On Tuesday, 4 May 2021 at 04:31:09 UTC-4, zelos...@gmail.com wrote:
> So Gabriel claims there are no valid real numbers. Gabriel, I am taking you up on it.
>
> To show this statement to be true you have to find an internal inconsistency. The fact it doesn't align with your preferred system does in anyway make them invalid. They are only incompatible with your system them.
>
> So The three champions are
> Eudoxus: https://arxiv.org/pdf/math/0405454.pdf

Eudoxus never talks about numbers, only magnitudes. The above PDF is written by the ignoramus called R.D. Arthan.

The Ancient Greeks did not recognise any numbers other than the rational numbers. This is not opinion but fact. Some publication by an English asswipe like Arthan won't change this fact. His PDF is absolute garbage.

Archimedes who was the greatest of the Ancients stated in his famous principle:

Given any magnitude x (either commensurable or incommensurable with any other magnitude), there exists rational numbers m and n such that m < x < n.

> Dedikind: https://www.math.u-bordeaux.fr/~pjaming/M1/exposes/MA1a.pdf
> Cauchy: https://www.math.wustl.edu/~kumar/courses/310-2009/peano.pdf

As for the above two clowns (Dedekind and Cauchy), you have been shown many times why their "constructions" are invalid.

https://drive.google.com/file/d/0B-mOEooW03iLSTROakNyVXlQUEU

>
> Find one internal inconsistency, that is a statement that is both true and false and provably so.

LMAO. A crank does not and cannot be reasoned with. Look, you are still struggling with Euler's S = Lim S bullshit.

>
> If you cannot, you cannot claim they are invalid, you can at most say incompatible with your ideas.

I can say they are garbage because my ideas are all that matter. Anything that comes out of anyone else's syphilitic brain is nonsense.

I and I alone, decide what is well-formed knowledge. No one else has this privilege. As the discoverer of the New Calculus, I am the greatest mathematician ever - a fact which is only denied by cranks like you.

>Eudoxus never talks about numbers, only magnitudes. The above PDF is written by the ignoramus called R.D. Arthan

Not a contradiction

>The Ancient Greeks did not recognise any numbers other than the rational numbers. This is not opinion but fact. Some publication by an English asswipe like Arthan won't change this fact. His PDF is absolute garbage.

Not relevant what ancient greeks did.

>Given any magnitude x (either commensurable or incommensurable with any other magnitude), there exists rational numbers m and n such that m < x < n

Irrelevant here.

So for hte eudoxus construction, you failed to show it is invalid.

>As for the above two clowns (Dedekind and Cauchy), you have been shown many times why their "constructions" are invalid.

Nothing in your link shows any contradiction.

Therefore you failed to show either are invalid.

>LMAO. A crank does not and cannot be reasoned with. Look, you are still struggling with Euler's S = Lim S bullshit

That is why you are unreasonable :)

No one today say S = Lim S today so tough shit.

Again, failed to show any contradiction.

>I can say they are garbage because my ideas are all that matter. Anything that comes out of anyone else's syphilitic brain is nonsense.

Narcissism, a hallmark of you. Your ideas are not all that matters cause soon, you will be dead and then forgotten.

>I and I alone, decide what is well-formed knowledge. No one else has this privilege. As the discoverer of the New Calculus, I am the greatest mathematician ever - a fact which is only denied by cranks like you.

No one has this privilege, not even you.

You are a nobody that failed to find a single contradiction here.

You couldn't do the challange like a proper mathematician, because you are not a mathematician.

On Wednesday, 5 May 2021 at 00:31:52 UTC-4, zelos...@gmail.com wrote:
> >Eudoxus never talks about numbers, only magnitudes. The above PDF is written by the ignoramus called R.D. Arthan
> Not a contradiction

It is most definitely illogical because a MAGNITUDE (Book 5, Def 1) is decidedly NOT a NUMBER (Book 7, Def 1).

There was no accident in those definitions and if you had studied or even read the Elements, you might at the very least have known these things. As it stands, you remain ignorant and defiant.

> >The Ancient Greeks did not recognise any numbers other than the rational numbers. This is not opinion but fact. Some publication by an English asswipe like Arthan won't change this fact. His PDF is absolute garbage.
> Not relevant what ancient greeks did.

Eudoxus was a Greek, you uneducated moron! You are the one who first mentioned his ideas.

> >Given any magnitude x (either commensurable or incommensurable with any other magnitude), there exists rational numbers m and n such that m < x < n
> Irrelevant here.

Not at all. It is most relevant because the method used by Eudoxus uses MAGNITUDES. You should try to understand your sources before you quote them! LMAO.

I stop here, because like a spoiled two year old brat, the only response you have is defiance.

Pitiful and pathetic you are.

>
> So for hte eudoxus construction, you failed to show it is invalid.
> >As for the above two clowns (Dedekind and Cauchy), you have been shown many times why their "constructions" are invalid.
> Nothing in your link shows any contradiction.
>
> Therefore you failed to show either are invalid.
> >LMAO. A crank does not and cannot be reasoned with. Look, you are still struggling with Euler's S = Lim S bullshit
> That is why you are unreasonable :)
>
> No one today say S = Lim S today so tough shit.
>
> Again, failed to show any contradiction.
> >I can say they are garbage because my ideas are all that matter. Anything that comes out of anyone else's syphilitic brain is nonsense.
> Narcissism, a hallmark of you. Your ideas are not all that matters cause soon, you will be dead and then forgotten.
> >I and I alone, decide what is well-formed knowledge. No one else has this privilege. As the discoverer of the New Calculus, I am the greatest mathematician ever - a fact which is only denied by cranks like you.
> No one has this privilege, not even you.
>
> You are a nobody that failed to find a single contradiction here.
>
> You couldn't do the challange like a proper mathematician, because you are not a mathematician.

On Wednesday, May 5, 2021 at 7:27:35 AM UTC-4, Eram semper recta wrote:
> On Wednesday, 5 May 2021 at 00:31:52 UTC-4, zelos...@gmail.com wrote:
> > >Eudoxus never talks about numbers, only magnitudes. The above PDF is written by the ignoramus called R.D. Arthan
> > Not a contradiction
> It is most definitely illogical because a MAGNITUDE (Book 5, Def 1) is decidedly NOT a NUMBER (Book 7, Def 1).
>
> There was no accident in those definitions and if you had studied or even read the Elements, you might at the very least have known these things. As it stands, you remain ignorant and defiant.
> > >The Ancient Greeks did not recognise any numbers other than the rational numbers. This is not opinion but fact. Some publication by an English asswipe like Arthan won't change this fact. His PDF is absolute garbage.
> > Not relevant what ancient greeks did.
> Eudoxus was a Greek, you uneducated moron! You are the one who first mentioned his ideas.
> > >Given any magnitude x (either commensurable or incommensurable with any other magnitude), there exists rational numbers m and n such that m < x < n
> > Irrelevant here.
> Not at all. It is most relevant because the method used by Eudoxus uses MAGNITUDES. You should try to understand your sources before you quote them! LMAO.
>
> I stop here, because like a spoiled two year old brat, the only response you have is defiance.
>
> Pitiful and pathetic you are.

Agreed Z is a rather poor backboard of the status quo system. The ball returns dully; just enough to get another swing in.

Here are some links dodging division within their first constructive statements, which he fails to put together as a standing conflict between ring theory and the rational value as constructed by division. There is a chicken and egg here. Which came first: the operator or the value? Well, the structural details of the real value are severely lacking in purity. However, the priests will continue to harness the next generation and declare them pure..

The fact remains that the mechanisms of addition and product were learned via digital analysis in grade school and that these mechanism go ignored in these documents as if those mechanism do not exist. This lack of regard for the modulo form of all instantiated values; all elementary instances; this cannot be a good correspondence. Yet this form of escapism firmly establishes higher mathematics. These mathematicians are nearly demanding that no actual instances ever be used in order that their works ever be fouled. Where is the multiplication of two real values actually established? The addition of two arbitrary real values? Are we really to believe that this is a two dimensional problem? This is the addition of three values a three dimensional problem?
"More precisely, a binary operation on a set S is a mapping of the elements of the Cartesian product S × S to S"
- https://en.wikipedia.org/wiki/Binary_operation

Is this the same Cartesian product that builds the plane as RxR? What gives here? These instances are just plain abusive.
It seems that functional analysis has placed itself beneath operator theory.. Surely this is a mistake. Beneath the sum?

> >
> > So for hte eudoxus construction, you failed to show it is invalid.
> > >As for the above two clowns (Dedekind and Cauchy), you have been shown many times why their "constructions" are invalid.
> > Nothing in your link shows any contradiction.
> >
> > Therefore you failed to show either are invalid.
> > >LMAO. A crank does not and cannot be reasoned with. Look, you are still struggling with Euler's S = Lim S bullshit
> > That is why you are unreasonable :)
> >
> > No one today say S = Lim S today so tough shit.
> >
> > Again, failed to show any contradiction.
> > >I can say they are garbage because my ideas are all that matter. Anything that comes out of anyone else's syphilitic brain is nonsense.
> > Narcissism, a hallmark of you. Your ideas are not all that matters cause soon, you will be dead and then forgotten.
> > >I and I alone, decide what is well-formed knowledge. No one else has this privilege. As the discoverer of the New Calculus, I am the greatest mathematician ever - a fact which is only denied by cranks like you.
> > No one has this privilege, not even you.
> >
> > You are a nobody that failed to find a single contradiction here.
> >
> > You couldn't do the challange like a proper mathematician, because you are not a mathematician.

On Wednesday, May 5, 2021 at 8:32:30 AM UTC-4, Timothy Golden wrote:
> On Wednesday, May 5, 2021 at 7:27:35 AM UTC-4, Eram semper recta wrote:
> > On Wednesday, 5 May 2021 at 00:31:52 UTC-4, zelos...@gmail.com wrote:
> > > >Eudoxus never talks about numbers, only magnitudes. The above PDF is written by the ignoramus called R.D. Arthan
> > > Not a contradiction
> > It is most definitely illogical because a MAGNITUDE (Book 5, Def 1) is decidedly NOT a NUMBER (Book 7, Def 1).
> >
> > There was no accident in those definitions and if you had studied or even read the Elements, you might at the very least have known these things. As it stands, you remain ignorant and defiant.
> > > >The Ancient Greeks did not recognise any numbers other than the rational numbers. This is not opinion but fact. Some publication by an English asswipe like Arthan won't change this fact. His PDF is absolute garbage.
> > > Not relevant what ancient greeks did.
> > Eudoxus was a Greek, you uneducated moron! You are the one who first mentioned his ideas.
> > > >Given any magnitude x (either commensurable or incommensurable with any other magnitude), there exists rational numbers m and n such that m < x < n
> > > Irrelevant here.
> > Not at all. It is most relevant because the method used by Eudoxus uses MAGNITUDES. You should try to understand your sources before you quote them! LMAO.
> >
> > I stop here, because like a spoiled two year old brat, the only response you have is defiance.
> >
> > Pitiful and pathetic you are.
> Agreed Z is a rather poor backboard of the status quo system. The ball returns dully; just enough to get another swing in.
>
> Here are some links dodging division within their first constructive statements, which he fails to put together as a standing conflict between ring theory and the rational value as constructed by division. There is a chicken and egg here. Which came first: the operator or the value? Well, the structural details of the real value are severely lacking in purity. However, the priests will continue to harness the next generation and declare them pure.
>
> The fact remains that the mechanisms of addition and product were learned via digital analysis in grade school and that these mechanism go ignored in these documents as if those mechanism do not exist. This lack of regard for the modulo form of all instantiated values; all elementary instances; this cannot be a good correspondence. Yet this form of escapism firmly establishes higher mathematics. These mathematicians are nearly demanding that no actual instances ever be used in order that their works ever be fouled. Where is the multiplication of two real values actually established? The addition of two arbitrary real values? Are we really to believe that this is a two dimensional problem? This is the addition of three values a three dimensional problem?
> "More precisely, a binary operation on a set S is a mapping of the elements of the Cartesian product S × S to S"
> - https://en.wikipedia.org/wiki/Binary_operation
>
> Is this the same Cartesian product that builds the plane as RxR? What gives here? These instances are just plain abusive.
> It seems that functional analysis has placed itself beneath operator theory. Surely this is a mistake. Beneath the sum?
> > >
> > > So for hte eudoxus construction, you failed to show it is invalid.
> > > >As for the above two clowns (Dedekind and Cauchy), you have been shown many times why their "constructions" are invalid.
> > > Nothing in your link shows any contradiction.
> > >
> > > Therefore you failed to show either are invalid.
> > > >LMAO. A crank does not and cannot be reasoned with. Look, you are still struggling with Euler's S = Lim S bullshit
> > > That is why you are unreasonable :)
> > >
> > > No one today say S = Lim S today so tough shit.
> > >
> > > Again, failed to show any contradiction.
> > > >I can say they are garbage because my ideas are all that matter. Anything that comes out of anyone else's syphilitic brain is nonsense.
> > > Narcissism, a hallmark of you. Your ideas are not all that matters cause soon, you will be dead and then forgotten.
> > > >I and I alone, decide what is well-formed knowledge. No one else has this privilege. As the discoverer of the New Calculus, I am the greatest mathematician ever - a fact which is only denied by cranks like you.
> > > No one has this privilege, not even you.
> > >
> > > You are a nobody that failed to find a single contradiction here.
> > >
> > > You couldn't do the challange like a proper mathematician, because you are not a mathematician.

This whole critical look at the rational value as illegitimate might be approachable simply by admitting that for any gradation of the unit value
1 / n
there exists a digit of finer gradation
10^-m
that will be finer than n. So for instance if n is ninths we simply go to tenths and admit that the range of representation is improved over the ninths.
This interpretation is a matter of admitting the breakage of the integer into finer parts yet we know that by remaining in decimal form that we always can return to that integer format which is the means of actually performing computations for the modern human. This return toward the mechanism of these operations rather than the standard flight away from those operations is the correct route to solidifying a new construction. Yet what we construct here is simply the decimal form. There is nothing new but the focus of breaking out of the integer form; though the terminology of the scalar is nearby. To scale the numbers differently is an interpretation. That the unit of the real line is in fact arbitrary as is the meter (or was the meter and now the second); all of Euclidean geometry is devoid of this and you may plot your geometry problem in any scale that is available to you but for the physical qualities of the materials in use. That our modulo- ten numerical system requires the utterance of
1 2 3 4 5 6 7 8 9 0
as its basis is one of the inconvenient points of the radix system. To build larger values and to build smaller values is roughly the challenge that is being accomplished. No; the old problems do not seem so relevant here. Yet in that every instance of their analysis will take place here in this mod-ten system by convention; this is elementary analysis.

On Wednesday, 5 May 2021 at 08:32:30 UTC-4, timba...@gmail.com wrote:
> On Wednesday, May 5, 2021 at 7:27:35 AM UTC-4, Eram semper recta wrote:
> > On Wednesday, 5 May 2021 at 00:31:52 UTC-4, zelos...@gmail.com wrote:
> > > >Eudoxus never talks about numbers, only magnitudes. The above PDF is written by the ignoramus called R.D. Arthan
> > > Not a contradiction
> > It is most definitely illogical because a MAGNITUDE (Book 5, Def 1) is decidedly NOT a NUMBER (Book 7, Def 1).
> >
> > There was no accident in those definitions and if you had studied or even read the Elements, you might at the very least have known these things. As it stands, you remain ignorant and defiant.
> > > >The Ancient Greeks did not recognise any numbers other than the rational numbers. This is not opinion but fact. Some publication by an English asswipe like Arthan won't change this fact. His PDF is absolute garbage.
> > > Not relevant what ancient greeks did.
> > Eudoxus was a Greek, you uneducated moron! You are the one who first mentioned his ideas.
> > > >Given any magnitude x (either commensurable or incommensurable with any other magnitude), there exists rational numbers m and n such that m < x < n
> > > Irrelevant here.
> > Not at all. It is most relevant because the method used by Eudoxus uses MAGNITUDES. You should try to understand your sources before you quote them! LMAO.
> >
> > I stop here, because like a spoiled two year old brat, the only response you have is defiance.
> >
> > Pitiful and pathetic you are.
> Agreed Z is a rather poor backboard of the status quo system. The ball returns dully; just enough to get another swing in.

I would hardly call it a "swing", rather much like a stubborn fool who knows he is whipped and incomprehensibly comes back for more.

>
> Here are some links dodging division within their first constructive statements, which he fails to put together as a standing conflict between ring theory and the rational value as constructed by division.

Ring theory has nothing to do with mathematics which is the science of <<measure>> and <<number>>.

Neither a "field" nor a "ring" has anything mathematical about it. Division is a misnomer in ring theory because unless numbers are discussed, there is no analogue to the actual arithmetic operator known as division.

Division in mathematics is an arithmetic operation derived from subtraction (which is the most primitive).

We say that p/q = p -:- q if and only if p > q and the obelus (-:-) means the following:

****Subtract q from p until the remainder r is less than q or there is no remainder left****

This is ALL that is meant by the operation of division. NOTHING ELSE. The <<number>> p/q is a NAME given to the above DIVISION MEASURE. Yes, you may have guessed by now that EVERY arithmetic operation is a form of MEASURE. My famous article on "How we got numbers" explains all these facts.

Multiplication is derived from division. We say pq = p x q iff pq is both the reciprocal measure of p using q AND the reciprocal measure of q using p. This is ALL that is meant by multiplication. NOTHING ELSE. The multiplicative operator in group theory has no relationship with the product operator (x).

So, Zelos writes about this bullshit because it is what he memorised in his courses and what is considered to be the interesting part of his laughable study in mythmatics.

> There is a chicken and egg here. Which came first: the operator or the value?

Not at all. The concept of magnitude came long before ratio which came long before number. The arithmetic operators were realised when my unbelievably brilliant ancestors began to discover the relationships between magnitudes.. All the theory of fractions (and hence number too!) is systematically compiled using MAGNITUDES. There is NOTHING even mentioned about NUMBER prior to Book 7 of the Elements.

The transition to the algebraic unit is done in Book 7 with the introduction of the ABSTRACT UNIT.

> Well, the structural details of the real value are severely lacking in purity.

Chuckle. There is NO SUCH THING as a "real value". If you mean a magnitude, then again you are WRONG because as I explained in the previous paragraph, the operations of arithmetic are realised entirely WITHOUT numbers.

> However, the priests will continue to harness the next generation and declare them pure.

Decrees are not part of mathematics, so the declarations of these morons will soon be discarded for what they are - utter and worthless trash.

>
> The fact remains that the mechanisms of addition and product were learned via digital analysis in grade school and that these mechanism go ignored in these documents as if those mechanism do not exist.

Huh? No. It depends on how long you've been around. I never once used a calculator or any other digital device at school because they simply had not been invented. LMAO. I will say that the introduction of these tools without teaching the fundamentals gives rise to more idiots the calibre of Zelos Malum. Technology is great but it should never replace understanding.

Students in my school days had to master decimal arithmetic ala Simon Stevin. You see, Stevin was a prelude to the DUMBIFICATION of mainstream academics. His famous De Thiende had a toxic effect on the understanding of mathematics because like a calculator, it was intended to make arithmetic operations easier for people who were too stupid to learn the theory of fractions and number in general.

It didn't end there. From Stevin, came the eventual idea of "infinite decimal" - a garbage concept that led to Euler's S = Lim S absurdity.

> This lack of regard for the modulo form of all instantiated values;

Incomprehensible nonsense! Only you know what the above sentence is intended to mean. Try communicating your ideas clearly!!!

And since the remainder of your comment appears to be dependent on the above gibberish sentence, I cannot continue to respond.

> all elementary instances; this cannot be a good correspondence. Yet this form of escapism firmly establishes higher mathematics. These mathematicians are nearly demanding that no actual instances ever be used in order that their works ever be fouled. Where is the multiplication of two real values actually established? The addition of two arbitrary real values? Are we really to believe that this is a two dimensional problem? This is the addition of three values a three dimensional problem?
> "More precisely, a binary operation on a set S is a mapping of the elements of the Cartesian product S × S to S"
> - https://en.wikipedia.org/wiki/Binary_operation
>
> Is this the same Cartesian product that builds the plane as RxR? What gives here? These instances are just plain abusive.
> It seems that functional analysis has placed itself beneath operator theory. Surely this is a mistake. Beneath the sum?
> > >
> > > So for hte eudoxus construction, you failed to show it is invalid.
> > > >As for the above two clowns (Dedekind and Cauchy), you have been shown many times why their "constructions" are invalid.
> > > Nothing in your link shows any contradiction.
> > >
> > > Therefore you failed to show either are invalid.
> > > >LMAO. A crank does not and cannot be reasoned with. Look, you are still struggling with Euler's S = Lim S bullshit
> > > That is why you are unreasonable :)
> > >
> > > No one today say S = Lim S today so tough shit.
> > >
> > > Again, failed to show any contradiction.
> > > >I can say they are garbage because my ideas are all that matter. Anything that comes out of anyone else's syphilitic brain is nonsense.
> > > Narcissism, a hallmark of you. Your ideas are not all that matters cause soon, you will be dead and then forgotten.
> > > >I and I alone, decide what is well-formed knowledge. No one else has this privilege. As the discoverer of the New Calculus, I am the greatest mathematician ever - a fact which is only denied by cranks like you.
> > > No one has this privilege, not even you.
> > >
> > > You are a nobody that failed to find a single contradiction here.
> > >
> > > You couldn't do the challange like a proper mathematician, because you are not a mathematician.

On 5/4/2021 6:40 PM, Eram semper recta wrote:
> On Tuesday, 4 May 2021 at 04:31:09 UTC-4, zelos...@gmail.com wrote:
>> So Gabriel claims there are no valid real numbers. Gabriel, I am taking you up on it.
>>
>> To show this statement to be true you have to find an internal inconsistency. The fact it doesn't align with your preferred system does in anyway make them invalid. They are only incompatible with your system them.
>>
>> So The three champions are
>> Eudoxus: https://arxiv.org/pdf/math/0405454.pdf
>
> Eudoxus never talks about numbers, only magnitudes. The above PDF is written by the ignoramus called R.D. Arthan.
>
> The Ancient Greeks did not recognise any numbers other than the rational numbers.
[...]

Using the infinite convergents of continued fractions, one can represent
real numbers using rational numbers.

>It is most definitely illogical because a MAGNITUDE (Book 5, Def 1) is decidedly NOT a NUMBER (Book 7, Def 1).

the Eudoxus construction do not use Euclides as a basis, so what they say is of no relevance to it.

>There was no accident in those definitions and if you had studied or even read the Elements, you might at the very least have known these things. As it stands, you remain ignorant and defiant.

I know what Elements say, I just say what it says is of no relevance to these constructions cause they do not use it as a basis.

>Eudoxus was a Greek, you uneducated moron! You are the one who first mentioned his ideas.

Maybe so, but Eudoxus construction was not by him so what he was is irrelevant.

>Not at all. It is most relevant because the method used by Eudoxus uses MAGNITUDES.

What he used is irrelevant, just cause his name is in the construction doesn't that mean anything about him is of relevance here.

>You should try to understand your sources before you quote them!

I understand the link I gave you, you clearly do not because if you had read it you would know
1: The article do not use Elements as basis
2: It is in no way saying anything of this is made by Eudoxus
3: That nothing about the ancient greeks is relevant to the construction.

>I stop here, because like a spoiled two year old brat, the only response you have is defiance.

Unlike you I can actually address the issue at hand instead of answering things of no relevance.

I asked you to find internal contradictions, you start citing the greeks which is not used by any of these constructions. That is nothing but pure idiocy.

On Thursday, May 6, 2021 at 1:25:49 AM UTC-4, zelos...@gmail.com wrote:
> >Agreed Z is a rather poor backboard of the status quo system. The ball returns dully; just enough to get another swing in.
> Why? Because I actually understand stuff and you have nothing to come with that is of any relevans?
> >Where is the multiplication of two real values actually established? The addition of two arbitrary real values?
> In the fucking constructions I gave you links to!

No Z. The reason that I can state that
2.5 + 1.2 = 3.7
is because I can do the digital computation. It is something that I learned in grade school. I took two elements and I crunched them into one.
This very detail you are unable to admit. The instantiation of concrete values is something your links do not allow. I stand by my claims here, and if you can show me where in any of those documents they tell me how to perform this addition, or any addition of concrete values as numbers, then I will concede the point. If you know your links so well why don't you link to a specific page? You see, all the while in the back of these high thinking mathematicians' heads they have these computational methods that they mastered that they are relying upon but do not care to admit it into the subject. It would wreck the seeming purity of their works. But where then does this leave those works? Why is it that we have to wait until an abstract algebra curriculum to take the simple operators sum and product more seriously and yet still lack the specifications of how to actually perform addition or multiplication? Indeed, it is quite possible that we cannot prove that for every real a and every real b there exists
a + b
since we cannot perform all these computations. Possibly here lays another avenue toward the binary operator definition but the failings of it are already exposed. Then too as we see that the sum is in fact n-ary we ought to have proven that
a + b + c + d + e + f
lays in the reals as well. It is factually true that computers will suffer an overflow or a loss of precision when handling such values except in the case of variable precision software. Still in hardware we do have an issue here. At least we can admit that. The human ought to have admitted that their own computational powers are severely limited. But no; instead we see the high flying mathematician escapes the lowly computable figure and moves to much higher ground. At this generation this move is engrained so that it takes the likes of me to shove your nose in it. I know it will be met with the usual dull thud here, and I'll barely even feel like striking the ball again.

Indeed closure is the principle that I am discussing above, and should it be true that values as operators are carried around unevaluated then we ought to admit that the form of such systems is more like
R + R
rather than
R x R
where an expression a+b arises. It is to say that since a is in R and b is in R and the result is not guaranteed to be in R, which is why we carry around the said sum, then we can only guarantee that the result is preserved as the expression is preserved, and it is not a two dimensional entity. It is two one dimensional entities. They do not form a plane, sir. On this point the ball does in fact land flat at the back board known as Zelos. This must mean that I am onto something.

Now Zelos comes back with a chuckle and says that this cannot possibly be correct for standard mathematicas yadda yadda yadda...
Obviously we are attempting to go beyond standard mathematics here sir.
Your own measly methods only show you to be the fraud that you are and the system as a fraud too.

Your own compilation of these facts is obviously not forthcoming here. We cannot evaluate an expression whose values are not filled in. This does not prevent analysis from occurring, but as to whether those constructions can be called elemental even: this is problematic. You cannot possibly wish to get in a fight with a computer on computation. Surely it is known that all humans will lose that fight. All that we can do is build a better computer. That or put a wrench in its gears, and this all too often is the human pursuit.

On Thursday, 6 May 2021 at 01:23:19 UTC-4, zelos...@gmail.com wrote:
> >It is most definitely illogical because a MAGNITUDE (Book 5, Def 1) is decidedly NOT a NUMBER (Book 7, Def 1).
> the Eudoxus construction do not use Euclides as a basis, so what they say is of no relevance to it.

Again, it matters very much because the ideas in your bogus nomenclature are irrelevant. I have directed my comments to the essence of your claims which you've totally ignored because you are a known idiot and a crank.

> >There was no accident in those definitions and if you had studied or even read the Elements, you might at the very least have known these things. As it stands, you remain ignorant and defiant.
> I know what Elements say, I just say what it says is of no relevance to these constructions cause they do not use it as a basis.

The idea of MAGNITUDE is USED. Study that PDF, you fucking imbecile!!! Why else would it be called Eudoxus... Tsk, tsk.

> >Eudoxus was a Greek, you uneducated moron! You are the one who first mentioned his ideas.
> Maybe so, but Eudoxus construction was not by him so what he was is irrelevant.

Eyes rolling. NO ONE CLAIMED SO. Strawman arguments are your speciality.

The concept of MAGNITUDE is VERY relevant in the Eudoxus "reals".

> >Not at all. It is most relevant because the method used by Eudoxus uses MAGNITUDES.
> What he used is irrelevant, just cause his name is in the construction doesn't that mean anything about him is of relevance here.

Address what I said, you idiot!!!!! I don't give a fuck about the name. I am talking about your PDF. READ IT, YOU FUCKING MORON.

> >You should try to understand your sources before you quote them!
> I understand the link I gave you, you clearly do not because if you had read it you would know

> 1: The article do not use Elements as basis

Grrrr. No one said it does.

> 2: It is in no way saying anything of this is made by Eudoxus

Again, strawman argument. No one said so.

> 3: That nothing about the ancient greeks is relevant to the construction.

FAIL. The PDF is about the use of the MAGNITUDE concept in a FAILED attempt to produce "real number".

> >I stop here, because like a spoiled two year old brat, the only response you have is defiance.
> Unlike you I can actually address the issue at hand instead of answering things of no relevance.
>
> I asked you to find internal contradictions, you start citing the greeks which is not used by any of these constructions. That is nothing but pure idiocy.

That is again your strawman argument.

From YOUR PDF:

"Magnitudes are said to be in the same ratio, the first to the second and the third to the fourth, when, if any equimultiples whatever are taken of the first and third, and any equimultiples whatever of the second and fourth, the former equimultiples alike exceed, are alike equal to, or alike fall short of, the latter equimultiples respectively taken in corresponding order..
Euclid. Elements of Geometry. Book V. Definition 5."

The ideas are taken directly from the ELEMENTS and the key feature that is used to arrive at De Morgan’s Colonnade and Fence, is the concept of MAGNITUDE.

From page 2:

"Let the distance between the columns be C and the distance between the railings be R. If the construction is continued indefinitely, an observer can compare C with R to any degree of accuracy without making any measurements just by counting the columns and railings."

READ IT MORON! You can't talk about <<distance>> until you have defined what it means. This was done in the Elements using the object called a <straight line>. The comical part "without making any measurements just by counting" is simply too hilarious.

To count is to measure and that's the first BIG ERROR. But there's no hope even if one reads the entire PDF since it is already off the rails from the very beginning.

FEF. Why am I wasting my time. You are an imbecile who cannot be fixed.

On Thursday, 6 May 2021 at 06:33:42 UTC-4, timba...@gmail.com wrote:
> On Thursday, May 6, 2021 at 1:25:49 AM UTC-4, zelos...@gmail.com wrote:
> > >Agreed Z is a rather poor backboard of the status quo system. The ball returns dully; just enough to get another swing in.
> > Why? Because I actually understand stuff and you have nothing to come with that is of any relevans?
> > >Where is the multiplication of two real values actually established? The addition of two arbitrary real values?
> > In the fucking constructions I gave you links to!
> No Z. The reason that I can state that
> 2.5 + 1.2 = 3.7
> is because I can do the digital computation. It is something that I learned in grade school. I took two elements and I crunched them into one.

I have already explained how this is done in geometry without the use of numbers at all. Not for one instance backing up the idiot Zelos Malum.

You can COMPUTE π x √2 EXACTLY in geometry IF you are able to construct either of these incommensurable magnitudes. However, you CANNOT, because there is NO ideal unit in geometry. Do you get this?

> This very detail you are unable to admit. The instantiation of concrete values is something your links do not allow. I stand by my claims here, and if you can show me where in any of those documents they tell me how to perform this addition, or any addition of concrete values as numbers, then I will concede the point.

While "concrete values" are nice, neither π nor √2 are concrete ever! I have shown you how to subtract, add, divide and multiply EXACTLY in geometry.

> If you know your links so well why don't you link to a specific page? You see, all the while in the back of these high thinking mathematicians' heads they have these computational methods that they mastered that they are relying upon but do not care to admit it into the subject. It would wreck the seeming purity of their works. But where then does this leave those works? Why is it that we have to wait until an abstract algebra curriculum to take the simple operators sum and product more seriously and yet still lack the specifications of how to actually perform addition or multiplication? Indeed, it is quite possible that we cannot prove that for every real a and every real b there exists
> a + b
> since we cannot perform all these computations.

We can prove that EVERY MAGNITUDE a + b has a result c in GEOMETRY. What we CANNOT do is the same thing in ALGEBRA which uses NOTHING ELSE but the ABSTRACT UNIT.

Study what I tell you. I KNOW BETTER THAN ANYONE ELSE ON THE PLANET. You will gain nothing by arguing with Malum.

> Possibly here lays another avenue toward the binary operator definition but the failings of it are already exposed. Then too as we see that the sum is in fact n-ary we ought to have proven that
> a + b + c + d + e + f
> lays in the reals as well. It is factually true that computers will suffer an overflow or a loss of precision when handling such values except in the case of variable precision software. Still in hardware we do have an issue here. At least we can admit that. The human ought to have admitted that their own computational powers are severely limited. But no; instead we see the high flying mathematician escapes the lowly computable figure and moves to much higher ground. At this generation this move is engrained so that it takes the likes of me to shove your nose in it. I know it will be met with the usual dull thud here, and I'll barely even feel like striking the ball again.
>
> Indeed closure is the principle that I am discussing above, and should it be true that values as operators are carried around unevaluated then we ought to admit that the form of such systems is more like
> R + R
> rather than
> R x R
> where an expression a+b arises. It is to say that since a is in R and b is in R and the result is not guaranteed to be in R, which is why we carry around the said sum, then we can only guarantee that the result is preserved as the expression is preserved, and it is not a two dimensional entity. It is two one dimensional entities. They do not form a plane, sir. On this point the ball does in fact land flat at the back board known as Zelos. This must mean that I am onto something.
>
> Now Zelos comes back with a chuckle and says that this cannot possibly be correct for standard mathematicas yadda yadda yadda...
> Obviously we are attempting to go beyond standard mathematics here sir.
> Your own measly methods only show you to be the fraud that you are and the system as a fraud too.
>
> Your own compilation of these facts is obviously not forthcoming here. We cannot evaluate an expression whose values are not filled in. This does not prevent analysis from occurring, but as to whether those constructions can be called elemental even: this is problematic. You cannot possibly wish to get in a fight with a computer on computation. Surely it is known that all humans will lose that fight. All that we can do is build a better computer. That or put a wrench in its gears, and this all too often is the human pursuit.

On Thursday, May 6, 2021 at 7:51:27 AM UTC-4, Eram semper recta wrote:
> On Thursday, 6 May 2021 at 06:33:42 UTC-4, timba...@gmail.com wrote:
> > On Thursday, May 6, 2021 at 1:25:49 AM UTC-4, zelos...@gmail.com wrote:
> > > >Agreed Z is a rather poor backboard of the status quo system. The ball returns dully; just enough to get another swing in.
> > > Why? Because I actually understand stuff and you have nothing to come with that is of any relevans?
> > > >Where is the multiplication of two real values actually established? The addition of two arbitrary real values?
> > > In the fucking constructions I gave you links to!
> > No Z. The reason that I can state that
> > 2.5 + 1.2 = 3.7
> > is because I can do the digital computation. It is something that I learned in grade school. I took two elements and I crunched them into one.
> I have already explained how this is done in geometry without the use of numbers at all. Not for one instance backing up the idiot Zelos Malum.

On just this one point, now, please, and thank you Eram for injecting some decent analysis. I will call you if I see a bluff or a blunder, but what it looks like is happening is that we are now engaged in three systems: your firstly geometrical completely lacking in what I will call a 'metric' though by the usage of this term I do not mean any hierarchical mumbo jumbo but something very primitive, as when one makes a couple of scratches on a piece of wood and declares them to be the working unit of the day.
It may occur to some that they can count this unit and that its multiples do take number readily, and that the remainder may be marked, even upon the same stick that marks the first unit, and so a secondary unit can alight from such work, though it is the result of the selection of the first unit it is guaranteed as a remainder to fit beneath the first and so any who doubt the method of organization may recover these details not so much informationally but rather materially and physically secure... for the day at least. And if the day is not long enough to finish the project then that stick will deserve some special notation or placement at the bench; likely right with the materials being worked. Box them away and the project can be put on hold. Another project can ensue that might even take a tertiary unital form.. Will the procedure ever finish? Will the project get done? Modern academia imposes deadlines and forms fake projects so that these issues go away. We now at the tenth generations let's say of such nonworks, and roughly four generations back the 'whole project' culture diminished with grandpa on the farm and all his grandchildren gone to the city to work in the mill. My great grandfather was a mill worker. I remember being a young boy and him teaching my brother and I how to use a file but the lesson clearly came onto dim heads. As to how much he knew I will never know and am only just getting handy now. Probably I shouldn't even call it that.

So Z exposes a third class system where instantiation is completely avoided under the guise of generality, but as the graphical solution does carry a sum mechanism, and the numerical solution does clearly and universally carry a sum mechanism, it is clear that within abstract algebra and other high fluting trades that seem to declare a sum mechanism that there is no actual core. These are stubs. They lead to non-instantiables. These non-instantiables are regarded by those who purvey them as superior to our forms, yet we have Z falsified so many ways, and this is as it is within buggy code under accumulation; make no mistake about it the overlap of these systems is substantial.

As to who will be the superior compiler: the computer or the human? We know already who will work the numbers fastest, yes?
Holdouts like Z whose teeth are falling out at every post are quaint instances of a game of head fuckery that went on for many generations when the very numbers and physical magnitudes and their possibilities were (and still are actually) open puzzles. This is what happens when you hand Z a hammer and a sharp chisel: he goes straight to his head.

It is a strange but true fact that my great grandfather did loose his marbles eventually in his nineties and that my grandmother cared for him through it all. At one point Grampy was so senile that he tried to cut off his penis with a hacksaw. The saddest part of the story really is to put this in perspective: nationally we have a formalized strategy known as MAD which as far as I know has never been recanted. Supposing Biden were to recant on MAD? What exactly would the follow-up look like? I don't think Grampy was successful in that last act I mentioned, but maybe there are rather more of his offspring around than I know of. Can you imagine what could go on at those mills with all those young women pent up in the work environment just happy to get some time in the yarn closet? Not quite sure how that analysis works out with MAD, but the automation industry must be very well and advanced within the defense industry. It is not so much of a rat's race any more. When will automation become a race? Is there any doubt that it has already won? For Z the computer will not be declared intelligent until it mimics him. This is a blunder. No. Upon covering a sufficient number of variations and developing a selective filtration system the computer's thought process will be sufficient. The question I think may be whether such a perfect orb should have solutions like theoretical physics? Without any inputs? This would be marvelous and in terms of metric ideals you could not hope for anything better. As for recovering all of modern mathematics: no. The proper orb is going to complain. When it tells them what they do not want to hear they will shut their ears; shut down the project; and start over again.

Did the soviets adopt MAD or did they have their own philosophy about the situation? As an American I have no idea. No doubt access and discussion of these details is actively discouraged. FAFA...

>
> You can COMPUTE π x √2 EXACTLY in geometry IF you are able to construct either of these incommensurable magnitudes. However, you CANNOT, because there is NO ideal unit in geometry. Do you get this?
> > This very detail you are unable to admit. The instantiation of concrete values is something your links do not allow. I stand by my claims here, and if you can show me where in any of those documents they tell me how to perform this addition, or any addition of concrete values as numbers, then I will concede the point.
> While "concrete values" are nice, neither π nor √2 are concrete ever! I have shown you how to subtract, add, divide and multiply EXACTLY in geometry.
> > If you know your links so well why don't you link to a specific page? You see, all the while in the back of these high thinking mathematicians' heads they have these computational methods that they mastered that they are relying upon but do not care to admit it into the subject. It would wreck the seeming purity of their works. But where then does this leave those works? Why is it that we have to wait until an abstract algebra curriculum to take the simple operators sum and product more seriously and yet still lack the specifications of how to actually perform addition or multiplication? Indeed, it is quite possible that we cannot prove that for every real a and every real b there exists
> > a + b
> > since we cannot perform all these computations.
> We can prove that EVERY MAGNITUDE a + b has a result c in GEOMETRY. What we CANNOT do is the same thing in ALGEBRA which uses NOTHING ELSE but the ABSTRACT UNIT.
>
> Study what I tell you. I KNOW BETTER THAN ANYONE ELSE ON THE PLANET. You will gain nothing by arguing with Malum.
> > Possibly here lays another avenue toward the binary operator definition but the failings of it are already exposed. Then too as we see that the sum is in fact n-ary we ought to have proven that
> > a + b + c + d + e + f
> > lays in the reals as well. It is factually true that computers will suffer an overflow or a loss of precision when handling such values except in the case of variable precision software. Still in hardware we do have an issue here. At least we can admit that. The human ought to have admitted that their own computational powers are severely limited. But no; instead we see the high flying mathematician escapes the lowly computable figure and moves to much higher ground. At this generation this move is engrained so that it takes the likes of me to shove your nose in it. I know it will be met with the usual dull thud here, and I'll barely even feel like striking the ball again.
> >
> > Indeed closure is the principle that I am discussing above, and should it be true that values as operators are carried around unevaluated then we ought to admit that the form of such systems is more like
> > R + R
> > rather than
> > R x R
> > where an expression a+b arises. It is to say that since a is in R and b is in R and the result is not guaranteed to be in R, which is why we carry around the said sum, then we can only guarantee that the result is preserved as the expression is preserved, and it is not a two dimensional entity. It is two one dimensional entities. They do not form a plane, sir. On this point the ball does in fact land flat at the back board known as Zelos. This must mean that I am onto something.
> >
> > Now Zelos comes back with a chuckle and says that this cannot possibly be correct for standard mathematicas yadda yadda yadda...
> > Obviously we are attempting to go beyond standard mathematics here sir.
> > Your own measly methods only show you to be the fraud that you are and the system as a fraud too.
> >
> > Your own compilation of these facts is obviously not forthcoming here. We cannot evaluate an expression whose values are not filled in. This does not prevent analysis from occurring, but as to whether those constructions can be called elemental even: this is problematic. You cannot possibly wish to get in a fight with a computer on computation. Surely it is known that all humans will lose that fight. All that we can do is build a better computer. That or put a wrench in its gears, and this all too often is the human pursuit.

On Thursday, 6 May 2021 at 08:57:07 UTC-4, timba...@gmail.com wrote:
> On Thursday, May 6, 2021 at 7:51:27 AM UTC-4, Eram semper recta wrote:
> > On Thursday, 6 May 2021 at 06:33:42 UTC-4, timba...@gmail.com wrote:
> > > On Thursday, May 6, 2021 at 1:25:49 AM UTC-4, zelos...@gmail.com wrote:
> > > > >Agreed Z is a rather poor backboard of the status quo system. The ball returns dully; just enough to get another swing in.
> > > > Why? Because I actually understand stuff and you have nothing to come with that is of any relevans?
> > > > >Where is the multiplication of two real values actually established? The addition of two arbitrary real values?
> > > > In the fucking constructions I gave you links to!
> > > No Z. The reason that I can state that
> > > 2.5 + 1.2 = 3.7
> > > is because I can do the digital computation. It is something that I learned in grade school. I took two elements and I crunched them into one.
> > I have already explained how this is done in geometry without the use of numbers at all. Not for one instance backing up the idiot Zelos Malum.
> On just this one point, now, please, and thank you Eram for injecting some decent analysis. I will call you if I see a bluff or a blunder, but what it looks like is happening is that we are now engaged in three systems: your firstly geometrical completely lacking in what I will call a 'metric' though by the usage of this term I do not mean any hierarchical mumbo jumbo but something very primitive, as when one makes a couple of scratches on a piece of wood and declares them to be the working unit of the day.

Not true that there is no metric in geometry. The metric can be almost any magnitude you please. However, this is where the abstract unit through generalisation finds its place in algebra.

> It may occur to some that they can count this unit and that its multiples do take number readily, and that the remainder may be marked, even upon the same stick that marks the first unit, and so a secondary unit can alight from such work, though it is the result of the selection of the first unit it is guaranteed as a remainder to fit beneath the first and so any who doubt the method of organization may recover these details not so much informationally but rather materially and physically secure... for the day at least. And if the day is not long enough to finish the project then that stick will deserve some special notation or placement at the bench; likely right with the materials being worked. Box them away and the project can be put on hold. Another project can ensue that might even take a tertiary unital form.

Well, this is where the standard physical "units and measures" make their debut.

> Will the procedure ever finish? Will the project get done? Modern academia imposes deadlines and forms fake projects so that these issues go away.

Wishful thinking because mainstream decrees and fundamentalism only sanctions contrary opinions that expose its ignorance. The issues never go away. Any healthy-minded average student who gets frustrated with his idiot teachers is proof that the issues are still here. The only exceptions are the sycophants like Malum, etc.

> We now at the tenth generations let's say of such nonworks, and roughly four generations back the 'whole project' culture diminished with grandpa on the farm and all his grandchildren gone to the city to work in the mill. My great grandfather was a mill worker. I remember being a young boy and him teaching my brother and I how to use a file but the lesson clearly came onto dim heads. As to how much he knew I will never know and am only just getting handy now. Probably I shouldn't even call it that.

The non-works and lack of progress in mainstream math academia goes back more than 200 years.

>
> So Z exposes a third class system where instantiation is completely avoided under the guise of generality, but as the graphical solution does carry a sum mechanism, and the numerical solution does clearly and universally carry a sum mechanism, it is clear that within abstract algebra and other high fluting trades that seem to declare a sum mechanism that there is no actual core. These are stubs. They lead to non-instantiables. These non-instantiables are regarded by those who purvey them as superior to our forms, yet we have Z falsified so many ways, and this is as it is within buggy code under accumulation; make no mistake about it the overlap of these systems is substantial.

Agreed! I am certain though that Zelos will not understand most of the above paragraph - it's simply way over his head.

Instantiation is the first and foremost step in my 4-step guideline for well formedness. If you can't instantiate a concept either intangibly or tangibly, then you have nothing. The stubs you refer to are like "virtual functions" that have no purpose whatsoever except to point nowhere. Chuckle. In essence, you can build whatever rot you like on these by letting your imagination run wild.

>
> As to who will be the superior compiler: the computer or the human?

Well, now that we are talking about my past means of making a living, I have only this left to say:

To become a master at any computer programming language means mastering the workings of its compiler.

Any old fool knows and understands what is an algorithm which is an algorithm no matter what the language - compiled or interpreted.

> We know already who will work the numbers fastest, yes?

Speed is not an indication of intelligence. Never has been.

> Holdouts like Z whose teeth are falling out at every post are quaint instances of a game of head fuckery that went on for many generations

and is still very much in play....

> when the very numbers and physical magnitudes and their possibilities were (and still are actually) open puzzles. This is what happens when you hand Z a hammer and a sharp chisel: he goes straight to his head.

All Zelos knows is what he has faithfully memorised. As long as he is a good boy and obeys his priests, his career of lifetime deception and worthlessness will be secure. There are those who go to university and never leave because the reality of the outside world is too harsh for them. Chuckle. It's far easier to bullshit young minds and if you are a pedophile (as many of them are!), then you have an extra perk - juicy young boys and girls. Chuckle.

>
> It is a strange but true fact that my great grandfather did loose his marbles eventually in his nineties and that my grandmother cared for him through it all. At one point Grampy was so senile that he tried to cut off his penis with a hacksaw.

Oooh. That's harsh.

> The saddest part of the story really is to put this in perspective: nationally we have a formalized strategy known as MAD which as far as I know has never been recanted.

MAD as in mutually assured destruction? This and worse in my opinion....

> Supposing Biden were to recant on MAD? What exactly would the follow-up look like? I don't think Grampy was successful in that last act I mentioned, but maybe there are rather more of his offspring around than I know of. Can you imagine what could go on at those mills with all those young women pent up in the work environment just happy to get some time in the yarn closet?

I can imagine but I have better things to think about. Ha, ha.

> Not quite sure how that analysis works out with MAD, but the automation industry must be very well and advanced within the defense industry. It is not so much of a rat's race any more. When will automation become a race? Is there any doubt that it has already won? For Z the computer will not be declared intelligent until it mimics him.

Oh, it's pretty easy to mimic Zelos. Proof: Almost 8 billion unbelievably stupid humans?

> This is a blunder. No. Upon covering a sufficient number of variations and developing a selective filtration system the computer's thought process will be sufficient. The question I think may be whether such a perfect orb should have solutions like theoretical physics? Without any inputs?

Theoretical physics ended when Einstein became famous. So I only know about theatrical physicists today. The Hawkings, etc.

> This would be marvelous and in terms of metric ideals you could not hope for anything better. As for recovering all of modern mathematics: no. The proper orb is going to complain. When it tells them what they do not want to hear they will shut their ears; shut down the project; and start over again.
>
> Did the soviets adopt MAD or did they have their own philosophy about the situation? As an American I have no idea. No doubt access and discussion of these details is actively discouraged. FAFA...

So I really don't know what you mean by MAD. You shouldn't assume that others know what you mean.

> >
> > You can COMPUTE π x √2 EXACTLY in geometry IF you are able to construct either of these incommensurable magnitudes. However, you CANNOT, because there is NO ideal unit in geometry. Do you get this?
> > > This very detail you are unable to admit.

Wrong. I have known and taught it all along!

> The instantiation of concrete values is something your links do not allow..

No, that is decidedly FALSE. You are not understanding if this is your belief.

> I stand by my claims here, and if you can show me where in any of those documents they tell me how to perform this addition, or any addition of concrete values as numbers, then I will concede the point.

On Thursday, May 6, 2021 at 7:51:27 AM UTC-4, I am super rectum (aka "John Gabriel", "Troll Boy") wrote:
> On Thursday, 6 May 2021 at 06:33:42 UTC-4, timba...@gmail.com wrote:
> > On Thursday, May 6, 2021 at 1:25:49 AM UTC-4, zelos...@gmail.com wrote:
> > > >Agreed Z is a rather poor backboard of the status quo system. The ball returns dully; just enough to get another swing in.
> > > Why? Because I actually understand stuff and you have nothing to come with that is of any relevans?
> > > >Where is the multiplication of two real values actually established? The addition of two arbitrary real values?
> > > In the fucking constructions I gave you links to!
> > No Z. The reason that I can state that
> > 2.5 + 1.2 = 3.7
> > is because I can do the digital computation. It is something that I learned in grade school. I took two elements and I crunched them into one.
> I have already explained how this is done in geometry without the use of numbers at all. Not for one instance backing up the idiot Zelos Malum.
>
> You can COMPUTE π x √2 EXACTLY in geometry IF you are able to construct either of these incommensurable magnitudes.

What do you tell a scientist who needs root 2 to 10 decimal places? Measure the length of the diagonal of a unit square? You wouldn't last to lunch time, Troll Boy!
__________________________________________________________________________________

Even at his advanced age (60+?), John Gabriel is STILL struggling with basic, elementary-school arithmetic. As he has repeatedly posted here:

"There are no points on a line."
--April 12, 2021

"Pi is NOT a number of ANY kind!"
--July 10, 2020

"1/2 not equal to 2/4"
--October 22, 2017

“1/3 does NOT mean 1 divided by 3 and never has meant that”
-- February 8, 2015

"3 =< 4 is nonsense.”
--October 28, 2017

"Zero is not a number."
-- Dec. 2, 2019

"0 is not required at all in mathematics, just like negative numbers."
-- Jan. 4, 2017

“There is no such thing as an empty set.”
--Oct. 4, 2019

“3 <=> 2 + 1 or 3 <=> 8 - 5, etc, are all propositions” (actually all are meaningless gibberish)
--Oct. 22, 2019

No math genius our JG, though he actually lists his job title as “mathematician” at Linkedin.com. Apparently, they do not verify your credentials.

Though really quite disturbing, interested readers should see: “About the spamming troll John Gabriel in his own words...” (lasted updated March 10, 2020) at https://groups.google.com/forum/#!msg/sci.math/PcpAzX5pDeY/1PDiSlK_BwAJ

Dan

Download my DC Proof 2.0 freeware at http://www.dcproof.com
Visit my Math Blog a http://www.dcproof.wordpress.com

On Thursday, May 6, 2021 at 11:58:16 AM UTC-4, Eram semper recta wrote:
> On Thursday, 6 May 2021 at 08:57:07 UTC-4, timba...@gmail.com wrote:
> > On Thursday, May 6, 2021 at 7:51:27 AM UTC-4, Eram semper recta wrote:
> > > On Thursday, 6 May 2021 at 06:33:42 UTC-4, timba...@gmail.com wrote:
> > > > On Thursday, May 6, 2021 at 1:25:49 AM UTC-4, zelos...@gmail.com wrote:
> > > > > >Agreed Z is a rather poor backboard of the status quo system. The ball returns dully; just enough to get another swing in.
> > > > > Why? Because I actually understand stuff and you have nothing to come with that is of any relevans?
> > > > > >Where is the multiplication of two real values actually established? The addition of two arbitrary real values?
> > > > > In the fucking constructions I gave you links to!
> > > > No Z. The reason that I can state that
> > > > 2.5 + 1.2 = 3.7
> > > > is because I can do the digital computation. It is something that I learned in grade school. I took two elements and I crunched them into one.
> > > I have already explained how this is done in geometry without the use of numbers at all. Not for one instance backing up the idiot Zelos Malum.
> > On just this one point, now, please, and thank you Eram for injecting some decent analysis. I will call you if I see a bluff or a blunder, but what it looks like is happening is that we are now engaged in three systems: your firstly geometrical completely lacking in what I will call a 'metric' though by the usage of this term I do not mean any hierarchical mumbo jumbo but something very primitive, as when one makes a couple of scratches on a piece of wood and declares them to be the working unit of the day.
> Not true that there is no metric in geometry. The metric can be almost any magnitude you please. However, this is where the abstract unit through generalisation finds its place in algebra.

This is where a few nicks on a stick establish a unit length that can be transferred. More carefully done they are scribed with a marking knife so that as you drag the marking knife's edge across the marking stick the edge will drop into the marking cut, thus establishing near perfect transfer to an adjacent piece of work material.
The same is true in metal with an awl and use of a square and flats on the pieces will help raise the precision.

> > It may occur to some that they can count this unit and that its multiples do take number readily, and that the remainder may be marked, even upon the same stick that marks the first unit, and so a secondary unit can alight from such work, though it is the result of the selection of the first unit it is guaranteed as a remainder to fit beneath the first and so any who doubt the method of organization may recover these details not so much informationally but rather materially and physically secure... for the day at least. And if the day is not long enough to finish the project then that stick will deserve some special notation or placement at the bench; likely right with the materials being worked. Box them away and the project can be put on hold. Another project can ensue that might even take a tertiary unital form.
> Well, this is where the standard physical "units and measures" make their debut.
Yes, but as we see Euclidean geometry needs no standard ruler. Scalable results seem always admissible
> > Will the procedure ever finish? Will the project get done? Modern academia imposes deadlines and forms fake projects so that these issues go away.
> Wishful thinking because mainstream decrees and fundamentalism only sanctions contrary opinions that expose its ignorance. The issues never go away. Any healthy-minded average student who gets frustrated with his idiot teachers is proof that the issues are still here. The only exceptions are the sycophants like Malum, etc.
> > We now at the tenth generations let's say of such nonworks, and roughly four generations back the 'whole project' culture diminished with grandpa on the farm and all his grandchildren gone to the city to work in the mill. My great grandfather was a mill worker. I remember being a young boy and him teaching my brother and I how to use a file but the lesson clearly came onto dim heads. As to how much he knew I will never know and am only just getting handy now. Probably I shouldn't even call it that.
> The non-works and lack of progress in mainstream math academia goes back more than 200 years.
> >
> > So Z exposes a third class system where instantiation is completely avoided under the guise of generality, but as the graphical solution does carry a sum mechanism, and the numerical solution does clearly and universally carry a sum mechanism, it is clear that within abstract algebra and other high fluting trades that seem to declare a sum mechanism that there is no actual core. These are stubs. They lead to non-instantiables. These non-instantiables are regarded by those who purvey them as superior to our forms, yet we have Z falsified so many ways, and this is as it is within buggy code under accumulation; make no mistake about it the overlap of these systems is substantial.
> Agreed! I am certain though that Zelos will not understand most of the above paragraph - it's simply way over his head.

I think this third method that lacks instantiation is really worth holding to.

>
> Instantiation is the first and foremost step in my 4-step guideline for well formedness. If you can't instantiate a concept either intangibly or tangibly, then you have nothing. The stubs you refer to are like "virtual functions" that have no purpose whatsoever except to point nowhere. Chuckle. In essence, you can build whatever rot you like on these by letting your imagination run wild.
> >
> > As to who will be the superior compiler: the computer or the human?
> Well, now that we are talking about my past means of making a living, I have only this left to say:
>
> To become a master at any computer programming language means mastering the workings of its compiler.
>
> Any old fool knows and understands what is an algorithm which is an algorithm no matter what the language - compiled or interpreted.
> > We know already who will work the numbers fastest, yes?
> Speed is not an indication of intelligence. Never has been.
> > Holdouts like Z whose teeth are falling out at every post are quaint instances of a game of head fuckery that went on for many generations
> and is still very much in play....
> > when the very numbers and physical magnitudes and their possibilities were (and still are actually) open puzzles. This is what happens when you hand Z a hammer and a sharp chisel: he goes straight to his head.
> All Zelos knows is what he has faithfully memorised. As long as he is a good boy and obeys his priests, his career of lifetime deception and worthlessness will be secure. There are those who go to university and never leave because the reality of the outside world is too harsh for them. Chuckle. It's far easier to bullshit young minds and if you are a pedophile (as many of them are!), then you have an extra perk - juicy young boys and girls. Chuckle.
> >
> > It is a strange but true fact that my great grandfather did loose his marbles eventually in his nineties and that my grandmother cared for him through it all. At one point Grampy was so senile that he tried to cut off his penis with a hacksaw.
> Oooh. That's harsh.
> > The saddest part of the story really is to put this in perspective: nationally we have a formalized strategy known as MAD which as far as I know has never been recanted.
> MAD as in mutually assured destruction? This and worse in my opinion....
> > Supposing Biden were to recant on MAD? What exactly would the follow-up look like? I don't think Grampy was successful in that last act I mentioned, but maybe there are rather more of his offspring around than I know of. Can you imagine what could go on at those mills with all those young women pent up in the work environment just happy to get some time in the yarn closet?
> I can imagine but I have better things to think about. Ha, ha.
> > Not quite sure how that analysis works out with MAD, but the automation industry must be very well and advanced within the defense industry. It is not so much of a rat's race any more. When will automation become a race? Is there any doubt that it has already won? For Z the computer will not be declared intelligent until it mimics him.
> Oh, it's pretty easy to mimic Zelos. Proof: Almost 8 billion unbelievably stupid humans?
> > This is a blunder. No. Upon covering a sufficient number of variations and developing a selective filtration system the computer's thought process will be sufficient. The question I think may be whether such a perfect orb should have solutions like theoretical physics? Without any inputs?
> Theoretical physics ended when Einstein became famous. So I only know about theatrical physicists today. The Hawkings, etc.
> > This would be marvelous and in terms of metric ideals you could not hope for anything better. As for recovering all of modern mathematics: no. The proper orb is going to complain. When it tells them what they do not want to hear they will shut their ears; shut down the project; and start over again.
> >
> > Did the soviets adopt MAD or did they have their own philosophy about the situation? As an American I have no idea. No doubt access and discussion of these details is actively discouraged. FAFA...
> So I really don't know what you mean by MAD. You shouldn't assume that others know what you mean.
> > >
> > > You can COMPUTE π x √2 EXACTLY in geometry IF you are able to construct either of these incommensurable magnitudes. However, you CANNOT, because there is NO ideal unit in geometry. Do you get this?
> > > > This very detail you are unable to admit.
> Wrong. I have known and taught it all along!
> > The instantiation of concrete values is something your links do not allow.
> No, that is decidedly FALSE. You are not understanding if this is your belief.
Well, I should not say that they do not allow it, but rather that they do not instantiate anything.
> > I stand by my claims here, and if you can show me where in any of those documents they tell me how to perform this addition, or any addition of concrete values as numbers, then I will concede the point.
> All my links show this and there is also mention of it in my free eBook.
> > > While "concrete values" are nice, neither π nor √2 are concrete ever! I have shown you how to subtract, add, divide and multiply EXACTLY in geometry.
>
> > > > If you know your links so well why don't you link to a specific page?
> So I don't talk about ruler or compass because none of these are required in mathematics. YES, you use them in physical construction, but that is not the same as the theory behind the perfect concepts from which the physical construction is realised.
>
> This is something you have failed (like Mueckenheim and many, many others) to understand.

On Friday, 7 May 2021 at 08:18:52 UTC-4, timba...@gmail.com wrote:
> On Thursday, May 6, 2021 at 11:58:16 AM UTC-4, Eram semper recta wrote:
> > On Thursday, 6 May 2021 at 08:57:07 UTC-4, timba...@gmail.com wrote:
> > > On Thursday, May 6, 2021 at 7:51:27 AM UTC-4, Eram semper recta wrote:
> > > > On Thursday, 6 May 2021 at 06:33:42 UTC-4, timba...@gmail.com wrote:
> > > > > On Thursday, May 6, 2021 at 1:25:49 AM UTC-4, zelos...@gmail.com wrote:
> > > > > > >Agreed Z is a rather poor backboard of the status quo system. The ball returns dully; just enough to get another swing in.
> > > > > > Why? Because I actually understand stuff and you have nothing to come with that is of any relevans?
> > > > > > >Where is the multiplication of two real values actually established? The addition of two arbitrary real values?
> > > > > > In the fucking constructions I gave you links to!
> > > > > No Z. The reason that I can state that
> > > > > 2.5 + 1.2 = 3.7
> > > > > is because I can do the digital computation. It is something that I learned in grade school. I took two elements and I crunched them into one.
> > > > I have already explained how this is done in geometry without the use of numbers at all. Not for one instance backing up the idiot Zelos Malum..
> > > On just this one point, now, please, and thank you Eram for injecting some decent analysis. I will call you if I see a bluff or a blunder, but what it looks like is happening is that we are now engaged in three systems: your firstly geometrical completely lacking in what I will call a 'metric' though by the usage of this term I do not mean any hierarchical mumbo jumbo but something very primitive, as when one makes a couple of scratches on a piece of wood and declares them to be the working unit of the day.
> > Not true that there is no metric in geometry. The metric can be almost any magnitude you please. However, this is where the abstract unit through generalisation finds its place in algebra.
> This is where a few nicks on a stick establish a unit length that can be transferred. More carefully done they are scribed with a marking knife so that as you drag the marking knife's edge across the marking stick the edge will drop into the marking cut, thus establishing near perfect transfer to an adjacent piece of work material.
> The same is true in metal with an awl and use of a square and flats on the pieces will help raise the precision.
> > > It may occur to some that they can count this unit and that its multiples do take number readily, and that the remainder may be marked, even upon the same stick that marks the first unit, and so a secondary unit can alight from such work, though it is the result of the selection of the first unit it is guaranteed as a remainder to fit beneath the first and so any who doubt the method of organization may recover these details not so much informationally but rather materially and physically secure... for the day at least. And if the day is not long enough to finish the project then that stick will deserve some special notation or placement at the bench; likely right with the materials being worked. Box them away and the project can be put on hold. Another project can ensue that might even take a tertiary unital form.
> > Well, this is where the standard physical "units and measures" make their debut.
> Yes, but as we see Euclidean geometry needs no standard ruler. Scalable results seem always admissible
> > > Will the procedure ever finish? Will the project get done? Modern academia imposes deadlines and forms fake projects so that these issues go away.
> > Wishful thinking because mainstream decrees and fundamentalism only sanctions contrary opinions that expose its ignorance. The issues never go away. Any healthy-minded average student who gets frustrated with his idiot teachers is proof that the issues are still here. The only exceptions are the sycophants like Malum, etc.
> > > We now at the tenth generations let's say of such nonworks, and roughly four generations back the 'whole project' culture diminished with grandpa on the farm and all his grandchildren gone to the city to work in the mill. My great grandfather was a mill worker. I remember being a young boy and him teaching my brother and I how to use a file but the lesson clearly came onto dim heads. As to how much he knew I will never know and am only just getting handy now. Probably I shouldn't even call it that.
> > The non-works and lack of progress in mainstream math academia goes back more than 200 years.
> > >
> > > So Z exposes a third class system where instantiation is completely avoided under the guise of generality, but as the graphical solution does carry a sum mechanism, and the numerical solution does clearly and universally carry a sum mechanism, it is clear that within abstract algebra and other high fluting trades that seem to declare a sum mechanism that there is no actual core. These are stubs. They lead to non-instantiables. These non-instantiables are regarded by those who purvey them as superior to our forms, yet we have Z falsified so many ways, and this is as it is within buggy code under accumulation; make no mistake about it the overlap of these systems is substantial.
> > Agreed! I am certain though that Zelos will not understand most of the above paragraph - it's simply way over his head.
> I think this third method that lacks instantiation is really worth holding to.
> >
> > Instantiation is the first and foremost step in my 4-step guideline for well formedness. If you can't instantiate a concept either intangibly or tangibly, then you have nothing. The stubs you refer to are like "virtual functions" that have no purpose whatsoever except to point nowhere. Chuckle. In essence, you can build whatever rot you like on these by letting your imagination run wild.
> > >
> > > As to who will be the superior compiler: the computer or the human?
> > Well, now that we are talking about my past means of making a living, I have only this left to say:
> >
> > To become a master at any computer programming language means mastering the workings of its compiler.
> >
> > Any old fool knows and understands what is an algorithm which is an algorithm no matter what the language - compiled or interpreted.
> > > We know already who will work the numbers fastest, yes?
> > Speed is not an indication of intelligence. Never has been.
> > > Holdouts like Z whose teeth are falling out at every post are quaint instances of a game of head fuckery that went on for many generations
> > and is still very much in play....
> > > when the very numbers and physical magnitudes and their possibilities were (and still are actually) open puzzles. This is what happens when you hand Z a hammer and a sharp chisel: he goes straight to his head.
> > All Zelos knows is what he has faithfully memorised. As long as he is a good boy and obeys his priests, his career of lifetime deception and worthlessness will be secure. There are those who go to university and never leave because the reality of the outside world is too harsh for them. Chuckle. It's far easier to bullshit young minds and if you are a pedophile (as many of them are!), then you have an extra perk - juicy young boys and girls. Chuckle.
> > >
> > > It is a strange but true fact that my great grandfather did loose his marbles eventually in his nineties and that my grandmother cared for him through it all. At one point Grampy was so senile that he tried to cut off his penis with a hacksaw.
> > Oooh. That's harsh.
> > > The saddest part of the story really is to put this in perspective: nationally we have a formalized strategy known as MAD which as far as I know has never been recanted.
> > MAD as in mutually assured destruction? This and worse in my opinion.....
> > > Supposing Biden were to recant on MAD? What exactly would the follow-up look like? I don't think Grampy was successful in that last act I mentioned, but maybe there are rather more of his offspring around than I know of.. Can you imagine what could go on at those mills with all those young women pent up in the work environment just happy to get some time in the yarn closet?
> > I can imagine but I have better things to think about. Ha, ha.
> > > Not quite sure how that analysis works out with MAD, but the automation industry must be very well and advanced within the defense industry. It is not so much of a rat's race any more. When will automation become a race? Is there any doubt that it has already won? For Z the computer will not be declared intelligent until it mimics him.
> > Oh, it's pretty easy to mimic Zelos. Proof: Almost 8 billion unbelievably stupid humans?
> > > This is a blunder. No. Upon covering a sufficient number of variations and developing a selective filtration system the computer's thought process will be sufficient. The question I think may be whether such a perfect orb should have solutions like theoretical physics? Without any inputs?
> > Theoretical physics ended when Einstein became famous. So I only know about theatrical physicists today. The Hawkings, etc.
> > > This would be marvelous and in terms of metric ideals you could not hope for anything better. As for recovering all of modern mathematics: no. The proper orb is going to complain. When it tells them what they do not want to hear they will shut their ears; shut down the project; and start over again.
> > >
> > > Did the soviets adopt MAD or did they have their own philosophy about the situation? As an American I have no idea. No doubt access and discussion of these details is actively discouraged. FAFA...
> > So I really don't know what you mean by MAD. You shouldn't assume that others know what you mean.
> > > >
> > > > You can COMPUTE π x √2 EXACTLY in geometry IF you are able to construct either of these incommensurable magnitudes. However, you CANNOT, because there is NO ideal unit in geometry. Do you get this?
> > > > > This very detail you are unable to admit.
> > Wrong. I have known and taught it all along!
> > > The instantiation of concrete values is something your links do not allow.
> > No, that is decidedly FALSE. You are not understanding if this is your belief.
> Well, I should not say that they do not allow it, but rather that they do not instantiate anything.
> > > I stand by my claims here, and if you can show me where in any of those documents they tell me how to perform this addition, or any addition of concrete values as numbers, then I will concede the point.
> > All my links show this and there is also mention of it in my free eBook..
> > > > While "concrete values" are nice, neither π nor √2 are concrete ever! I have shown you how to subtract, add, divide and multiply EXACTLY in geometry.
> >
> > > > > If you know your links so well why don't you link to a specific page?
> > So I don't talk about ruler or compass because none of these are required in mathematics. YES, you use them in physical construction, but that is not the same as the theory behind the perfect concepts from which the physical construction is realised.
> >
> > This is something you have failed (like Mueckenheim and many, many others) to understand.
> Actually this notion of 'perfect concept' may be the corresponding model in our mind. This is a notion of perfect precision, and in order to achieve perfect precision we might as well admit that there is a range of precision. Sloppy work can sometimes be good enough, and when it is; all the better to be fast and efficient. The notion that close enough is good enough may be far more realistic than perfection ever will be. Perfection will never be done.
> > > You see, all the while in the back of these high thinking mathematicians' heads they have these computational methods that they mastered that they are relying upon but do not care to admit it into the subject. It would wreck the seeming purity of their works.
> > Purity in their works?! LMAO. Every one of their thoughts is piss and shit. Chuckle.
> > > But where then does this leave those works?
> > In an incinerator.
> > > Why is it that we have to wait until an abstract algebra curriculum to take the simple operators sum and product more seriously and yet still lack the specifications of how to actually perform addition or multiplication?
> > Right. You don't have to wait. In fact, you don't need to know anything about abstract algebra as conceived by the baboons of mainstream academia.
> > > Indeed, it is quite possible that we cannot prove that for every real a and every real b there exists
> > > > > a + b
> > > > > since we cannot perform all these computations.
> > > > We can prove that EVERY MAGNITUDE a + b has a result c in GEOMETRY. What we CANNOT do is the same thing in ALGEBRA which uses NOTHING ELSE but the ABSTRACT UNIT.
> > > >
> > > > Study what I tell you. I KNOW BETTER THAN ANYONE ELSE ON THE PLANET.. You will gain nothing by arguing with Malum.
> > > > > Possibly here lays another avenue toward the binary operator definition but the failings of it are already exposed. Then too as we see that the sum is in fact n-ary we ought to have proven that
> > > > > a + b + c + d + e + f
> > > > > lays in the reals as well. It is factually true that computers will suffer an overflow or a loss of precision when handling such values except in the case of variable precision software. Still in hardware we do have an issue here. At least we can admit that. The human ought to have admitted that their own computational powers are severely limited. But no; instead we see the high flying mathematician escapes the lowly computable figure and moves to much higher ground. At this generation this move is engrained so that it takes the likes of me to shove your nose in it. I know it will be met with the usual dull thud here, and I'll barely even feel like striking the ball again.
> > > > >
> > > > > Indeed closure is the principle that I am discussing above, and should it be true that values as operators are carried around unevaluated then we ought to admit that the form of such systems is more like
> > > > > R + R
> > > > > rather than
> > > > > R x R
> > > > > where an expression a+b arises. It is to say that since a is in R and b is in R and the result is not guaranteed to be in R, which is why we carry around the said sum, then we can only guarantee that the result is preserved as the expression is preserved, and it is not a two dimensional entity. It is two one dimensional entities. They do not form a plane, sir. On this point the ball does in fact land flat at the back board known as Zelos. This must mean that I am onto something.
> > > > >
> > > > > Now Zelos comes back with a chuckle and says that this cannot possibly be correct for standard mathematicas yadda yadda yadda...
> > > > > Obviously we are attempting to go beyond standard mathematics here sir.
> > > > > Your own measly methods only show you to be the fraud that you are and the system as a fraud too.
> > > > >
> > > > > Your own compilation of these facts is obviously not forthcoming here. We cannot evaluate an expression whose values are not filled in. This does not prevent analysis from occurring, but as to whether those constructions can be called elemental even: this is problematic. You cannot possibly wish to get in a fight with a computer on computation. Surely it is known that all humans will lose that fight. All that we can do is build a better computer. That or put a wrench in its gears, and this all too often is the human pursuit.
> > Look, where Zelos is concerned, I am merely having fun kicking his arse.. I have no doubt in my mind that he is beyond hope and that no amount of reason or clarity can heal a brainwashed individual. Zelos cannot be reasoned with.
> Agreed. Integrity is badly lacking.
> Sadly he is the only one here piping up on some of my threads.

>Again, it matters very much because the ideas in your bogus nomenclature are irrelevant. I have directed my comments to the essence of your claims which you've totally ignored because you are a known idiot and a crank.

You are trying to go for a straw man, cause again bringing up the greeks is ireelevant here as they do not use the Elements/Euclides as the base.

>The idea of MAGNITUDE is USED. Study that PDF, you fucking imbecile!!! Why else would it be called Eudoxus... Tsk, tsk.

It would be used for many reasons, honour the person, it has a superficial resemblance to some things eudoxus dealt with, etc etc etc.

>Eyes rolling. NO ONE CLAIMED SO. Strawman arguments are your speciality.

Then stop bringing up Eudoxus the person.

>The concept of MAGNITUDE is VERY relevant in the Eudoxus "reals".

not really, it is not used in any definition. If you read the document it uses it as an intuitive starting point for why it would work but afterward leaves it behind for formal definitions that do not use those.

>Address what I said, you idiot!!!!! I don't give a fuck about the name. I am talking about your PDF. READ IT, YOU FUCKING MORON.

Did you read beyond the part of intuitive justification?

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.

Where in this is anything you want?

>Grrrr. No one said it does.

Don't bring them up then.

>Again, strawman argument. No one said so.

Don't bring him up then.

>FAIL. The PDF is about the use of the MAGNITUDE concept in a FAILED attempt to produce "real number".

No it doesn't, it uses it as an intuitive starting point to derive the concept but when you look at all the definitions, not at a single point do they use "magnitude"

For example:
Definition 2The abelian groupEofEudoxus realsis the quotient groupS/B.

No magnitude in sight

>The ideas are taken directly from the ELEMENTS and the key feature that is used to arrive at De Morgan’s Colonnade and Fence, is the concept of MAGNITUDE.

That is the intuitive concept, not the formal construction.

Go past that and look at THE DEFINITIONS! what do THEY say?
None uses "magnitude" so tough shit.

>is because I can do the digital computation.

You don't do computation in mathematics for fuck sake.

>Indeed closure is the principle that I am discussing above, and should it be true that values as operators are carried around unevaluated

There is nothing "unevaluated" in mathematics for fuck sake.

>Obviously we are attempting to go beyond standard mathematics here sir.

No, you are just not understanding mathematics. You are a pseudointellectual, you are trying to pretend to be smart but you have no intelligence worth speaking off.

On Saturday, 8 May 2021 at 02:56:28 UTC-4, zelos...@gmail.com wrote:

<drivel galore>

> >The ideas are taken directly from the ELEMENTS and the key feature that is used to arrive at De Morgan’s Colonnade and Fence, is the concept of MAGNITUDE.
>
> That is the intuitive concept, not the formal construction.

It has everything to do with the invalid construction. Just because some group theory is interjected makes it valid? LMAO.
> Go past that and look at THE DEFINITIONS! what do THEY say?

The word <<magnitude>> itself does not have to be used. It is directly IMPLIED. And again, that is why the drivel was named after Eudoxus.

> None uses "magnitude" so tough shit.

Childish as usual.

> <drivel galore>

Translation: Things Gabriel cannot argue against.

>It has everything to do with the invalid construction. Just because some group theory is interjected makes it valid? LMAO.

The fact you cannot find any internal contradiction is what makes them valid.

>The word <<magnitude>> itself does not have to be used. It is directly IMPLIED. And again, that is why the drivel was named after Eudoxus.

That is the intuitive idea behind it, but not the formal construction. Look at the formal definition and state where they use it. They use almost homomorphisms for the construction, no magnitudes.

On Monday, 10 May 2021 at 00:40:19 UTC-4, zelos...@gmail.com wrote:
> > <drivel galore>
>
> Translation: Things Gabriel cannot argue against.

I know that you are bored beyond belief and have lots of time to argue. I do not - especially when I know that reason is futile where you are concerned. You are nothing but a stubborn moron.

> >It has everything to do with the invalid construction. Just because some group theory is interjected makes it valid? LMAO.
> The fact you cannot find any internal contradiction is what makes them valid.

I have found many contradictions (internal is not even relevant), but the contradictions are a consequence of the accident of such syhpilitic thoughts, the truth is that set theory fails right from the beginning.

> >The word <<magnitude>> itself does not have to be used. It is directly IMPLIED. And again, that is why the drivel was named after Eudoxus.

> That is the intuitive idea behind it, but not the formal construction.

Every time you use that word, you prove my point that you're an idiot. My intuition tells me you are a moron and my intuition is better than anyone else's I know. LMAO.

> Look at the formal definition and state where they use it. They use almost homomorphisms for the construction, no magnitudes.

See people, clueless moron Malum thinks that homomorphisms is a good enough word (which Malum does not even understand!) to support his delusions about the very theory he has never understood, but has memorised quite well. Chuckle.

Malum, you cannot intimidate me with words like "homomorphism", because unlike you I am Greek and have studied the shit which you advocate but have never understood. LMAO. In other words, what I am telling you idiot, is that whatever you have thought, I have already thought about it many decades ago and am light years ahead of you.

Sheeeesh, it must suck to be you!! Chuckle.

>I know that you are bored beyond belief and have lots of time to argue. I do not - especially when I know that reason is futile where you are concerned. You are nothing but a stubborn moron.

Translation: Excuse making

>I have found many contradictions (internal is not even relevant), but the contradictions are a consequence of the accident of such syhpilitic thoughts, the truth is that set theory fails right from the beginning.

Internal is the relevant one here because a contradiction with your preferred stupid system just means they are incompatible, not that the construction itself is invalid.

>Every time you use that word, you prove my point that you're an idiot. My intuition tells me you are a moron and my intuition is better than anyone else's I know. LMAO

Like Trump, you're better than anyone in everything, huh?

Sounds like Narcissistic personality disorder to me.

>See people, clueless moron Malum thinks that homomorphisms is a good enough word (which Malum does not even understand!) to support his delusions about the very theory he has never understood, but has memorised quite well. Chuckle.

And here we see Gabriel not responding because he doesn't understand how it works in mathematics.

>Malum, you cannot intimidate me with words like "homomorphism"'

why would that be intimidating? Is your ego that fragile?

>because unlike you I am Greek

Your nationality is of no relevance

>and have studied the shit which you advocate but have never understood.

Yet you constantly fail to address things properly, telling me you are lying here.

>In other words, what I am telling you idiot, is that whatever you have thought, I have already thought about it many decades ago and am light years ahead of you.

Then address things properly rather than making all these stupid arguments and pathetic attempts to feel big.

>Sheeeesh, it must suck to be you!! Chuckle.

Why? It is fun when narcissists like you are being stupid :)

Answer me directly, where in any of these is there any "magnitude"?

Definition 1 A function f from Z to Z is said to be an almost homomorphism iff. the function df from Z×Z to Z defined by df(p,q) = f(p+q)−f(p)−f(q) has bounded range, i.e., for some integer C, |df (p, q)|. < C for all p, q ∈ Z.

The function df measures the extent to which f fails to be a genuine homo- morphism: f is a genuine homomorphism iff. df is identically 0. Note that the requirement on an almost homomorphism is not that df(p,q) be non-zero for only finitely many p and q, but that values taken on by df (p, q) be bounded as
2
p and q range over Z. Typically, if df (p, q) is non-zero for some p and q, there will be infinitely many pairs (r, s) for which df (r, s) = df (p, q).
The set Z → Z of all functions from Z to Z becomes an abelian group if we add and invert functions pointwise: (f + g)(p) = f (p) + g(p), (−f )(p) = −f (p). It is easily checked that if f and g are almost homomorphisms then so are f + g and −f. Writing S for the set of all almost homomorphisms from Z to Z, this shows that S is a subgroup of Z → Z. Let us write B for the set of all functions from Z to Z whose range is bounded. B is a subgroup of S.

Definition 2 The abelian group E of Eudoxus reals is the quotient group S/B..

On Tuesday, 11 May 2021 at 00:39:42 UTC-4, incorrigible crank zelos...@gmail.com wrote:

> Yet you constantly fail to address things properly, telling me you are lying here.

You are truly an embarrassment to yourself. Do you realise that anyone looking back on the thread can see that it is I and I alone who have been addressing the issues? Are you really that stupid?

AGAIN, for the THIRD time you are asked to show how you would define multiplication using set theory and then demonstrate the product 2.1 by 2.2.

You pathetic, lying, piece of shit! LMAO.

You make Donald Trump look genuine with your level of fakeness, Chuckle.

>You are truly an embarrassment to yourself. Do you realise that anyone looking back on the thread can see that it is I and I alone who have been addressing the issues? Are you really that stupid?

They will see you won't. I asked for you to give an internal contradiction, you have FAILED at it.

>AGAIN, for the THIRD time you are asked to show how you would define multiplication using set theory and then demonstrate the product 2.1 by 2.2

For rational numbers?
a/b=[(a,b)]
[(a,b)][(c,d)]=[(ac,bd)]
2.1=21/10=[(21,10)]
2.2=22/10=[(22,10)]
2.1*2.2=[(21,10)][(22,10)]=[(462,100)]=4.62

For real numbers it is slightly different but essentially boils down to the same.

>ou pathetic, lying, piece of shit! LMAO.

Nope, that is you. Again, show us a genuine internal contradiction. DO not cite what you think shit should be, cite an internal contradiction where a predicate is shown to be both true and false at the same time.

On Tuesday, 11 May 2021 at 08:41:57 UTC-4, zelos...@gmail.com wrote:
> >You are truly an embarrassment to yourself. Do you realise that anyone looking back on the thread can see that it is I and I alone who have been addressing the issues? Are you really that stupid?
> They will see you won't. I asked for you to give an internal contradiction, you have FAILED at it.

Poor MALUM. Just repeating lies won't make them true. Tsk, tsk.

> >AGAIN, for the THIRD time you are asked to show how you would define multiplication using set theory and then demonstrate the product 2.1 by 2.2

> For rational numbers?
> a/b=[(a,b)]
> [(a,b)][(c,d)]=[(ac,bd)]
> 2.1=21/10=[(21,10)]
> 2.2=22/10=[(22,10)]
> 2.1*2.2=[(21,10)][(22,10)]=[(462,100)]=4.62

I wish I could say "Nice try!". LMAO.

No Malum. You'd have to be a lot more convincing that that.

I might be inclined to let you go with a/b=[(a,b)] but that's about all.

In step 2, ie, [(a,b)][(c,d)]=[(ac,bd)] , you've already assumed that ac is the product of a x c.

Compare your drivel with:

So what you are looking at is the product of 21/10 and 11/5.

In geometry, multiplication is defined as the *reciprocal measure* of division.

Formal definition in my world famous article called How we got numbers:

A quotient (or division) is that positive rational number, that is measured in terms of two numbers. In its most primitive form, a quotient is simply the ratio of two magnitudes which both share a common measure (divisor).

So we actually determine 21/10 x 11/5 either as:

i. 21/10 -:- 5/11
ii. 11/5 -:- 10/21

I'll show you (i) and leave (ii) as an exercise.

Using similar triangles from which ALL the arithmetic operations are defined we proceed as follows:

(21+21+21+21+21+21+21+21+21+21+21) / (10+10+10+10+10+10+10+10+10+10+10)
/ (5 + 5 + 5 +5 + 5 + 5 + 5 + 5 + 5 +5 ) / (11+11+11+11+11+11+11+11+11+11)
= (231/110) / (50/110)
= 231/50

So, we find the product using the proportional sides of similar triangles. Now since 231 > 50, we can apply the obelus division algorithm, ie
231 -:- 50 = 4.62

231 - 50 = 181
181 - 50 = 131
131 - 50 = 81
81 - 50 = 31

We have reached the stopping condition, ie 31 (remainder) < 50 (divisor). Since we subtracted four times, the partial quotient is 4 but if we add the remainder, then we get the full quotient 4 + 31/50 = 4.62

Again, my article explains all these details:

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

You see Malum, what you scribbled is like a tiny Pigeon's wet fart, not even smelly at that! LMAO.

On the other hand what I have shown you is that multiplication was defined LONG before number was realised and that its properties were transferred to algebra (a weaker form of geometry) via the ABSTRACT UNIT.