8/16/2023 5:48 PM, mitchr...@gmail.com wrote:
> >>> On Wednesday, August 16, 2023 at 5:25:59 PM UTC-7, Chris M. Thomasson wrote:
> >>>> On 8/16/2023 4:49 PM, mitchr...@gmail.com wrote:
> >>>>> On Wednesday, August 16, 2023 at 12:32:49 PM UTC-7, Chris M.. Thomasson wrote:
> >>>>>> On 8/15/2023 12:29 PM, mitchr...@gmail.com wrote:
> >>>>>>> it behaves like zero but is not.
> >>>>>>> .999 repeating plus an infinitesimal
> >>>>>>> sums to the first integer.
> >>>>>>> All integers are the same...
> >>>>>> Why do you think that negative numbers do not exist?
> >>>>>>
> >>>>>> A negative number is less than zero. Got it?
> >>>>>
> >>>>> There is nothing less than zero.
> >>>>
> >>>>
> >>>>> Zero quantity math wins.
> >>>> So you say 2 - 4 is not possible and any calculator that can compute it
> >>>> is wrong?
> >>>
> >>> Yes. That is its mistaken subtraction that is overshooting.
> >>> Can you compute it and how do you know it is right?
> >> Yes. 2 - 4 = -2 It is right because -2 + 4 = 2
> >
> > There is no negative 2. That is a subtraction in your equation instead.
> Four subtracted from two is negative two

No. That is an overshoot of subtraction that does not apply.
There is nothing below 0.

> >
> >>
> >> Where did you totally seem to manage to skip negative numbers when you
> >> went to school? Think of a number line with a zero in it. Left negative,
> >> right positive, middle is the zero at origin.

On 8/17/2023 10:15 AM, mitchr...@gmail.com wrote:
> On Wednesday, August 16, 2023 at 8:15:30 PM UTC-7, Chris M. Thomasson wrote:
>> On 8/16/2023 6:58 PM, mitchr...@gmail.com wrote:
>>> On Wednesday, August 16, 2023 at 5:51:30 PM UTC-7, Chris M. Thomasson wrote:
>>>> On 8/16/2023 5:48 PM, mitchr...@gmail.com wrote:
>>>>> On Wednesday, August 16, 2023 at 5:25:59 PM UTC-7, Chris M. Thomasson wrote:
>>>>>> On 8/16/2023 4:49 PM, mitchr...@gmail.com wrote:
>>>>>>> On Wednesday, August 16, 2023 at 12:32:49 PM UTC-7, Chris M. Thomasson wrote:
>>>>>>>> On 8/15/2023 12:29 PM, mitchr...@gmail.com wrote:
>>>>>>>>> it behaves like zero but is not.
>>>>>>>>> .999 repeating plus an infinitesimal
>>>>>>>>> sums to the first integer.
>>>>>>>>> All integers are the same...
>>>>>>>> Why do you think that negative numbers do not exist?
>>>>>>>>
>>>>>>>> A negative number is less than zero. Got it?
>>>>>>>
>>>>>>> There is nothing less than zero.
>>>>>>
>>>>>>
>>>>>>> Zero quantity math wins.
>>>>>> So you say 2 - 4 is not possible and any calculator that can compute it
>>>>>> is wrong?
>>>>>
>>>>> Yes. That is its mistaken subtraction that is overshooting.
>>>>> Can you compute it and how do you know it is right?
>>>> Yes. 2 - 4 = -2 It is right because -2 + 4 = 2
>>>
>>> There is no negative 2. That is a subtraction in your equation instead.
>> Four subtracted from two is negative two
>
> No. That is an overshoot of subtraction that does not apply.
> There is nothing below 0.

An overshoot? My god. Tell that to the Bank! WOW!!!!

>
>>>
>>>>
>>>> Where did you totally seem to manage to skip negative numbers when you
>>>> went to school? Think of a number line with a zero in it. Left negative,
>>>> right positive, middle is the zero at origin.

On Thursday, August 17, 2023 at 11:04:43 AM UTC-7, Chris M. Thomasson wrote:
> On 8/17/2023 10:15 AM, mitchr...@gmail.com wrote:
> > On Wednesday, August 16, 2023 at 8:15:30 PM UTC-7, Chris M. Thomasson wrote:
> >> On 8/16/2023 6:58 PM, mitchr...@gmail.com wrote:
> >>> On Wednesday, August 16, 2023 at 5:51:30 PM UTC-7, Chris M. Thomasson wrote:
> >>>> On 8/16/2023 5:48 PM, mitchr...@gmail.com wrote:
> >>>>> On Wednesday, August 16, 2023 at 5:25:59 PM UTC-7, Chris M. Thomasson wrote:
> >>>>>> On 8/16/2023 4:49 PM, mitchr...@gmail.com wrote:
> >>>>>>> On Wednesday, August 16, 2023 at 12:32:49 PM UTC-7, Chris M. Thomasson wrote:
> >>>>>>>> On 8/15/2023 12:29 PM, mitchr...@gmail.com wrote:
> >>>>>>>>> it behaves like zero but is not.
> >>>>>>>>> .999 repeating plus an infinitesimal
> >>>>>>>>> sums to the first integer.
> >>>>>>>>> All integers are the same...
> >>>>>>>> Why do you think that negative numbers do not exist?
> >>>>>>>>
> >>>>>>>> A negative number is less than zero. Got it?
> >>>>>>>
> >>>>>>> There is nothing less than zero.
> >>>>>>
> >>>>>>
> >>>>>>> Zero quantity math wins.
> >>>>>> So you say 2 - 4 is not possible and any calculator that can compute it
> >>>>>> is wrong?
> >>>>>
> >>>>> Yes. That is its mistaken subtraction that is overshooting.
> >>>>> Can you compute it and how do you know it is right?
> >>>> Yes. 2 - 4 = -2 It is right because -2 + 4 = 2
> >>>
> >>> There is no negative 2. That is a subtraction in your equation instead.
> >> Four subtracted from two is negative two
> >
> > No. That is an overshoot of subtraction that does not apply.
> > There is nothing below 0.
> An overshoot? My god. Tell that to the Bank! WOW!!!!

Yes. There is nothing below zero. Subtraction is not a negative quantity.
It is a negative operation for a positive. Attaching your "-" does not
change its absolute value's reality.

Mitchell Raemsch

> >>>
> >>>>
> >>>> Where did you totally seem to manage to skip negative numbers when you
> >>>> went to school? Think of a number line with a zero in it. Left negative,
> >>>> right positive, middle is the zero at origin.

On 8/17/2023 1:15 PM, mitchr...@gmail.com wrote:
> On Wednesday, August 16, 2023 at 8:15:30 PM UTC-7, Chris M. Thomasson wrote:
>> On 8/16/2023 6:58 PM, mitchr...@gmail.com wrote:
>>> On Wednesday, August 16, 2023 at 5:51:30 PM UTC-7, Chris M. Thomasson wrote:
>>>> On 8/16/2023 5:48 PM, mitchr...@gmail.com wrote:
>>>>> On Wednesday, August 16, 2023 at 5:25:59 PM UTC-7, Chris M. Thomasson wrote:
>>>>>> On 8/16/2023 4:49 PM, mitchr...@gmail.com wrote:
>>>>>>> On Wednesday, August 16, 2023 at 12:32:49 PM UTC-7, Chris M. Thomasson wrote:
>>>>>>>> On 8/15/2023 12:29 PM, mitchr...@gmail.com wrote:
>>>>>>>>> it behaves like zero but is not.
>>>>>>>>> .999 repeating plus an infinitesimal
>>>>>>>>> sums to the first integer.
>>>>>>>>> All integers are the same...
>>>>>>>> Why do you think that negative numbers do not exist?
>>>>>>>>
>>>>>>>> A negative number is less than zero. Got it?
>>>>>>>
>>>>>>> There is nothing less than zero.
>>>>>>
>>>>>>
>>>>>>> Zero quantity math wins.
>>>>>> So you say 2 - 4 is not possible and any calculator that can compute it
>>>>>> is wrong?
>>>>>
>>>>> Yes. That is its mistaken subtraction that is overshooting.
>>>>> Can you compute it and how do you know it is right?
>>>> Yes. 2 - 4 = -2 It is right because -2 + 4 = 2
>>>
>>> There is no negative 2. That is a subtraction in your equation instead.
>> Four subtracted from two is negative two
>
> No. That is an overshoot of subtraction that does not apply.
> There is nothing below 0.
>
What about charged objects, Roy? I can have an object with a charge of
+2 coulombs, subtract 4 coulombs of charge from it and the result is the
object charged with a charge of -2 coulombs. You won't answer the
reality of negative electric charges.

On Thursday, August 17, 2023 at 8:10:22 PM UTC+2, mitchr...@gmail.com wrote:
> On Thursday, August 17, 2023 at 11:04:43 AM UTC-7, Chris M. Thomasson wrote:
> > On 8/17/2023 10:15 AM, mitchr...@gmail.com wrote:
> > > On Wednesday, August 16, 2023 at 8:15:30 PM UTC-7, Chris M. Thomasson wrote:
> > >> On 8/16/2023 6:58 PM, mitchr...@gmail.com wrote:
> > >>> On Wednesday, August 16, 2023 at 5:51:30 PM UTC-7, Chris M. Thomasson wrote:
> > >>>> On 8/16/2023 5:48 PM, mitchr...@gmail.com wrote:
> > >>>>> On Wednesday, August 16, 2023 at 5:25:59 PM UTC-7, Chris M. Thomasson wrote:
> > >>>>>> On 8/16/2023 4:49 PM, mitchr...@gmail.com wrote:
> > >>>>>>> On Wednesday, August 16, 2023 at 12:32:49 PM UTC-7, Chris M. Thomasson wrote:
> > >>>>>>>> On 8/15/2023 12:29 PM, mitchr...@gmail.com wrote:
> > >>>>>>>>> it behaves like zero but is not.
> > >>>>>>>>> .999 repeating plus an infinitesimal
> > >>>>>>>>> sums to the first integer.
> > >>>>>>>>> All integers are the same...
> > >>>>>>>> Why do you think that negative numbers do not exist?
> > >>>>>>>>
> > >>>>>>>> A negative number is less than zero. Got it?
> > >>>>>>>
> > >>>>>>> There is nothing less than zero.
> > >>>>>>
> > >>>>>>
> > >>>>>>> Zero quantity math wins.
> > >>>>>> So you say 2 - 4 is not possible and any calculator that can compute it
> > >>>>>> is wrong?
> > >>>>>
> > >>>>> Yes. That is its mistaken subtraction that is overshooting.
> > >>>>> Can you compute it and how do you know it is right?
> > >>>> Yes. 2 - 4 = -2 It is right because -2 + 4 = 2
> > >>>
> > >>> There is no negative 2. That is a subtraction in your equation instead.
> > >> Four subtracted from two is negative two
> > >
> > > No. That is an overshoot of subtraction that does not apply.
> > > There is nothing below 0.
> > An overshoot? My god. Tell that to the Bank! WOW!!!!
> Yes. There is nothing below zero. Subtraction is not a negative quantity.
> It is a negative operation for a positive. Attaching your "-" does not
> change its absolute value's reality.
>
> Mitchell Raemsch
> > >>>
> > >>>>
> > >>>> Where did you totally seem to manage to skip negative numbers when you
> > >>>> went to school? Think of a number line with a zero in it. Left negative,
> > >>>> right positive, middle is the zero at origin.

Then why did my beer freeze when I put it in the freezer

On Thursday, August 17, 2023 at 3:59:05 AM UTC+2, mitchr...@gmail.com wrote:
> On Wednesday, August 16, 2023 at 5:51:30 PM UTC-7, Chris M. Thomasson wrote:
> > On 8/16/2023 5:48 PM, mitchr...@gmail.com wrote:
> > > On Wednesday, August 16, 2023 at 5:25:59 PM UTC-7, Chris M. Thomasson wrote:
> > >> On 8/16/2023 4:49 PM, mitchr...@gmail.com wrote:
> > >>> On Wednesday, August 16, 2023 at 12:32:49 PM UTC-7, Chris M.. Thomasson wrote:
> > >>>> On 8/15/2023 12:29 PM, mitchr...@gmail.com wrote:
> > >>>>> it behaves like zero but is not.
> > >>>>> .999 repeating plus an infinitesimal
> > >>>>> sums to the first integer.
> > >>>>> All integers are the same...
> > >>>> Why do you think that negative numbers do not exist?
> > >>>>
> > >>>> A negative number is less than zero. Got it?
> > >>>
> > >>> There is nothing less than zero.
> > >>
> > >>
> > >>> Zero quantity math wins.
> > >> So you say 2 - 4 is not possible and any calculator that can compute it
> > >> is wrong?
> > >
> > > Yes. That is its mistaken subtraction that is overshooting.
> > > Can you compute it and how do you know it is right?
> > Yes. 2 - 4 = -2 It is right because -2 + 4 = 2
> There is no negative 2. That is a subtraction in your equation instead.
> >
> > Where did you totally seem to manage to skip negative numbers when you
> > went to school? Think of a number line with a zero in it. Left negative,
> > right positive, middle is the zero at origin.

In group theory there is no subtraction, only addition. Every element has an additive inverse, with 0 being the additive identity.

On Friday, August 18, 2023 at 1:14:46 AM UTC+2, Kevin S wrote:

> In group theory there is no subtraction, only addition. Every element has an additive inverse, with 0 being the additive identity.

Right. And then we may define

a - b := a + (-b) .

:-P

On Friday, August 18, 2023 at 1:12:45 AM UTC+2, Kevin S wrote:

> Then why did my beer freeze when I put it in the freezer?

You put it in there too long.