Meritocracy used his or her keyboard to write :
> On 5/17/2021 2:32 PM, Julio Di Egidio wrote:
>> On Monday, 17 May 2021 at 21:29:10 UTC+2, Julio Di Egidio wrote:
>>> On Monday, 17 May 2021 at 20:39:54 UTC+2, Alan Mackenzie wrote:
>>>> Julio Di Egidio <ju...@diegidio.name> wrote:
>>>>> On Monday, 17 May 2021 at 19:32:21 UTC+2, Alan Mackenzie wrote:
>>>>>> Eram semper recta <thenewc...@gmail.com> wrote:
>>>>>>> On Monday, 17 May 2021 at 08:15:50 UTC-4, timba...@gmail.com wrote: [
>>>>>>> .... ]
>>>>>>>> Should it then be stated that integers can be constructed out of
>>>>>>>> rational numbers?
>>>>
>>>>>> Definitely not.
>>>>
>>>>> I agree with the overall sentiment, but that's not true: one can build
>>>>> numbers bottom up from the naturals, but it is also possible to go
>>>>> top-down from the reals.
>>>>
>>>> How, then, does one construct the reals in such a system? And having
>>>> the reals, how does one then derive the rationals?
>>> The same way one constructs the naturals in the other: postulate some
>>> primitives, in that case "continuity" in some form.
>>
>> ... then the rationals are some specific subset/substructure of the reals
>> ...
>
> start with natural numbers

This approach makes the most sense to me since it is logical that
mankind counted suns moons and seasons before the underlying geometry
behind these relations was even being guessed at.

On Monday, 17 May 2021 at 22:25:51 UTC+2, Alan Mackenzie wrote:
> Julio Di Egidio <ju...@diegidio.name> wrote:
> > On Monday, 17 May 2021 at 21:29:10 UTC+2, Julio Di Egidio wrote:
> >> On Monday, 17 May 2021 at 20:39:54 UTC+2, Alan Mackenzie wrote:
> >> > Julio Di Egidio <ju...@diegidio.name> wrote:
> >> > > On Monday, 17 May 2021 at 19:32:21 UTC+2, Alan Mackenzie wrote:
> >> > >> Eram semper recta <thenewc...@gmail.com> wrote:
> >> > >> > On Monday, 17 May 2021 at 08:15:50 UTC-4, timba...@gmail.com wrote:
> >> > >> [ .... ]
> >> > >> >> Should it then be stated that integers can be constructed out of
> >> > >> >> rational numbers?
>
> >> > >> Definitely not.
>
> >> > > I agree with the overall sentiment, but that's not true: one can build
> >> > > numbers bottom up from the naturals, but it is also possible to go
> >> > > top-down from the reals.
>
> >> > How, then, does one construct the reals in such a system? And having
> >> > the reals, how does one then derive the rationals?
>
> >> The same way one constructs the naturals in the other: postulate some
> >> primitives, in that case "continuity" in some form.
>
> > ... then the rationals are some specific subset/substructure of the
> > reals ...
> OK. That could be interesting, I've never seen it done that way before.
> I suppose that's more or less the way Mr. Gabriel's construction of
> numbers is supposed to work. Or something like that.
> > Sorry, I do not have ready references but shouldn't be too hard to find.
> Thanks, that's OK!
> >> > > By the way, the fact that theorems (to the extent that they apply) do
> >> > > not transpose easily if at all in standard mathematic, essentially due
> >> > > to a mixture of semantic with encoding aspects, is the main motivation
> >> > > for Univalent Foundations and the stronger notion of equality that it
> >> > > introduces ("equivalence is the same as equality"): such that e.g. the
> >> > > rational 2/1 is in fact the same as the integer 2 in that theory, and
> >> > > the same theorems apply to both.
>
> >> > How can that be, when integers and ratonals both have properties that
> >> > the other doesn't? For example, the rationals are topologically dense,
> >> > the integers have factorisations.
>
> >> To the extent that they apply: i.e. there is an overlap as of course
> >> the integers are a subset as well as substructure of the rationals,
> >> and so on. In standard formal mathematics you can hardly even say that
> >> 2/1 the rational number is equal to 2 the integer.
> No, you would say there is a mapping of the integers into the rational
> numbers, and then have to go through all the boring stuff about proving
> the mapping preserves this, that and the other.

Only to a certain extent... Do you think those guys are just wasting their time?

HTH,

Julio

On 5/17/2021 4:58 PM, FromTheRafters wrote:
> Meritocracy used his or her keyboard to write :

>> start with natural numbers
>
> This approach makes the most sense to me since it is
> logical that mankind counted suns moons and seasons
> before the underlying geometry behind these relations
> was even being guessed at.

Matt Ridley points to archeological evidence that there
have been goods exchanged over long distances for
pretty much as long as there have been human beings.
I'm going to guess that the ability to distinguish between
six arrow-heads and seven arrow-heads has been important
for that long.

Ridley ( _The Rational Optimist_ 2010) argues that this
exchange between strangers (unthinkable in other species)
is the force driving our extraordinary specialization. Some
tribes hunt deer, some tribes catch fish. Each get better
at what they do. They trade. Each is better off for
the other's R&D.

We've gotten so much better at hunting deer and catching fish
that we can walk on our Moon, and maybe destroy our planet.
(Power is not the same as wisdom.)

| Exchange is to cultural evolution as sex is to
| biological evolution.
| -- Matt Ridley, ibidem

måndag 17 maj 2021 kl. 13:30:01 UTC+2 skrev Eram semper recta:
> On Monday, 17 May 2021 at 01:11:26 UTC-4, zelos...@gmail.com wrote:
> > >Eudoxus of Cnidus used only **magnitudes** and that bullshit construction in the pdf you provided tries to build on his ideas albeit unsuccessfully.
> >
> > Who cares? We are not talking about his work.
> >
> > >Even the dumbest on this newsgroup know that you are an idiot. You were asked to demonstrate what that operator x (multiplication) means. Not only did you fail dismally in assuming that it means ac, but you failed to understand the question!
> >
> > There it is the multiplication of integers, duh.
> Newsflash: Integers are RATIONAL NUMBERS.
>
> Eyes rolling and FACEPALM.

To be pedantic, integers are their own set distinct from rational numbers but there is a natural injection when you localize them to make the rational numbers so one can with sloppy language say that integers are a subset of rationals despite it being technically false.

Cue you saying shit you do not understand in a pathetic attempt to disagree..

When you construction N -> Z -> Q -> R in that order you are free to assume the properties of the elements before in the chain. So I can assume the integer addition/multiplication which is what I did.

>Again, integers are rational numbers

The image of the natural monomorphism is a subset of rationals but integers are constructed before rationals.

>The FACT that you can multiply numerators by numerators and denominators by denominators is a consequence of what is transferred to algebra FROM GEOMETRY, you utter moron

In this construction it isn't, it is so by definition.

>You show with every post, your pitiful ineptitude to understand not only mathematics, but also the rudiments of English grammar.

And yet you're the one that shows you do not understand localization or anything else.

>FALSE. Every number (without exception) is a RATIONAL NUMBER

Except the irrational numbers, complex numbers, hyperreal numbers, hyperintegers, hyperrationals, p-adic numbers, etc etc etc

>and the arithmetic operations are transferred from GEOMETRY to ALGEBRA applicable ONLY to RATIONAL NUMBERS. In geometry we can multiply pi by sqrt2 exactly based on a given UNIT. In algebra, we cannot do this with the ABSTRACT UNIT. Try to understand, you pathetic crank!

I didn't use geometry in the construction because we don't use it anymore for it. Abstract algebra can do the job for us just fine once we got Natural numbers.

>See, there you go again.... Chuckle. The bullshit Eudoxus definition as I have demonstrated to you is based on MAGNITUDES and extrapolated to your delusional conclusions about real numbers. There is nothing in Arfan's PDF that even resembles rational thought. It is BULLSHIT in the simplest terms. Only deluded, uneducated, ignorant teacher sycophants like you fall for that kind of drivel. LMAO.

Then tell me, where in the following passage is there anything about magnitudes?

Definition 1A functionffromZtoZis said to be analmost homomorphismiff. the functiondffromZ×ZtoZdefined bydf(p, q) =f(p+q)−f(p)−f(q)has bounded range, i.e., for some integerC,|df(p, q)|. < Cfor allp, q∈Z.The functiondfmeasures the extent to whichffails to be a genuine homo-morphism:fis a genuine homomorphism iff.dfis identically 0. Note that therequirement on an almost homomorphism isnotthatdf(p, q) be non-zero foronly finitely manypandq, but that values taken on bydf(p, q) be bounded as2
pandqrange overZ. Typically, ifdf(p, q) is non-zero for somepandq, therewill be infinitely many pairs (r, s) for whichdf(r, s) =df(p, q).The setZ→Zof all functions fromZtoZbecomes an abelian group if weadd and invert functions pointwise: (f+g)(p) =f(p) +g(p), (−f)(p) =−f(p).It is easily checked that iffandgare almost homomorphisms then so aref+gand−f. WritingSfor the set of all almost homomorphisms fromZtoZ, thisshows thatSis a subgroup ofZ→Z. Let us writeBfor the set of all functionsfromZtoZwhose range is bounded.Bis a subgroup ofS.Definition 2The abelian groupEofEudoxus realsis the quotient groupS/B.Let me spell out what this means: elements ofEare equivalence classes, [f]say, wherefis an almost homomorphism fromZtoZ, i.e.,fis a function fromZtoZsuch thatdf(p, q) =f(p, q)−f(p)−f(q) defines a function fromZ×ZtoZwhose range is bounded. We have [f] = [g] iff. the differencef−ghas boundedrange, i.e., iff.|f(p)−g(p)|< Cfor someCand allpinZ. The addition andinverse inEare induced by the pointwise addition and inverse of representingalmost homomorphisms: [f] + [g] = [f+g],−[f] = [−f] wheref+gand−faredefined by (f+g)(p) =f(p) +g(p) and (−f)(p) =−f(p) for allpinZ.For example, if integersAandBare given, the linear functionf(p) =Ap+Bis an almost homomorphism, withdf(p, q) =−B. Ifg(p) =Cp+Dis anothersuch function then [f] = [g] iff.A=C. It follows that we can define a one-one mappingEfromZintoEby settingAE= [p7→Ap]. This mapping is ahomomorphism: (A+B)E=AE+BE.Our aim is now to show that the groupEof Eudoxus reals is isomorphic tothe group of real numbers under addition. To do this, we will prove “from firstprinciples”, i.e., using only elementary set theory and integer arithmetic, that,likeR,Ecan be equipped with an ordering and a multiplication that make itinto a complete ordered field. Any two complete ordered fieldsare isomorphicand soEandR(howsoeverRbe constructed) are isomorphic.

All I see is almost homomorphisms.

On Tuesday, 18 May 2021 at 00:42:03 UTC-4, zelos...@gmail.com wrote:
> måndag 17 maj 2021 kl. 13:30:01 UTC+2 skrev Eram semper recta:
> > On Monday, 17 May 2021 at 01:11:26 UTC-4, zelos...@gmail.com wrote:
> > > >Eudoxus of Cnidus used only **magnitudes** and that bullshit construction in the pdf you provided tries to build on his ideas albeit unsuccessfully.
> > >
> > > Who cares? We are not talking about his work.
> > >
> > > >Even the dumbest on this newsgroup know that you are an idiot. You were asked to demonstrate what that operator x (multiplication) means. Not only did you fail dismally in assuming that it means ac, but you failed to understand the question!
> > >
> > > There it is the multiplication of integers, duh.
> > Newsflash: Integers are RATIONAL NUMBERS.
> >
> > Eyes rolling and FACEPALM.

<drivel>

> When you construction N -> Z -> Q -> R in that order you are free to assume the properties of the elements before in the chain. So I can assume the integer addition/multiplication which is what I did.

Your laughable construction is wrong and you don't get to assume properties of the parts and then apply to the whole. Chuckle.

***The parts are not the whole***

I stand under correction but I think WM gave you a lesson on this?

Actually, here is the correct sequence:

Concept of magnitude or size
-> Ratio of magnitudes ( p:q )
-> The Unit ( p:u and q:u where the unit is u:u )
-> Number ( p/u and q/u)
-> Rational numbers ( which are actually ratios of numbers, ie, p/q )

> The image of the natural monomorphism is a subset of rationals but integers are constructed before rationals.

Rubbish. That is only the case in your bogus set theoretical construction. It's only opinion.

> In this construction it isn't, it is so by definition.

LMAO. No moron, the definition comes from GEOMETRY. You didn't define shit where ac = a x c. You got this from the brilliance of my ancestors. You are nothing but a stupid fuck. Chuckle.

>> FALSE. Every number (without exception) is a RATIONAL NUMBER

> Except the irrational numbers, complex numbers, hyperreal numbers, hyperintegers, hyperrationals, p-adic numbers, etc etc etc

Assertions are not well-formed concepts. Chuckle. None of the above are numbers because ....

A number is a name given to a **measure** that describes a magnitude or size.

THIS AND NOTHING ELSE. Chuckle.

> > and the arithmetic operations are transferred from GEOMETRY to ALGEBRA applicable ONLY to RATIONAL NUMBERS. In geometry we can multiply pi by sqrt2 exactly based on a given UNIT. In algebra, we cannot do this with the ABSTRACT UNIT. Try to understand, you pathetic crank!

> I didn't use geometry in the construction because we don't use it anymore for it.

You didn't use geometry because you don't know anything about geometry. Chuckle.

> Abstract algebra can do the job for us just fine once we got Natural numbers.

LMAO. You're a moron and nothing will ever change this. You can't use abstract algebra to construct the concept of number. The ONLY way it can be done is through geometry. In your bogus construction, you ASSUME the properties of multiplication as transferred to algebra from geometry.

You wouldn't even know how to multiply 2 by 3 without geometry. The knowledge of the operation of multiplication comes completely from geometry, at least the only well-formed knowledge. Chuckle.

> > The fact that you have to precede the object with the adjective "valid" is very telling! :-)

> Yes, you say they are invalid, yet fail to provide anything that shows them as invalid. Which is an internal contradiction.

Incorrect assertion again.

> > Come on Zelos, you are smarter than the rest of these morons and I want to keep beating your arse. Chuckle.

> You have yet to beat me in anything, especially mathematics.

Man, I am cleaning you out with every comment. LMAO. I have been almost merciless with you. In fact, I feel sorry that I have been so ruthless, but your stupidity calls for this treatment so that others can be warned.

> >So, explain to me what multiplication of rational numbers means.... I know you love circularity, but try not to use multiplication before you define it and remember you were asked for a GENERAL definition. You up to it or still searching for answers? LMAO.

> I already gave you it
> https://proofwiki.org/wiki/Localization_of_Ring_Exists
> Read up on it again in the generalized sense.

LMAO. You gave nothing but this garbage:

------------------------------------------------------------------------
i. a/b=[(a,b)]
ii. [(a,b)][(c,d)]=[(ac,bd)]
iii. 2.1=21/10=[(21,10)]
iv. 2.2=22/10=[(22,10)]
v. 2.1*2.2=[(21,10)][(22,10)]=[(462,100)]=4.62
-------------------------------------------------------------------------

>>I refresh my explanation here to help you! :-)
> >Step ii is obviously circular in that it assumes multiplication by rational numbers is already defined. The subsequent steps are wrong for too many reasons to address.

> > Assuming multiplication on integer is not the same as assuming multiplication on rational numbers.

> I did not assume multiplication of rational numbers, only integers.

For the thousandth time, integers ARE rational numbers. The properties that apply to integers DO NOT apply to the WHOLE, you fucking moron! Can you interpret 3/4 x 5/6 in the same way you interpret 2 x 3 as two lots of 3? You can't, you incorrigible dimwit!!!

The properties of the parts are NOT the properties of the whole.

WM already gave you that lesson.

On Tuesday, 18 May 2021 at 09:31:08 UTC-4, Eram semper recta wrote:
> On Tuesday, 18 May 2021 at 00:42:03 UTC-4, zelos...@gmail.com wrote:
> > måndag 17 maj 2021 kl. 13:30:01 UTC+2 skrev Eram semper recta:
> > > On Monday, 17 May 2021 at 01:11:26 UTC-4, zelos...@gmail.com wrote:
> > > > >Eudoxus of Cnidus used only **magnitudes** and that bullshit construction in the pdf you provided tries to build on his ideas albeit unsuccessfully.
> > > >
> > > > Who cares? We are not talking about his work.
> > > >
> > > > >Even the dumbest on this newsgroup know that you are an idiot. You were asked to demonstrate what that operator x (multiplication) means. Not only did you fail dismally in assuming that it means ac, but you failed to understand the question!
> > > >
> > > > There it is the multiplication of integers, duh.
> > > Newsflash: Integers are RATIONAL NUMBERS.
> > >
> > > Eyes rolling and FACEPALM.
> <drivel>
> > When you construction N -> Z -> Q -> R in that order you are free to assume the properties of the elements before in the chain. So I can assume the integer addition/multiplication which is what I did.
> Your laughable construction is wrong and you don't get to assume properties of the parts and then apply to the whole. Chuckle.
>
> ***The parts are not the whole***
>
> I stand under correction but I think WM gave you a lesson on this?
>
> Actually, here is the correct sequence:
>
> Concept of magnitude or size
> -> Ratio of magnitudes ( p:q )
> -> The Unit ( p:u and q:u where the unit is u:u )
> -> Number ( p/u and q/u)
> -> Rational numbers ( which are actually ratios of numbers, ie, p/q )
> > The image of the natural monomorphism is a subset of rationals but integers are constructed before rationals.
> Rubbish. That is only the case in your bogus set theoretical construction.. It's only opinion.
> > In this construction it isn't, it is so by definition.
> LMAO. No moron, the definition comes from GEOMETRY. You didn't define shit where ac = a x c. You got this from the brilliance of my ancestors. You are nothing but a stupid fuck. Chuckle.
> >> FALSE. Every number (without exception) is a RATIONAL NUMBER
>
> > Except the irrational numbers, complex numbers, hyperreal numbers, hyperintegers, hyperrationals, p-adic numbers, etc etc etc
> Assertions are not well-formed concepts. Chuckle. None of the above are numbers because ....
>
> A number is a name given to a **measure** that describes a magnitude or size.
>
> THIS AND NOTHING ELSE. Chuckle.
> > > and the arithmetic operations are transferred from GEOMETRY to ALGEBRA applicable ONLY to RATIONAL NUMBERS. In geometry we can multiply pi by sqrt2 exactly based on a given UNIT. In algebra, we cannot do this with the ABSTRACT UNIT. Try to understand, you pathetic crank!
>
> > I didn't use geometry in the construction because we don't use it anymore for it.
> You didn't use geometry because you don't know anything about geometry. Chuckle.
> > Abstract algebra can do the job for us just fine once we got Natural numbers.
> LMAO. You're a moron and nothing will ever change this. You can't use abstract algebra to construct the concept of number. The ONLY way it can be done is through geometry. In your bogus construction, you ASSUME the properties of multiplication as transferred to algebra from geometry.
>
> You wouldn't even know how to multiply 2 by 3 without geometry. The knowledge of the operation of multiplication comes completely from geometry, at least the only well-formed knowledge. Chuckle.
> > > The fact that you have to precede the object with the adjective "valid" is very telling! :-)
>
> > Yes, you say they are invalid, yet fail to provide anything that shows them as invalid. Which is an internal contradiction.
> Incorrect assertion again.
> > > Come on Zelos, you are smarter than the rest of these morons and I want to keep beating your arse. Chuckle.
>
> > You have yet to beat me in anything, especially mathematics.
> Man, I am cleaning you out with every comment. LMAO. I have been almost merciless with you. In fact, I feel sorry that I have been so ruthless, but your stupidity calls for this treatment so that others can be warned.
> > >So, explain to me what multiplication of rational numbers means.... I know you love circularity, but try not to use multiplication before you define it and remember you were asked for a GENERAL definition. You up to it or still searching for answers? LMAO.
>
> > I already gave you it
> > https://proofwiki.org/wiki/Localization_of_Ring_Exists
> > Read up on it again in the generalized sense.
> LMAO. You gave nothing but this garbage:
> ------------------------------------------------------------------------
> i. a/b=[(a,b)]
> ii. [(a,b)][(c,d)]=[(ac,bd)]
> iii. 2.1=21/10=[(21,10)]
> iv. 2.2=22/10=[(22,10)]
> v. 2.1*2.2=[(21,10)][(22,10)]=[(462,100)]=4.62
> -------------------------------------------------------------------------
> >>I refresh my explanation here to help you! :-)
> > >Step ii is obviously circular in that it assumes multiplication by rational numbers is already defined. The subsequent steps are wrong for too many reasons to address.
>
> > > Assuming multiplication on integer is not the same as assuming multiplication on rational numbers.
>
> > I did not assume multiplication of rational numbers, only integers.
> For the thousandth time, integers ARE rational numbers. The properties that apply to integers DO NOT apply to the WHOLE, you fucking moron! Can you interpret 3/4 x 5/6 in the same way you interpret 2 x 3 as two lots of 3? You can't, you incorrigible dimwit!!!
>
> The properties of the parts are NOT the properties of the whole.

You were asked for the generalisation of multiplication.

All operations of arithmetic can be stated strictly in terms of subtraction.. Addition is derived immediately from subtraction.

Division:

A quotient ps/qr is the rational number that is measured in terms of two numbers p/q and r/s.

ps/qr = [ p/q +p/q + ...n times ] / [ r/s + r/s+... n times ] where n=q or n=s.

Example: 2/3 -:- 5/6 = 4/5

p/q = 2/3 and r/s = 5/6

2/3 -:- 5/6 = [ 2/3 + 2/3 + 2/3 ] / [ 5/6 + 5/6 + 5/6] = [2] / [ 5/2] = [2 + 2] / [5/2 + 5/2] = 4 / 5

After the second equals sign, cancellation is again possible by Book 5, Proposition 12.

So the ENTIRE operation is done through geometry using similar triangles. No numbers are even required in the geometric definition, only magnitudes.

Multiplication:

The product (or multiplication) of two numbers p/q and r/s, that is, pr/qs is the quotient of either number
with the reciprocal of the other.

pr/qs = [ p/q +p/q + ...n times ] / [ s/r + s/r+... n times ] where n=q or n=r.

Example: 2/3 x 5/6 = 5/9

p/q = 2/3 and s/r = 6/5

2/3 x 5/6 = [2/3+2/3+2/3] / [6/5+6/5+6/5] = [2] / [18/5] = [ 2+2+2+2+2 ] / [18/5+18/5+18/5+18/5+18/5] = 10 / 18 = 5/9

AND

pr/qs = [ r/s + r/s+... n times ] / [ s/p + s/p+... n times ] where n=p or n=s.

This part is left as an exercise.

NOTE: The above definitions work on ANY magnitude. There is no need to have a separate interpretation for integers and fractions.

All these details are explained in my world famous article:

https://drive.google.com/file/d/0B-mOEooW03iLYTg1TGY4RTIwakU

>
> WM already gave you that lesson.

On Monday, May 17, 2021 at 4:58:56 PM UTC-4, FromTheRafters wrote:
> Meritocracy used his or her keyboard to write :
> > On 5/17/2021 2:32 PM, Julio Di Egidio wrote:
> >> On Monday, 17 May 2021 at 21:29:10 UTC+2, Julio Di Egidio wrote:
> >>> On Monday, 17 May 2021 at 20:39:54 UTC+2, Alan Mackenzie wrote:
> >>>> Julio Di Egidio <ju...@diegidio.name> wrote:
> >>>>> On Monday, 17 May 2021 at 19:32:21 UTC+2, Alan Mackenzie wrote:
> >>>>>> Eram semper recta <thenewc...@gmail.com> wrote:
> >>>>>>> On Monday, 17 May 2021 at 08:15:50 UTC-4, timba...@gmail.com wrote: [
> >>>>>>> .... ]
> >>>>>>>> Should it then be stated that integers can be constructed out of
> >>>>>>>> rational numbers?
> >>>>
> >>>>>> Definitely not.
> >>>>
> >>>>> I agree with the overall sentiment, but that's not true: one can build
> >>>>> numbers bottom up from the naturals, but it is also possible to go
> >>>>> top-down from the reals.
> >>>>
> >>>> How, then, does one construct the reals in such a system? And having
> >>>> the reals, how does one then derive the rationals?
> >>> The same way one constructs the naturals in the other: postulate some
> >>> primitives, in that case "continuity" in some form.
> >>
> >> ... then the rationals are some specific subset/substructure of the reals
> >> ...
> >
> > start with natural numbers
> This approach makes the most sense to me since it is logical that
> mankind counted suns moons and seasons before the underlying geometry
> behind these relations was even being guessed at.

Well, no doubt man was custom cutting saplings to fit in his shelter as well. The sense of continuous nature versus discrete is fundamental. We ought to admit that we do not have a true continuum representative in our mathematics. We always will settle for close enough. The only way we rest is by admitting that we can raise our resolution finer, and yet the physicists are telling us that we will bottom out at the Planck length. Mental purity is not what it seems. Our fundamental means are mimicry and variation. Without the mimicry it is unlikely that any of us would arrive here. Unfortunately our ability to break away from embedded assumptions is limited. Clearly this environment is one in which we should attempt such. Usenet is a fine place for such attempts. I can and do use polysign numbers as an instance that proves this possibility. The opportunity of another such discovery may be sitting beneath all of our noses and goes unleveraged for one invalid assumption that acts as an inhibitory filter on a class of solutions.

The freedoms and conflicts that have built the real number suggest that we actually have far greater freedom than we are taking. That the continuum could be so contaminated by singularities such as the square root of two and have an outstanding set of discrete integers embedded in it back in its beginnings; these details are how real analysis becomes a course that attempts to tuck and fold the human mind more than it is a build of a perfect number system.

Physical correspondence is something that the modern mathematician has escaped; that is the ground of the physicist. This divorce was completed generations ago, right? Well I happily declare that this artifice is merely another tuck and fold of the human mind, and that we obey this programming is indicative of the human mind more than it is perfection. The mathematicians sense of perfection is supposedly how they can rest their case, but this is not at all where we have landed. The sea of accumulation in the stacks and the terminology on the wikipedia in this day are not desirable. Simplicity is ultimately what is desirable. In Kant's day and in Descarte's day there was nature and man and common men had skills far beyond today's common man. The going to school to learn to read and write and do arithmetic was something that goes atop those basic skills that farmers and laborers had. Now playing with paper and pencil are the common skills, and we are left lacking the skills to survive in nature. Deadlines run us now why? To get a grade. The artifice of academia has brought us to this post-human state where we now ought to drop the tool-maker criterion from the defining qualities of the human. We have arrived in material wealth via mass production which marginalizes another type of richness that culturally is lost. Of course the rediscovery of those details is possible and I do encourage it. But these things are of the physical world. I cannot revere academia as it stands today. Corrections are in order. Unification is something that physicists have sought but have mathematicians sought it?

It is true that the continuous and the discrete do pair in our dimensional awareness. The dimension is discrete while the rendering within the discrete dimensions are continuous. 3D space is not 2.345D space; this latter does not exist other than as a cheap dropout form in fractal analysis. Mathematics seems to have thrown away any concern over dimensional analysis when they impose the cartesian product on the sum as is done within AA. This is a fail point and does need correction. The sum as a fundamental and emergent physical operator deserves better than this.

On 5/18/2021 9:13 AM, Timothy Golden wrote:
> On Monday, May 17, 2021 at 4:58:56 PM UTC-4, FromTheRafters wrote:
>> Meritocracy used his or her keyboard to write :
>>> On 5/17/2021 2:32 PM, Julio Di Egidio wrote:
>>>> On Monday, 17 May 2021 at 21:29:10 UTC+2, Julio Di Egidio wrote:
>>>>> On Monday, 17 May 2021 at 20:39:54 UTC+2, Alan Mackenzie wrote:
>>>>>> Julio Di Egidio <ju...@diegidio.name> wrote:
>>>>>>> On Monday, 17 May 2021 at 19:32:21 UTC+2, Alan Mackenzie wrote:
>>>>>>>> Eram semper recta <thenewc...@gmail.com> wrote:
>>>>>>>>> On Monday, 17 May 2021 at 08:15:50 UTC-4, timba...@gmail.com wrote: [
>>>>>>>>> .... ]
>>>>>>>>>> Should it then be stated that integers can be constructed out of
>>>>>>>>>> rational numbers?
>>>>>>
>>>>>>>> Definitely not.
>>>>>>
>>>>>>> I agree with the overall sentiment, but that's not true: one can build
>>>>>>> numbers bottom up from the naturals, but it is also possible to go
>>>>>>> top-down from the reals.
>>>>>>
>>>>>> How, then, does one construct the reals in such a system? And having
>>>>>> the reals, how does one then derive the rationals?
>>>>> The same way one constructs the naturals in the other: postulate some
>>>>> primitives, in that case "continuity" in some form.
>>>>
>>>> ... then the rationals are some specific subset/substructure of the reals
>>>> ...
>>>
>>> start with natural numbers
>> This approach makes the most sense to me since it is logical that
>> mankind counted suns moons and seasons before the underlying geometry
>> behind these relations was even being guessed at.
>
> Well, no doubt man was custom cutting saplings to fit in his shelter as well.

they only had stones in the Stone age, the round ones. Could not cut,
but could smash a sapling

>The sense of continuous nature versus discrete is fundamental.

I smell a BOT

> We ought to admit that we do not have a true continuum representative in our mathematics. We always will settle for close enough. The only way we rest is by admitting that we can raise our resolution finer, and yet the physicists are telling us that we will bottom out at the Planck length. Mental purity is not what it seems. Our fundamental means are mimicry and variation. Without the mimicry it is unlikely that any of us would arrive here. Unfortunately our ability to break away from embedded assumptions is limited. Clearly this environment is one in which we should attempt such. Usenet is a fine place for such attempts. I can and do use polysign numbers as an instance that proves this possibility. The opportunity of another such discovery may be sitting beneath all of our noses and goes unleveraged for one invalid assumption that acts as an inhibitory filter on a class of solutions.

Polysign numbers are used in signing Polyethylene containers only

>
> The freedoms and conflicts that have built the real number suggest that we actually have far greater freedom than we are taking.

where is that BOT SMELL coming from ? like confused OIL....

> That the continuum could be so contaminated by singularities such as the square root of two and have an outstanding set of discrete integers embedded in it back in its beginnings; these details are how real analysis becomes a course that attempts to tuck and fold the human mind more than it is a build of a perfect number system.

HA, 100% pure BOT CCHHATTER, you are BOT. ChatterBot

I compact the rest and analyze it, you BOT are plugged up with too many
s, t and n characters, get brain enema fast

> Physicalcorrespondenceissomethingthatthemodernmathematicianhases
caped;thatisthegroundofthephysicist.Thisdivorcewascompletedgenera
tionsago,rightWellIhappilydeclarethatthisartificeismerelyanothert
uckandfoldofthehumanmind,andthatweobeythisprogrammingisindicative
ofthehumanmindmorethanitisperfection.Themathematicianssenseofperf
ectionissupposedlyhowtheycanresttheircase,butthisisnotatallwherew
ehavelanded.Theseaofaccumulationinthestacksandtheterminologyonthe
wikipediainthisdayarenotdesirable.Simplicityisultimatelywhatisdes
irable.InKant'sdayandinDescarte'sdaytherewasnatureandmanandcommon
menhadskillsfarbeyondtoday'scommonman.Thegoingtoschooltolearntore
adandwriteanddoarithmeticwassomethingthatgoesatopthosebasicskills
thatfarmersandlaborershad.Nowplayingwithpaperandpencilarethecommo
nskills,andweareleftlackingtheskillstosurviveinnature.Deadlinesrun
usnowwhy?Togetagrade.Theartificeofacademiahasbroughtustothisposthu
manstatewherewenowoughttodropthetoolmakercriterionfromthedefiningq
ualitiesofthehuman.Wehavearrivedinmaterialwealthviamassproductionwh
ichmarginalizesanothertypeofrichnessthatculturallyislost.Ofcourset
herediscoveryofthosedetailsispossibleandIdoencourageit.Butthesethi
ngsareofthephysicalworld.Icannotrevereacademiaasitstandstoday.Corr
ectionsareinorder.Unificationissomethingthatphysicistshavesoughtbu
thavemathematicianssoughtitbullshitbullshitbullshitbullshitbullsh
Itistruethatthecontinuousandthediscretedopairinourdimensionalawa
reness.Thedimensionisdiscretewhiletherenderingwithinthediscretedim
ensionsarecontinuous.3Dspaceisnot2.345Dspace;thislatterdoesnotexis
totherthanasacheapdropoutforminfractalanalysis.Mathematicsseemstoha
vethrownawayanyconcernoverdimensionalanalysiswhentheyimposethecarte
sianproductonthesumasisdonewithinAA.Thisisafailpointanddoesneedcor
rection.Thesumasafundamentalandemergentphysicaloperatordeservesbetterthanthis.

e: 195
a: 167
t: 167
i: 150
s: 136
n: 127
o: 120
h: 108
r: 98
d: 73
c: 64
l: 58
m: 55
u: 40
p: 35
y: 29
w: 28
g: 27
f: 26
..: 22
v: 15
b: 11
T: 9
k: 9
I: 5
,: 4
D: 4
': 3
3: 2
;: 2
W: 2
A: 2
2: 1
4: 1
5: 1
P: 1
S: 1
K: 1
N: 1
?: 1
q: 1
z: 1
O: 1
B: 1
C: 1
U: 1
↵: 1
>: 1
x: 1
M: 1

>

>Your laughable construction is wrong and you don't get to assume properties of the parts and then apply to the whole. Chuckle.

They work perfectly fine, you being too stupid to understand is a fault on you, not the construction.

>Concept of magnitude or size

Which is irrelevant here.

>Rubbish. That is only the case in your bogus set theoretical construction. It's only opinion.

It is so in standard mathematics, get over it already.

>xLMAO. No moron, the definition comes from GEOMETRY. You didn't define shit where ac = a x c. You got this from the brilliance of my ancestors. You are nothing but a stupid fuck. Chuckle.

That is your opinion or anything.

I didn't define integer multiplication cause you wanted rational, I am free to assume it from Z then.

>Assertions are not well-formed concepts. Chuckle. None of the above are numbers because ....

Except they are.

>A number is a name given to a **measure** that describes a magnitude or size.
>THIS AND NOTHING ELSE. Chuckle.

This is nothing but your personal view, nothing else.

>You didn't use geometry because you don't know anything about geometry. Chuckle.

I know it quite fine, it is however not necessary in number construction.

>LMAO. You're a moron and nothing will ever change this. You can't use abstract algebra to construct the concept of number. The ONLY way it can be done is through geometry.

We construct structures that we call numbers. Get over it already.

>In your bogus construction, you ASSUME the properties of multiplication as transferred to algebra from geometry.

Not at all, I'd be more than happy to go through each step in the chain but I bet that is far beyond your dumb brain can handle.

>You wouldn't even know how to multiply 2 by 3 without geometry. The knowledge of the operation of multiplication comes completely from geometry, at least the only well-formed knowledge. Chuckle.

Not at all, we can use peanos to work it out just fine.

>Incorrect assertion again.

Very correct, if you disagree, show one statement in the construction where it is both true and false at the sametime or fails to give the properties of real numbers.

Hint, you never have, all you do is bitch that it doesn't fit your narrow views.

>Man, I am cleaning you out with every comment. LMAO. I have been almost merciless with you. In fact, I feel sorry that I have been so ruthless, but your stupidity calls for this treatment so that others can be warned

Dream on, but delusions is how you feed your narcissistic ego, yes no?

>LMAO. You gave nothing but this garbage:

Which follows from localization.

>For the thousandth time, integers ARE rational numbers.

We show they are a substructure of it AFTER we have constructed rational numbers. Before that we do not know and once we do know, we have already constructed rationals using integers and never had them before. Please learn this for once.

On Wednesday, 19 May 2021 at 01:33:10 UTC-4, zelos...@gmail.com wrote:

<too much bullshit by Zelos Malum and too little time to respond>

> >LMAO. No moron, the definition comes from GEOMETRY. You didn't define shit where ac = a x c. You got this from the brilliance of my ancestors. You are nothing but a stupid fuck. Chuckle.
>
> That is your opinion or anything.

It is FACT.

>
> I didn't define integer multiplication cause you wanted rational, I am free to assume it from Z then.

Liar. I said multiplication defined for ALL numbers, meaning Q.

Z and N are irrelevant - these came long after Q.

<more Malum Bullshit>

> >LMAO. You're a moron and nothing will ever change this. You can't use abstract algebra to construct the concept of number. The ONLY way it can be done is through geometry.
> We construct structures that we call numbers. Get over it already.

By structures, Malum means set theory, fields, etc. All the typical bullshit one finds in abstract algebra which is not mathematics at all.

> >In your bogus construction, you ASSUME the properties of multiplication as transferred to algebra from geometry.
> Not at all, I'd be more than happy to go through each step in the chain but I bet that is far beyond your dumb brain can handle.

Crank, if you could have, you would have done so already. You've already experienced one FAILED attempt.

> >You wouldn't even know how to multiply 2 by 3 without geometry. The knowledge of the operation of multiplication comes completely from geometry, at least the only well-formed knowledge. Chuckle.
> Not at all, we can use peanos to work it out just fine.

Chuckle. Anyone with a modicum of intelligence knows that Peano was nothing but a stupid ape and that his juvenile "axioms" are the joke of the 20th century.

> Very correct, if you disagree, show one statement in the construction where it is both true and false at the sametime or fails to give the properties of real numbers.

Been done. Your dumb and biased brain is too stupid to see reason.

> >Man, I am cleaning you out with every comment. LMAO. I have been almost merciless with you. In fact, I feel sorry that I have been so ruthless, but your stupidity calls for this treatment so that others can be warned
> Dream on, but delusions is how you feed your narcissistic ego, yes no?

Oh the irony! From the man who claims "Mathematics is not about measure and number". LMAO

Malum, Delusion is thy name! Chuckle.

> >LMAO. You gave nothing but this garbage:
> Which follows from localization.

Bullshit as already explained in my previous comment.

>It is FACT.

It is your opinion, not a fact.

>Liar. I said multiplication defined for ALL numbers, meaning Q.

except R, C, R*, Q*, Z*, p-adic, etc etc

>Z and N are irrelevant - these came long after Q.

Historically maybe, but we aren't discussing the history, we are discussing consturction order and construction order wise you go N, then Z, then Q

>By structures, Malum means set theory, fields, etc. All the typical bullshit one finds in abstract algebra which is not mathematics at all.

It is very much mathematics

>Crank, if you could have, you would have done so already. You've already experienced one FAILED attempt.

I wouldn't because you are intellectually incapable of understanding how one construct things in mathematics. You have demonstrated it here.

I did not fail, I showed how multiplication is defined in Q in the standard construction of it from Z.

>Chuckle. Anyone with a modicum of intelligence knows that Peano was nothing but a stupid ape and that his juvenile "axioms" are the joke of the 20th century

Anyone with a base line intelligence knows you are wrong so sorry, the ape is you.

>Been done. Your dumb and biased brain is too stupid to see reason.

You never did, you bitched about irrelevant things, talking about "magnitudes" when Eudoxus construction uses ALMOST HOMOMORPHISMS!

Which was entirelly IRRELEVANT!

>Oh the irony! From the man who claims "Mathematics is not about measure and number".

Because it isn't.

>Bullshit as already explained in my previous comment.

Which I deconstructed and showed how you are wrong

On Thursday, 20 May 2021 at 01:39:05 UTC-4, zelos...@gmail.com wrote:
> >It is FACT.
>
> It is your opinion, not a fact.

I have shown you over and over again that it is a FACT. All you do is whine and complain.

> >Liar. I said multiplication defined for ALL numbers, meaning Q.
> except R, C, R*, Q*, Z*, p-adic, etc etc

Except NONE of those are numbers. The only numbers are those in Q. NOTHING ELSE.

> >Z and N are irrelevant - these came long after Q.
> Historically maybe, but we aren't discussing the history, we are discussing consturction order and construction order wise you go N, then Z, then Q

LMAO. "Historically maybe"?! Too funny. Pay attention stupid! I never discuss anything with you. I lecture you.
You just proved to yourself that Z and N came long after Q. If either Z or N could have been derived before Q, then that's how my brilliant ancestors would have done it, but it was not possible to examine parts of Q until they constructed Q - the only true numbers.

Your constructions are drivel. Every thought of yours is pure piss and shit.. You have brain syphilis and I am afraid to tell you that it is incurable.

> >By structures, Malum means set theory, fields, etc. All the typical bullshit one finds in abstract algebra which is not mathematics at all.
> It is very much mathematics
> >Crank, if you could have, you would have done so already. You've already experienced one FAILED attempt.
> I wouldn't because you are intellectually incapable of understanding how one construct things in mathematics. You have demonstrated it here.
>
> I did not fail, I showed how multiplication is defined in Q in the standard construction of it from Z.

You failed ALSO in this, idiot. Your joke construction is circular because Z is a part of Q. In mathematics, WE construct sound proofs, not silly little circular arguments which students are taught to emulate. Chuckle.

> >Chuckle. Anyone with a modicum of intelligence knows that Peano was nothing but a stupid ape and that his juvenile "axioms" are the joke of the 20th century
> Anyone with a base line intelligence knows you are wrong so sorry, the ape is you.

Oh the irony! Peano would not be worthy enough to lick the dust off my shoes.

https://youtu.be/lAD-pfSNdSs

> >Been done. Your dumb and biased brain is too stupid to see reason.
> You never did, you bitched about irrelevant things, talking about "magnitudes" when Eudoxus construction uses ALMOST HOMOMORPHISMS!

I tore apart your silly and juvenile Wiki Link here

https://drive.google.com/file/d/1prDylUU3U8GK6N8jK8WdN6nMnuF1xepe

and talked about your stupidity in a special video presentation:

https://youtu.be/Ysn_pQ7mdeI

>
> Which was entirelly IRRELEVANT!
> >Oh the irony! From the man who claims "Mathematics is not about measure and number".
> Because it isn't.

Because it very much is and was and always will be. :) There is no other reason that mathematics was realised. The drivel you think about is not mathematics, but something entirely different - the product of sick minds.

> >Bullshit as already explained in my previous comment.
> Which I deconstructed and showed how you are wrong

You've done a lot of deconstruction of your own arguments - over and over again, because you are a natural born idiot. LMAO.

>I have shown you over and over again that it is a FACT. All you do is whine and complain.

no, you have shown it is your opinion. Compatible with ancient greeks does not make it a fact.

>xcept NONE of those are numbers. The only numbers are those in Q. NOTHING ELSE

They are numbers

they are all called numbers, we have therefore decided they are numbers there. You don't want it but none cares what you think or fell.

>LMAO. "Historically maybe"?! Too funny. Pay attention stupid! I never discuss anything with you. I lecture you.

To lexture you would need to know something, you don't know anything of any value.

>You just proved to yourself that Z and N came long after Q. If either Z or N could have been derived before Q, then that's how my brilliant ancestors would have done it, but it was not possible to examine parts of Q until they constructed Q - the only true numbers.

I said they might have historically, but chronological order does not equal construction order in modern time. Understand this.

In modern construction you start with N, then you construct Z from it, then from Z you construct Q.

That is the order today so Q comes constructionwise, after Z

>Your constructions are drivel. Every thought of yours is pure piss and shit. You have brain syphilis and I am afraid to tell you that it is incurable..

This is just Gerbil for "Too advanced for Gerbil to understand"

>You failed ALSO in this, idiot. Your joke construction is circular because Z is a part of Q. In mathematics, WE construct sound proofs, not silly little circular arguments which students are taught to emulate. Chuckle.

Z is constructed before Q, then from Z we construct Q, there is nothing circular.

We start with Z, construct Q, show there is a natural injection i such that i(Z) is isomorphic to Z, we then sloppily say that Z is a subset of Q.

>Oh the irony! Peano would not be worthy enough to lick the dust off my shoes

He is way smarter than you :)

>I tore apart your silly and juvenile Wiki Link here
>
>and talked about your stupidity in a special video presentation:

You bitch about the same things I have addressed, all you've done is once again demonstrate your ignorance.

>ou've done a lot of deconstruction of your own arguments - over and over again, because you are a natural born idiot. LMAO.

I have addressed your points and shown them all to be wrong, as always.

You have never done it. Address the Eudoxus construction without bitching about magnitudes, which it does not use, it uses almost homomorphisms.

>Man, you get dumber by the minute. That is not at all the case because that statement is part of your spoof which I see you modified since yesterday in the Wiki. Alas, it is still delusional as ever and wrong as ever.

"Define a relation ∼ on the Cartesian product 𝐴×𝑆

by:

(𝑎,𝑠)∼(𝑏,𝑡)⟺∃𝑢∈𝑆:𝑎𝑡𝑢=𝑏𝑠𝑢"

Oh look, it say define!

>You cannot define an equivalence relation as "Equivalent" to another given equivalence, because if you do this, then by implication you ACCEPT all the properties of that relation. YOU UTTER IMBECILE! Chuckle.

You can use other relations to define new ones. The relation is accepted and used, there is no issue with this.

>YOU do NO such thing. I can tell that Wiki has your signature on it - clearly the work of an idiot.

I haven't written it, others have cause this is basic mathematics at university level.

>It holds in ALL mathematics. I never talk about your BULLSHIT, only mathematics. LMAO again

It only holds in equivalence relations by definition, again I provided other relations where they are VIOLATED.

>You have ringworm in your brain, idiot! You have been shown that "localisation of a ring" does not provide any description of multiplication, that it merely ASSUMES these properties from GEOMETRY. The stupid moron is once again YOU!

You imbecile, it defines it's multiplication in terms of a given multiplication from a ring that we are localizing. Are you seriously this mentally retarded?

>I quickly dismissed Malum's drivel by pointing out its circularity. Then Malum wrote an article about Localisation of a ring on that ultra-shit site WikiProof (run by mainstream morons) which I corrected in an article:

Yet you couldn't point it out.

Your idea of circularity goes
John Gabriel thinks only in terms of Q and wants to start there
Zelos argues Q is constructed from Z
Ergo circular cause Q is first by John Gerbil.

In the actual construction we have
First, construct N in any manner
Second, use N to construct Z using abstract algebra. Prove it is a ring and fullfill the category theory requirement.
Third, construct Q from Z using localization of a ring.

There is no circularity in this as it starts with one, then go from one to the other.

On Friday, 21 May 2021 at 02:53:18 UTC-4, zelos...@gmail.com wrote:

> >Man, you get dumber by the minute. That is not at all the case because that statement is part of your spoof which I see you modified since yesterday in the Wiki. Alas, it is still delusional as ever and wrong as ever.

> "Define a relation ∼ on the Cartesian product 𝐴×𝑆
>
> by:
>
> (𝑎,𝑠)∼(𝑏,𝑡)⟺∃𝑢∈𝑆:𝑎𝑡𝑢=𝑏𝑠𝑢"
>
> Oh look, it say define!

"You are the Son of God." John 1:34

Oh look, it says Jesus is the Son of God.

LMAO.

See folks? A purported master math graduate too stupid to see the error of his ways and stubbornly refusing correction.

Malum has missed several points in my lectures to him:

1. He was asked to describe the process of multiplication of rational numbers exactly. Malum failed.
2. He then tried to avoid the task by "re-defining" the proportion 𝑎𝑡𝑢=𝑏𝑠𝑢 as an equivalence relation (𝑎,𝑠)∼(𝑏,𝑡) and being so incorrigibly stupid as not to notice the circularity.
3. Malum frantically tried several hand waving arguments in order to convince. Alas, in mathematics, real mathematicians rely only on cold, hard facts, never on intuition and syphilitic definitions that lead nowhere and are not mathematics.

I gave him he answers:

In geometry, the operations of arithmetic are well defined long before the Ancient Greeks establish the transition to algebra via the abstract unit in Book 7.

I showed Malum how to do this with the following. Whilst I have used numbers here, the same is accomplished with ONLY magnitudes in geometry.

All operations of arithmetic can be stated strictly in terms of subtraction.. Addition is derived immediately from subtraction.

Division:

A quotient ps/qr is the rational number that is measured in terms of two numbers p/q and r/s.

ps/qr = [ p/q +p/q + ...n times ] / [ r/s + r/s+... n times ] where n=q or n=s.

Example: 2/3 -:- 5/6 = 4/5

p/q = 2/3 and r/s = 5/6

2/3 -:- 5/6 = [ 2/3 + 2/3 + 2/3 ] / [ 5/6 + 5/6 + 5/6] = [2] / [ 5/2] = [2 + 2] / [5/2 + 5/2] = 4 / 5

After the second equals sign, cancellation is again possible by Book 5, Proposition 12.

So the ENTIRE operation is done through geometry using similar triangles. No numbers are even required in the geometric definition, only magnitudes.

Multiplication:

The product (or multiplication) of two numbers p/q and r/s, that is, pr/qs is the quotient of either number
with the reciprocal of the other.

pr/qs = [ p/q +p/q + ...n times ] / [ s/r + s/r+... n times ] where n=q or n=r.

Example: 2/3 x 5/6 = 5/9

p/q = 2/3 and s/r = 6/5

2/3 x 5/6 = [2/3+2/3+2/3] / [6/5+6/5+6/5] = [2] / [18/5] = [ 2+2+2+2+2 ] / [18/5+18/5+18/5+18/5+18/5] = 10 / 18 = 5/9

AND

pr/qs = [ r/s + r/s+... n times ] / [ s/p + s/p+... n times ] where n=p or n=s.

This part is left as an exercise.

NOTE: The above definitions work on ANY magnitude. There is no need to have a separate interpretation for integers and fractions.

All these details are explained in my world famous article:

https://drive.google.com/file/d/0B-mOEooW03iLYTg1TGY4RTIwakU

Compare this clarity with the bullshit of Zelos Malum:

------------------------------------------------------------------------
i. a/b=[(a,b)]
ii. [(a,b)][(c,d)]=[(ac,bd)]
iii. 2.1=21/10=[(21,10)]
iv. 2.2=22/10=[(22,10)]
v. 2.1*2.2=[(21,10)][(22,10)]=[(462,100)]=4.62
-------------------------------------------------------------------------

I quickly dismissed Malum's drivel by pointing out its circularity. Then Malum wrote an article about Localisation of a ring on that ultra-shit site WikiProof (run by mainstream morons) which I corrected in an article:

https://drive.google.com/drive/folders/0B-mOEooW03iLTklGSVhwTzBsNjg

and gave a short lecture in a video:

https://youtu.be/Ysn_pQ7mdeI

I do know better than anyone else!

To understand mathematics, you need me! Only I can guide you to a perfect understanding. The fakes and bull-shitters called professors of mathematics don't have a clue even of what it means to be a number.

On Friday, 21 May 2021 at 07:48:52 UTC-4, Eram semper recta wrote:
> On Friday, 21 May 2021 at 02:53:18 UTC-4, zelos...@gmail.com wrote:
>
> > >Man, you get dumber by the minute. That is not at all the case because that statement is part of your spoof which I see you modified since yesterday in the Wiki. Alas, it is still delusional as ever and wrong as ever.
>
> > "Define a relation ∼ on the Cartesian product 𝐴×𝑆
> >
> > by:
> >
> > (𝑎,𝑠)∼(𝑏,𝑡)⟺∃𝑢∈𝑆:𝑎𝑡𝑢=𝑏𝑠𝑢"
> >
> > Oh look, it say define!
> "You are the Son of God." John 1:34
>
> Oh look, it says Jesus is the Son of God.
>
> LMAO.
>
> See folks? A purported master math graduate too stupid to see the error of his ways and stubbornly refusing correction.
>
> Malum has missed several points in my lectures to him:
>
> 1. He was asked to describe the process of multiplication of rational numbers exactly. Malum failed.
> 2. He then tried to avoid the task by "re-defining" the proportion 𝑎𝑡𝑢=𝑏𝑠𝑢 as an equivalence relation (𝑎,𝑠)∼(𝑏,𝑡) and being so incorrigibly stupid as not to notice the circularity.
> 3. Malum frantically tried several hand waving arguments in order to convince. Alas, in mathematics, real mathematicians rely only on cold, hard facts, never on intuition and syphilitic definitions that lead nowhere and are not mathematics.
>
> I gave him he answers:
> In geometry, the operations of arithmetic are well defined long before the Ancient Greeks establish the transition to algebra via the abstract unit in Book 7.
> I showed Malum how to do this with the following. Whilst I have used numbers here, the same is accomplished with ONLY magnitudes in geometry.
>
> All operations of arithmetic can be stated strictly in terms of subtraction. Addition is derived immediately from subtraction.
>
> Division:
>
> A quotient ps/qr is the rational number that is measured in terms of two numbers p/q and r/s.
>
> ps/qr = [ p/q +p/q + ...n times ] / [ r/s + r/s+... n times ] where n=q or n=s.
>
>
> Example: 2/3 -:- 5/6 = 4/5
>
> p/q = 2/3 and r/s = 5/6
>
> 2/3 -:- 5/6 = [ 2/3 + 2/3 + 2/3 ] / [ 5/6 + 5/6 + 5/6] = [2] / [ 5/2] = [2 + 2] / [5/2 + 5/2] = 4 / 5
>
> After the second equals sign, cancellation is again possible by Book 5, Proposition 12.
>
> So the ENTIRE operation is done through geometry using similar triangles. No numbers are even required in the geometric definition, only magnitudes.
>
>
> Multiplication:
>
> The product (or multiplication) of two numbers p/q and r/s, that is, pr/qs is the quotient of either number
> with the reciprocal of the other.
>
> pr/qs = [ p/q +p/q + ...n times ] / [ s/r + s/r+... n times ] where n=q or n=r.
>
> Example: 2/3 x 5/6 = 5/9
>
> p/q = 2/3 and s/r = 6/5
>
> 2/3 x 5/6 = [2/3+2/3+2/3] / [6/5+6/5+6/5] = [2] / [18/5] = [ 2+2+2+2+2 ] / [18/5+18/5+18/5+18/5+18/5] = 10 / 18 = 5/9
>
> AND
>
> pr/qs = [ r/s + r/s+... n times ] / [ s/p + s/p+... n times ] where n=p or n=s.
>
> This part is left as an exercise.
>
> NOTE: The above definitions work on ANY magnitude. There is no need to have a separate interpretation for integers and fractions.
>
> All these details are explained in my world famous article:
>
> https://drive.google.com/file/d/0B-mOEooW03iLYTg1TGY4RTIwakU
>
> Compare this clarity with the bullshit of Zelos Malum:
>
> ------------------------------------------------------------------------
> i. a/b=[(a,b)]
> ii. [(a,b)][(c,d)]=[(ac,bd)]
> iii. 2.1=21/10=[(21,10)]
> iv. 2.2=22/10=[(22,10)]
> v. 2.1*2.2=[(21,10)][(22,10)]=[(462,100)]=4.62
> -------------------------------------------------------------------------
> I quickly dismissed Malum's drivel by pointing out its circularity. Then Malum wrote an article about Localisation of a ring on that ultra-shit site WikiProof (run by mainstream morons) which I corrected in an article:
> https://drive.google.com/drive/folders/0B-mOEooW03iLTklGSVhwTzBsNjg
>
> and gave a short lecture in a video:
>
> https://youtu.be/Ysn_pQ7mdeI
>
> I do know better than anyone else!
>
> To understand mathematics, you need me! Only I can guide you to a perfect understanding. The fakes and bull-shitters called professors of mathematics don't have a clue even of what it means to be a number.

Folks, the ONLY valid numbers are the RATIONAL NUMBERS. In fact, we have never used anything but rational numbers in any STEM discipline because ...

A number is a name given to a MEASURE that describes a magnitude or size.

THIS AND NOTHING ELSE.

Malum failed to describe multiplication because he has no clue what it means or where it comes from, but I have shown you all:

Whilst I have used numbers here, the same is accomplished with ONLY magnitudes in geometry.

All operations of arithmetic can be stated strictly in terms of subtraction.. Addition is derived immediately from subtraction.

Division:

A quotient ps/qr is the rational number that is measured in terms of two numbers p/q and r/s.

ps/qr = [ p/q +p/q + ...n times ] / [ r/s + r/s+... n times ] where n=q or n=s.

Example: 2/3 -:- 5/6 = 4/5

p/q = 2/3 and r/s = 5/6

2/3 -:- 5/6 = [ 2/3 + 2/3 + 2/3 ] / [ 5/6 + 5/6 + 5/6] = [2] / [ 5/2] = [2 + 2] / [5/2 + 5/2] = 4 / 5

After the second equals sign, cancellation is again possible by Book 5, Proposition 12.

So the ENTIRE operation is done through geometry using similar triangles. No numbers are even required in the geometric definition, only magnitudes.

Multiplication:

The product (or multiplication) of two numbers p/q and r/s, that is, pr/qs is the quotient of either number
with the reciprocal of the other.

pr/qs = [ p/q +p/q + ...n times ] / [ s/r + s/r+... n times ] where n=q or n=r.

Example: 2/3 x 5/6 = 5/9

p/q = 2/3 and s/r = 6/5

2/3 x 5/6 = [2/3+2/3+2/3] / [6/5+6/5+6/5] = [2] / [18/5] = [ 2+2+2+2+2 ] / [18/5+18/5+18/5+18/5+18/5] = 10 / 18 = 5/9

AND

pr/qs = [ r/s + r/s+... n times ] / [ s/p + s/p+... n times ] where n=p or n=s.

This part is left as an exercise.

NOTE: The above definitions work on ANY magnitude. There is no need to have a separate interpretation for integers and fractions.

All these details are explained in my world famous article:

https://drive.google.com/file/d/0B-mOEooW03iLYTg1TGY4RTIwakU

Compare this clarity with the bullshit of Zelos Malum:

------------------------------------------------------------------------
i. a/b=[(a,b)]
ii. [(a,b)][(c,d)]=[(ac,bd)]
iii. 2.1=21/10=[(21,10)]
iv. 2.2=22/10=[(22,10)]
v. 2.1*2.2=[(21,10)][(22,10)]=[(462,100)]=4.62
-------------------------------------------------------------------------

or his more recent hand waving drivel about "localisation of a ring". LMAO.

I quickly dismissed Malum's drivel by pointing out its circularity. Then Malum wrote an article about Localisation of a ring on that ultra-shit site WikiProof (run by mainstream morons) which I corrected in an article:

https://drive.google.com/drive/folders/0B-mOEooW03iLTklGSVhwTzBsNjg

and gave a short lecture in a video:

https://youtu.be/Ysn_pQ7mdeI

I do know better than anyone else!

To understand mathematics, you need me! Only I can guide you to a perfect understanding. The fakes and bull-shitters called professors of mathematics don't have a clue even of what it means to be a number.

On Saturday, 22 May 2021 at 13:48:40 UTC-4, mitchr...@gmail.com wrote:
> Fundamental first quantities are real.
> Calculus recognized it...

Please go away, moron.

>
> Mitchell Raemsch

On Saturday, 22 May 2021 at 13:35:09 UTC-4, Eram semper recta wrote:
> On Friday, 21 May 2021 at 07:48:52 UTC-4, Eram semper recta wrote:
> > On Friday, 21 May 2021 at 02:53:18 UTC-4, zelos...@gmail.com wrote:
> >
> > > >Man, you get dumber by the minute. That is not at all the case because that statement is part of your spoof which I see you modified since yesterday in the Wiki. Alas, it is still delusional as ever and wrong as ever.
> >
> > > "Define a relation ∼ on the Cartesian product 𝐴×𝑆
> > >
> > > by:
> > >
> > > (𝑎,𝑠)∼(𝑏,𝑡)⟺∃𝑢∈𝑆:𝑎𝑡𝑢=𝑏𝑠𝑢"
> > >
> > > Oh look, it say define!
> > "You are the Son of God." John 1:34
> >
> > Oh look, it says Jesus is the Son of God.
> >
> > LMAO.
> >
> > See folks? A purported master math graduate too stupid to see the error of his ways and stubbornly refusing correction.
> >
> > Malum has missed several points in my lectures to him:
> >
> > 1. He was asked to describe the process of multiplication of rational numbers exactly. Malum failed.
> > 2. He then tried to avoid the task by "re-defining" the proportion 𝑎𝑡𝑢=𝑏𝑠𝑢 as an equivalence relation (𝑎,𝑠)∼(𝑏,𝑡) and being so incorrigibly stupid as not to notice the circularity.
> > 3. Malum frantically tried several hand waving arguments in order to convince. Alas, in mathematics, real mathematicians rely only on cold, hard facts, never on intuition and syphilitic definitions that lead nowhere and are not mathematics.
> >
> > I gave him he answers:
> > In geometry, the operations of arithmetic are well defined long before the Ancient Greeks establish the transition to algebra via the abstract unit in Book 7.
> > I showed Malum how to do this with the following. Whilst I have used numbers here, the same is accomplished with ONLY magnitudes in geometry.
> >
> > All operations of arithmetic can be stated strictly in terms of subtraction. Addition is derived immediately from subtraction.
> >
> > Division:
> >
> > A quotient ps/qr is the rational number that is measured in terms of two numbers p/q and r/s.
> >
> > ps/qr = [ p/q +p/q + ...n times ] / [ r/s + r/s+... n times ] where n=q or n=s.
> >
> >
> > Example: 2/3 -:- 5/6 = 4/5
> >
> > p/q = 2/3 and r/s = 5/6
> >
> > 2/3 -:- 5/6 = [ 2/3 + 2/3 + 2/3 ] / [ 5/6 + 5/6 + 5/6] = [2] / [ 5/2] = [2 + 2] / [5/2 + 5/2] = 4 / 5
> >
> > After the second equals sign, cancellation is again possible by Book 5, Proposition 12.
> >
> > So the ENTIRE operation is done through geometry using similar triangles. No numbers are even required in the geometric definition, only magnitudes.
> >
> >
> > Multiplication:
> >
> > The product (or multiplication) of two numbers p/q and r/s, that is, pr/qs is the quotient of either number
> > with the reciprocal of the other.
> >
> > pr/qs = [ p/q +p/q + ...n times ] / [ s/r + s/r+... n times ] where n=q or n=r.
> >
> > Example: 2/3 x 5/6 = 5/9
> >
> > p/q = 2/3 and s/r = 6/5
> >
> > 2/3 x 5/6 = [2/3+2/3+2/3] / [6/5+6/5+6/5] = [2] / [18/5] = [ 2+2+2+2+2 ] / [18/5+18/5+18/5+18/5+18/5] = 10 / 18 = 5/9
> >
> > AND
> >
> > pr/qs = [ r/s + r/s+... n times ] / [ s/p + s/p+... n times ] where n=p or n=s.
> >
> > This part is left as an exercise.
> >
> > NOTE: The above definitions work on ANY magnitude. There is no need to have a separate interpretation for integers and fractions.
> >
> > All these details are explained in my world famous article:
> >
> > https://drive.google.com/file/d/0B-mOEooW03iLYTg1TGY4RTIwakU
> >
> > Compare this clarity with the bullshit of Zelos Malum:
> >
> > ------------------------------------------------------------------------
> > i. a/b=[(a,b)]
> > ii. [(a,b)][(c,d)]=[(ac,bd)]
> > iii. 2.1=21/10=[(21,10)]
> > iv. 2.2=22/10=[(22,10)]
> > v. 2.1*2.2=[(21,10)][(22,10)]=[(462,100)]=4.62
> > -------------------------------------------------------------------------
> > I quickly dismissed Malum's drivel by pointing out its circularity. Then Malum wrote an article about Localisation of a ring on that ultra-shit site WikiProof (run by mainstream morons) which I corrected in an article:
> > https://drive.google.com/drive/folders/0B-mOEooW03iLTklGSVhwTzBsNjg
> >
> > and gave a short lecture in a video:
> >
> > https://youtu.be/Ysn_pQ7mdeI
> >
> > I do know better than anyone else!
> >
> > To understand mathematics, you need me! Only I can guide you to a perfect understanding. The fakes and bull-shitters called professors of mathematics don't have a clue even of what it means to be a number.
> Folks, the ONLY valid numbers are the RATIONAL NUMBERS. In fact, we have never used anything but rational numbers in any STEM discipline because ...
>
> A number is a name given to a MEASURE that describes a magnitude or size.
>
> THIS AND NOTHING ELSE.
>
> Malum failed to describe multiplication because he has no clue what it means or where it comes from, but I have shown you all:
> Whilst I have used numbers here, the same is accomplished with ONLY magnitudes in geometry.
>
> All operations of arithmetic can be stated strictly in terms of subtraction. Addition is derived immediately from subtraction.
>
> Division:
>
> A quotient ps/qr is the rational number that is measured in terms of two numbers p/q and r/s.
>
> ps/qr = [ p/q +p/q + ...n times ] / [ r/s + r/s+... n times ] where n=q or n=s.
>
>
> Example: 2/3 -:- 5/6 = 4/5
>
> p/q = 2/3 and r/s = 5/6
>
> 2/3 -:- 5/6 = [ 2/3 + 2/3 + 2/3 ] / [ 5/6 + 5/6 + 5/6] = [2] / [ 5/2] = [2 + 2] / [5/2 + 5/2] = 4 / 5
>
> After the second equals sign, cancellation is again possible by Book 5, Proposition 12.
>
> So the ENTIRE operation is done through geometry using similar triangles. No numbers are even required in the geometric definition, only magnitudes.
>
>
> Multiplication:
>
> The product (or multiplication) of two numbers p/q and r/s, that is, pr/qs is the quotient of either number
> with the reciprocal of the other.
>
> pr/qs = [ p/q +p/q + ...n times ] / [ s/r + s/r+... n times ] where n=q or n=r.
>
> Example: 2/3 x 5/6 = 5/9
>
> p/q = 2/3 and s/r = 6/5
>
> 2/3 x 5/6 = [2/3+2/3+2/3] / [6/5+6/5+6/5] = [2] / [18/5] = [ 2+2+2+2+2 ] / [18/5+18/5+18/5+18/5+18/5] = 10 / 18 = 5/9
>
> AND
>
> pr/qs = [ r/s + r/s+... n times ] / [ s/p + s/p+... n times ] where n=p or n=s.
>
> This part is left as an exercise.
>
> NOTE: The above definitions work on ANY magnitude. There is no need to have a separate interpretation for integers and fractions.
>
> All these details are explained in my world famous article:
>
> https://drive.google.com/file/d/0B-mOEooW03iLYTg1TGY4RTIwakU
>
> Compare this clarity with the bullshit of Zelos Malum:
>
> ------------------------------------------------------------------------
> i. a/b=[(a,b)]
> ii. [(a,b)][(c,d)]=[(ac,bd)]
> iii. 2.1=21/10=[(21,10)]
> iv. 2.2=22/10=[(22,10)]
> v. 2.1*2.2=[(21,10)][(22,10)]=[(462,100)]=4.62
> -------------------------------------------------------------------------
> or his more recent hand waving drivel about "localisation of a ring". LMAO.
> I quickly dismissed Malum's drivel by pointing out its circularity. Then Malum wrote an article about Localisation of a ring on that ultra-shit site WikiProof (run by mainstream morons) which I corrected in an article:
>
> https://drive.google.com/drive/folders/0B-mOEooW03iLTklGSVhwTzBsNjg
>
> and gave a short lecture in a video:
>
> https://youtu.be/Ysn_pQ7mdeI
>
> I do know better than anyone else!
>
> To understand mathematics, you need me! Only I can guide you to a perfect understanding. The fakes and bull-shitters called professors of mathematics don't have a clue even of what it means to be a number.

Yes, I do know better than any of you morons! I'll always know better.

>Oh look, it says Jesus is the Son of God.

Which in christian theology he is :) Definitionally so.

However comparing mathematics, which makes no statements about reality, with something that do make statements about reality, is at best fallacious and at worst dishonest.

>1. He was asked to describe the process of multiplication of rational numbers exactly. Malum failed.

Incorrect, I succeeded, you wanted it defined there, I gave definition based on the construction and provided links to it.

>2. He then tried to avoid the task by "re-defining" the proportion 𝑎𝑡𝑢=𝑏𝑠𝑢 as an equivalence relation (𝑎,𝑠)∼(𝑏,𝑡) and being so incorrigibly stupid as not to notice the circularity.

Incorrect, as always. That is the definition of an eqvuialence relation in localization and there is nothing circular in it. Given a ring we have multiplication already defined so we can utilize it as we see fit.

>3. Malum frantically tried several hand waving arguments in order to convince. Alas, in mathematics, real mathematicians rely only on cold, hard facts, never on intuition and syphilitic definitions that lead nowhere and are not mathematics.

This is just your personal opinion. In mathematics we define things and deduce from these definitions new lemmas, theorems, etc etc.

You do not dictate what is and isn't mathematics.

>I gave him he answers:

Nobody cares what ancient greeks did, they are not foundational to mathematics that we use today.

>I quickly dismissed Malum's drivel by pointing out its circularity. Then Malum wrote an article about Localisation of a ring on that ultra-shit site WikiProof (run by mainstream morons) which I corrected in an article:

Yet you could provide no circularity.

Circularity is:
1: Assume P
2: ...
3: Conclude P

You have done this
1: Assume all sets are finite
2: Therefore they have an end.
3: N does not have an end
4: There N is not a set
5: Therefore only finite sets exists.

What mathematics have done on this that you bitch about is
1: Assume some structure exists that is NNO
2: From 1, construct Z
3: From 2, construct Q.

There is nothing circular here.

>Folks, the ONLY valid numbers are the RATIONAL NUMBERS.

Which is just your opinion.

>In fact, we have never used anything but rational numbers in any STEM discipline because

Tell that to quantum mechanics where complex numbers are used regularly.

And everything einstein.

Even electrical engineering uses complex.

>A number is a name given to a MEASURE that describes a magnitude or size.

This is nothing but your preferred idea.

>THIS AND NOTHING ELSE.

This is just your opinion.

>Malum failed to describe multiplication because he has no clue what it means or where it comes from, but I have shown you all:

I succeeded, you however failed to go beyond your preferred system. You are so closed minded you cannot go beyond your own.

>or his more recent hand waving drivel about "localisation of a ring". LMAO

it is a legit method of constructing structures in algebra, get over it.

söndag 23 maj 2021 kl. 01:40:12 UTC+2 skrev Eram semper recta:
> On Saturday, 22 May 2021 at 13:35:09 UTC-4, Eram semper recta wrote:
> > On Friday, 21 May 2021 at 07:48:52 UTC-4, Eram semper recta wrote:
> > > On Friday, 21 May 2021 at 02:53:18 UTC-4, zelos...@gmail.com wrote:
> > >
> > > > >Man, you get dumber by the minute. That is not at all the case because that statement is part of your spoof which I see you modified since yesterday in the Wiki. Alas, it is still delusional as ever and wrong as ever..
> > >
> > > > "Define a relation ∼ on the Cartesian product 𝐴×𝑆
> > > >
> > > > by:
> > > >
> > > > (𝑎,𝑠)∼(𝑏,𝑡)⟺∃𝑢∈𝑆:𝑎𝑡𝑢=𝑏𝑠𝑢"
> > > >
> > > > Oh look, it say define!
> > > "You are the Son of God." John 1:34
> > >
> > > Oh look, it says Jesus is the Son of God.
> > >
> > > LMAO.
> > >
> > > See folks? A purported master math graduate too stupid to see the error of his ways and stubbornly refusing correction.
> > >
> > > Malum has missed several points in my lectures to him:
> > >
> > > 1. He was asked to describe the process of multiplication of rational numbers exactly. Malum failed.
> > > 2. He then tried to avoid the task by "re-defining" the proportion 𝑎𝑡𝑢=𝑏𝑠𝑢 as an equivalence relation (𝑎,𝑠)∼(𝑏,𝑡) and being so incorrigibly stupid as not to notice the circularity.
> > > 3. Malum frantically tried several hand waving arguments in order to convince. Alas, in mathematics, real mathematicians rely only on cold, hard facts, never on intuition and syphilitic definitions that lead nowhere and are not mathematics.
> > >
> > > I gave him he answers:
> > > In geometry, the operations of arithmetic are well defined long before the Ancient Greeks establish the transition to algebra via the abstract unit in Book 7.
> > > I showed Malum how to do this with the following. Whilst I have used numbers here, the same is accomplished with ONLY magnitudes in geometry.
> > >
> > > All operations of arithmetic can be stated strictly in terms of subtraction. Addition is derived immediately from subtraction.
> > >
> > > Division:
> > >
> > > A quotient ps/qr is the rational number that is measured in terms of two numbers p/q and r/s.
> > >
> > > ps/qr = [ p/q +p/q + ...n times ] / [ r/s + r/s+... n times ] where n=q or n=s.
> > >
> > >
> > > Example: 2/3 -:- 5/6 = 4/5
> > >
> > > p/q = 2/3 and r/s = 5/6
> > >
> > > 2/3 -:- 5/6 = [ 2/3 + 2/3 + 2/3 ] / [ 5/6 + 5/6 + 5/6] = [2] / [ 5/2] = [2 + 2] / [5/2 + 5/2] = 4 / 5
> > >
> > > After the second equals sign, cancellation is again possible by Book 5, Proposition 12.
> > >
> > > So the ENTIRE operation is done through geometry using similar triangles. No numbers are even required in the geometric definition, only magnitudes.
> > >
> > >
> > > Multiplication:
> > >
> > > The product (or multiplication) of two numbers p/q and r/s, that is, pr/qs is the quotient of either number
> > > with the reciprocal of the other.
> > >
> > > pr/qs = [ p/q +p/q + ...n times ] / [ s/r + s/r+... n times ] where n=q or n=r.
> > >
> > > Example: 2/3 x 5/6 = 5/9
> > >
> > > p/q = 2/3 and s/r = 6/5
> > >
> > > 2/3 x 5/6 = [2/3+2/3+2/3] / [6/5+6/5+6/5] = [2] / [18/5] = [ 2+2+2+2+2 ] / [18/5+18/5+18/5+18/5+18/5] = 10 / 18 = 5/9
> > >
> > > AND
> > >
> > > pr/qs = [ r/s + r/s+... n times ] / [ s/p + s/p+... n times ] where n=p or n=s.
> > >
> > > This part is left as an exercise.
> > >
> > > NOTE: The above definitions work on ANY magnitude. There is no need to have a separate interpretation for integers and fractions.
> > >
> > > All these details are explained in my world famous article:
> > >
> > > https://drive.google.com/file/d/0B-mOEooW03iLYTg1TGY4RTIwakU
> > >
> > > Compare this clarity with the bullshit of Zelos Malum:
> > >
> > > ------------------------------------------------------------------------
> > > i. a/b=[(a,b)]
> > > ii. [(a,b)][(c,d)]=[(ac,bd)]
> > > iii. 2.1=21/10=[(21,10)]
> > > iv. 2.2=22/10=[(22,10)]
> > > v. 2.1*2.2=[(21,10)][(22,10)]=[(462,100)]=4.62
> > > -------------------------------------------------------------------------
> > > I quickly dismissed Malum's drivel by pointing out its circularity. Then Malum wrote an article about Localisation of a ring on that ultra-shit site WikiProof (run by mainstream morons) which I corrected in an article:
> > > https://drive.google.com/drive/folders/0B-mOEooW03iLTklGSVhwTzBsNjg
> > >
> > > and gave a short lecture in a video:
> > >
> > > https://youtu.be/Ysn_pQ7mdeI
> > >
> > > I do know better than anyone else!
> > >
> > > To understand mathematics, you need me! Only I can guide you to a perfect understanding. The fakes and bull-shitters called professors of mathematics don't have a clue even of what it means to be a number.
> > Folks, the ONLY valid numbers are the RATIONAL NUMBERS. In fact, we have never used anything but rational numbers in any STEM discipline because ....
> >
> > A number is a name given to a MEASURE that describes a magnitude or size.
> >
> > THIS AND NOTHING ELSE.
> >
> > Malum failed to describe multiplication because he has no clue what it means or where it comes from, but I have shown you all:
> > Whilst I have used numbers here, the same is accomplished with ONLY magnitudes in geometry.
> >
> > All operations of arithmetic can be stated strictly in terms of subtraction. Addition is derived immediately from subtraction.
> >
> > Division:
> >
> > A quotient ps/qr is the rational number that is measured in terms of two numbers p/q and r/s.
> >
> > ps/qr = [ p/q +p/q + ...n times ] / [ r/s + r/s+... n times ] where n=q or n=s.
> >
> >
> > Example: 2/3 -:- 5/6 = 4/5
> >
> > p/q = 2/3 and r/s = 5/6
> >
> > 2/3 -:- 5/6 = [ 2/3 + 2/3 + 2/3 ] / [ 5/6 + 5/6 + 5/6] = [2] / [ 5/2] = [2 + 2] / [5/2 + 5/2] = 4 / 5
> >
> > After the second equals sign, cancellation is again possible by Book 5, Proposition 12.
> >
> > So the ENTIRE operation is done through geometry using similar triangles. No numbers are even required in the geometric definition, only magnitudes.
> >
> >
> > Multiplication:
> >
> > The product (or multiplication) of two numbers p/q and r/s, that is, pr/qs is the quotient of either number
> > with the reciprocal of the other.
> >
> > pr/qs = [ p/q +p/q + ...n times ] / [ s/r + s/r+... n times ] where n=q or n=r.
> >
> > Example: 2/3 x 5/6 = 5/9
> >
> > p/q = 2/3 and s/r = 6/5
> >
> > 2/3 x 5/6 = [2/3+2/3+2/3] / [6/5+6/5+6/5] = [2] / [18/5] = [ 2+2+2+2+2 ] / [18/5+18/5+18/5+18/5+18/5] = 10 / 18 = 5/9
> >
> > AND
> >
> > pr/qs = [ r/s + r/s+... n times ] / [ s/p + s/p+... n times ] where n=p or n=s.
> >
> > This part is left as an exercise.
> >
> > NOTE: The above definitions work on ANY magnitude. There is no need to have a separate interpretation for integers and fractions.
> >
> > All these details are explained in my world famous article:
> >
> > https://drive.google.com/file/d/0B-mOEooW03iLYTg1TGY4RTIwakU
> >
> > Compare this clarity with the bullshit of Zelos Malum:
> >
> > ------------------------------------------------------------------------
> > i. a/b=[(a,b)]
> > ii. [(a,b)][(c,d)]=[(ac,bd)]
> > iii. 2.1=21/10=[(21,10)]
> > iv. 2.2=22/10=[(22,10)]
> > v. 2.1*2.2=[(21,10)][(22,10)]=[(462,100)]=4.62
> > -------------------------------------------------------------------------
> > or his more recent hand waving drivel about "localisation of a ring". LMAO.
> > I quickly dismissed Malum's drivel by pointing out its circularity. Then Malum wrote an article about Localisation of a ring on that ultra-shit site WikiProof (run by mainstream morons) which I corrected in an article:
> >
> > https://drive.google.com/drive/folders/0B-mOEooW03iLTklGSVhwTzBsNjg
> >
> > and gave a short lecture in a video:
> >
> > https://youtu.be/Ysn_pQ7mdeI
> >
> > I do know better than anyone else!
> >
> > To understand mathematics, you need me! Only I can guide you to a perfect understanding. The fakes and bull-shitters called professors of mathematics don't have a clue even of what it means to be a number.
> Yes, I do know better than any of you morons! I'll always know better.

On Friday, 21 May 2021 at 07:48:52 UTC-4, Eram semper recta wrote:
> On Friday, 21 May 2021 at 02:53:18 UTC-4, zelos...@gmail.com wrote:
>
> > >Man, you get dumber by the minute. That is not at all the case because that statement is part of your spoof which I see you modified since yesterday in the Wiki. Alas, it is still delusional as ever and wrong as ever.
>
> > "Define a relation ∼ on the Cartesian product 𝐴×𝑆
> >
> > by:
> >
> > (𝑎,𝑠)∼(𝑏,𝑡)⟺∃𝑢∈𝑆:𝑎𝑡𝑢=𝑏𝑠𝑢"
> >
> > Oh look, it say define!
> "You are the Son of God." John 1:34
>
> Oh look, it says Jesus is the Son of God.
>
> LMAO.
>
> See folks? A purported master math graduate too stupid to see the error of his ways and stubbornly refusing correction.
>
> Malum has missed several points in my lectures to him:
>
> 1. He was asked to describe the process of multiplication of rational numbers exactly. Malum failed.
> 2. He then tried to avoid the task by "re-defining" the proportion 𝑎𝑡𝑢=𝑏𝑠𝑢 as an equivalence relation (𝑎,𝑠)∼(𝑏,𝑡) and being so incorrigibly stupid as not to notice the circularity.
> 3. Malum frantically tried several hand waving arguments in order to convince. Alas, in mathematics, real mathematicians rely only on cold, hard facts, never on intuition and syphilitic definitions that lead nowhere and are not mathematics.
>
> I gave him he answers:
> In geometry, the operations of arithmetic are well defined long before the Ancient Greeks establish the transition to algebra via the abstract unit in Book 7.
> I showed Malum how to do this with the following. Whilst I have used numbers here, the same is accomplished with ONLY magnitudes in geometry.
>
> All operations of arithmetic can be stated strictly in terms of subtraction. Addition is derived immediately from subtraction.
>
> Division:
>
> A quotient ps/qr is the rational number that is measured in terms of two numbers p/q and r/s.
>
> ps/qr = [ p/q +p/q + ...n times ] / [ r/s + r/s+... n times ] where n=q or n=s.
>
>
> Example: 2/3 -:- 5/6 = 4/5
>
> p/q = 2/3 and r/s = 5/6
>
> 2/3 -:- 5/6 = [ 2/3 + 2/3 + 2/3 ] / [ 5/6 + 5/6 + 5/6] = [2] / [ 5/2] = [2 + 2] / [5/2 + 5/2] = 4 / 5
>
> After the second equals sign, cancellation is again possible by Book 5, Proposition 12.
>
> So the ENTIRE operation is done through geometry using similar triangles. No numbers are even required in the geometric definition, only magnitudes.
>
>
> Multiplication:
>
> The product (or multiplication) of two numbers p/q and r/s, that is, pr/qs is the quotient of either number
> with the reciprocal of the other.
>
> pr/qs = [ p/q +p/q + ...n times ] / [ s/r + s/r+... n times ] where n=q or n=r.
>
> Example: 2/3 x 5/6 = 5/9
>
> p/q = 2/3 and s/r = 6/5
>
> 2/3 x 5/6 = [2/3+2/3+2/3] / [6/5+6/5+6/5] = [2] / [18/5] = [ 2+2+2+2+2 ] / [18/5+18/5+18/5+18/5+18/5] = 10 / 18 = 5/9
>
> AND
>
> pr/qs = [ r/s + r/s+... n times ] / [ s/p + s/p+... n times ] where n=p or n=s.
>
> This part is left as an exercise.
>
> NOTE: The above definitions work on ANY magnitude. There is no need to have a separate interpretation for integers and fractions.
>
> All these details are explained in my world famous article:
>
> https://drive.google.com/file/d/0B-mOEooW03iLYTg1TGY4RTIwakU
>
> Compare this clarity with the bullshit of Zelos Malum:
>
> ------------------------------------------------------------------------
> i. a/b=[(a,b)]
> ii. [(a,b)][(c,d)]=[(ac,bd)]
> iii. 2.1=21/10=[(21,10)]
> iv. 2.2=22/10=[(22,10)]
> v. 2.1*2.2=[(21,10)][(22,10)]=[(462,100)]=4.62
> -------------------------------------------------------------------------
> I quickly dismissed Malum's drivel by pointing out its circularity. Then Malum wrote an article about Localisation of a ring on that ultra-shit site WikiProof (run by mainstream morons) which I corrected in an article:
> https://drive.google.com/drive/folders/0B-mOEooW03iLTklGSVhwTzBsNjg
>
> and gave a short lecture in a video:
>
> https://youtu.be/Ysn_pQ7mdeI
>
> I do know better than anyone else!
>
> To understand mathematics, you need me! Only I can guide you to a perfect understanding. The fakes and bull-shitters called professors of mathematics don't have a clue even of what it means to be a number.

It is a lost cause responding to Malum. I repeat the evidence in this comment.

Those who have a brain will learn. Those who do not, will not.

You cannot understand mathematics unless you study what I and I alone teach you. I am the greatest mathematician today.

If you said this, you would no doubt be a mentally ill crank, but I am the exception. Mainstream academics hate me for this. :)

On Monday, May 24, 2021 at 1:15:11 PM UTC+1, Eram semper recta wrote:

"I am the greatest mathematician today. "

Mr Gabriel...stop...please...my sides...they're splitting LMAO.

Kind..chuckle...regards...

måndag 24 maj 2021 kl. 14:15:11 UTC+2 skrev Eram semper recta:
> On Friday, 21 May 2021 at 07:48:52 UTC-4, Eram semper recta wrote:
> > On Friday, 21 May 2021 at 02:53:18 UTC-4, zelos...@gmail.com wrote:
> >
> > > >Man, you get dumber by the minute. That is not at all the case because that statement is part of your spoof which I see you modified since yesterday in the Wiki. Alas, it is still delusional as ever and wrong as ever.
> >
> > > "Define a relation ∼ on the Cartesian product 𝐴×𝑆
> > >
> > > by:
> > >
> > > (𝑎,𝑠)∼(𝑏,𝑡)⟺∃𝑢∈𝑆:𝑎𝑡𝑢=𝑏𝑠𝑢"
> > >
> > > Oh look, it say define!
> > "You are the Son of God." John 1:34
> >
> > Oh look, it says Jesus is the Son of God.
> >
> > LMAO.
> >
> > See folks? A purported master math graduate too stupid to see the error of his ways and stubbornly refusing correction.
> >
> > Malum has missed several points in my lectures to him:
> >
> > 1. He was asked to describe the process of multiplication of rational numbers exactly. Malum failed.
> > 2. He then tried to avoid the task by "re-defining" the proportion 𝑎𝑡𝑢=𝑏𝑠𝑢 as an equivalence relation (𝑎,𝑠)∼(𝑏,𝑡) and being so incorrigibly stupid as not to notice the circularity.
> > 3. Malum frantically tried several hand waving arguments in order to convince. Alas, in mathematics, real mathematicians rely only on cold, hard facts, never on intuition and syphilitic definitions that lead nowhere and are not mathematics.
> >
> > I gave him he answers:
> > In geometry, the operations of arithmetic are well defined long before the Ancient Greeks establish the transition to algebra via the abstract unit in Book 7.
> > I showed Malum how to do this with the following. Whilst I have used numbers here, the same is accomplished with ONLY magnitudes in geometry.
> >
> > All operations of arithmetic can be stated strictly in terms of subtraction. Addition is derived immediately from subtraction.
> >
> > Division:
> >
> > A quotient ps/qr is the rational number that is measured in terms of two numbers p/q and r/s.
> >
> > ps/qr = [ p/q +p/q + ...n times ] / [ r/s + r/s+... n times ] where n=q or n=s.
> >
> >
> > Example: 2/3 -:- 5/6 = 4/5
> >
> > p/q = 2/3 and r/s = 5/6
> >
> > 2/3 -:- 5/6 = [ 2/3 + 2/3 + 2/3 ] / [ 5/6 + 5/6 + 5/6] = [2] / [ 5/2] = [2 + 2] / [5/2 + 5/2] = 4 / 5
> >
> > After the second equals sign, cancellation is again possible by Book 5, Proposition 12.
> >
> > So the ENTIRE operation is done through geometry using similar triangles. No numbers are even required in the geometric definition, only magnitudes.
> >
> >
> > Multiplication:
> >
> > The product (or multiplication) of two numbers p/q and r/s, that is, pr/qs is the quotient of either number
> > with the reciprocal of the other.
> >
> > pr/qs = [ p/q +p/q + ...n times ] / [ s/r + s/r+... n times ] where n=q or n=r.
> >
> > Example: 2/3 x 5/6 = 5/9
> >
> > p/q = 2/3 and s/r = 6/5
> >
> > 2/3 x 5/6 = [2/3+2/3+2/3] / [6/5+6/5+6/5] = [2] / [18/5] = [ 2+2+2+2+2 ] / [18/5+18/5+18/5+18/5+18/5] = 10 / 18 = 5/9
> >
> > AND
> >
> > pr/qs = [ r/s + r/s+... n times ] / [ s/p + s/p+... n times ] where n=p or n=s.
> >
> > This part is left as an exercise.
> >
> > NOTE: The above definitions work on ANY magnitude. There is no need to have a separate interpretation for integers and fractions.
> >
> > All these details are explained in my world famous article:
> >
> > https://drive.google.com/file/d/0B-mOEooW03iLYTg1TGY4RTIwakU
> >
> > Compare this clarity with the bullshit of Zelos Malum:
> >
> > ------------------------------------------------------------------------
> > i. a/b=[(a,b)]
> > ii. [(a,b)][(c,d)]=[(ac,bd)]
> > iii. 2.1=21/10=[(21,10)]
> > iv. 2.2=22/10=[(22,10)]
> > v. 2.1*2.2=[(21,10)][(22,10)]=[(462,100)]=4.62
> > -------------------------------------------------------------------------
> > I quickly dismissed Malum's drivel by pointing out its circularity. Then Malum wrote an article about Localisation of a ring on that ultra-shit site WikiProof (run by mainstream morons) which I corrected in an article:
> > https://drive.google.com/drive/folders/0B-mOEooW03iLTklGSVhwTzBsNjg
> >
> > and gave a short lecture in a video:
> >
> > https://youtu.be/Ysn_pQ7mdeI
> >
> > I do know better than anyone else!
> >
> > To understand mathematics, you need me! Only I can guide you to a perfect understanding. The fakes and bull-shitters called professors of mathematics don't have a clue even of what it means to be a number.
> It is a lost cause responding to Malum. I repeat the evidence in this comment.
>
> Those who have a brain will learn. Those who do not, will not.
>
> You cannot understand mathematics unless you study what I and I alone teach you. I am the greatest mathematician today.
>
> If you said this, you would no doubt be a mentally ill crank, but I am the exception. Mainstream academics hate me for this. :)

1: You have provided no evidence
2: You are not a great mathematician, you're not even a mathematician.
3:No one hates you other htan for you spreading misinformation.