/sci/ - Science & Math

>wall-of-text schizo
errytime

>>12027632
Did you misspell "every" on purpose?

>>12027907
What sort of dominance or preeminence does your discovery make requirements of others be the unwilling subjects of your new teachings and discoveries?

>>12027596
Tooker, Tooker, Tooker
You can't write stuff like that. You can't define [math]\infty[/math] as [math]\lim\limits_{x \rightarrow 0^+} \frac{1}{x}[/math], because that limit is not defined. Your refusal to understand that [math]\lim\limits_{x \rightarrow 0^+} \frac{1}{x} = \infty[/math] is just a shorthand to say that that function is divergent in 0, and not the definition of an object is the root of all your problems.
And sure you can always just define [math]\overline{\mathbb{R}}=\mathbb{R}\cup \left \{ -\infty, \infty \right \}[/math] with [math]\infty[/math] having the properties you want, but then THAT SET IS NOT A FIELD, so you can't go using comparators and operators willy-nilly, nor calling members of that set "numbers".
In the same vein, you can't call infinity an "endpoint", unless you define what endpoints are, and it's different from the conventional understanding of a point.
As for the whole construction of your geometric middle, it's a word salad I can't make sense of. You speak of a circle being at infinity without ever defining what it means in a geometrical sense.
cont.

>>12027978
Pretty sure his primary claim is that he providing the definition of said limit.

Ultimately I'm just watching translators argue over grammar so pedantic that it would seem that the mathematics of agreeability or agreeance is obviously not a field covered by Tooker.

>>12027978
cont.
Pic related is a contradiction. [math][0,\infty][\math] is not bounded, it is not a line segment but a ray.
cont.

Tooker MIGHT be saying that the presentation layer of information is always false, so let's all fuck the communal mongoose carcass every weekend.

>>12027982
>Pretty sure his primary claim is that he providing the definition of said limit.
He later provides the definition of [math]\widehat{\infty}[\math], which relies on this inconsistent definition of [math]\infty[\math]

>>12027994
Is that before or after he threatens to kill everyone by some divine will or power? So hard to keep up with the scriptures don't-cha-know.

>>12027985
cont.
This is the word salad that makes no sense. First off if we're talking pure non-analytic geometry, what is this talk of conformal transformation? That only makes sense in analytic geometry. Plus, a chart like the one given as example is only defined on the open segment AB, it's not defined in B.
Plus, charting [math]x=tan(x')[/math] changes circles into something that is not a circle, so for sure it would change the geometrical properties.

>>12028007
Stop! Please! This mathematically descriptive strip-tease is too perfect! Aaaaah! My abelians!

>>12027596
have you managed to define real numbers without using real numbers yet ?

>>12027978
>THAT SET IS NOT A FIELD
Yes, that's correct. It is not a field and number fields did not exist in 1859 when RH was published.

>>12027982
not only that, but this is the commonly accepted definition of that symbol

>>12027942
If the Lord is with me, then I will always win making war on the unwilling.

>>12028021
yes. have you read any of the papers i did it in?

>>12028024
no

>>12028022
>Yes, that's correct
Then you can't use any of the theorems and calculus rules that are commonly accepted on the reals without proving them first. History has nothing to do with the validity of a proof.

>>12028007
>it's not defined in B
The definition at B follows from Definition 2.2.2.

>charting x=tan(x) changes circles into something that is not a circle
no it doesn't

>>12028028
calculus and "theorems" were around for a long times before fields got invented. Furthermore, "theorems" already proofs.

>>12028022
If your Lord agrees with you, then you can rape unimpeded and uninterrupted?

>>12028041
The Lord agreeing with me likely has some correlation with my disinterest in raping.

>>12028047
Then why ignore the willing to wage war on the unwilling? Surely the willing has a lower barrier of entry or ignition point.

>>12028047
how is addition and multiplication of real numbers defined ?

>>12028054
My whim.

>>12028060
Then what does what your whim once was then become so we know when not to take you so seriously.

>>12028055
If you're interested, why not read the paper?

>>12028065
I don't know what the future holds.

>>12028066
Because the paper argues definitions, it doesn't provide an analysis, solution, or output space. If there is no efficiency argument OR priority improvement presentation then what are YOU interrupting?

>>12028039
>no it doesn't
Tooker, baby, those are not circles.

>>12028073
So you did read a paper then? I'm pretty sure I tend toward the
>definitions
>axioms
>theorems
>applications
format in this paper:
Fractional Distance: The Topology of the Real Number Line with Applications to the Riemann Hypothesis
https://vixra.org/abs/1906.0237

>>12028084
How much product with your paper yield if interpreted to the full extent that your imagination gifts it sufficient confidence to do so?

>>12028076
due to your faggotry, i will not post the obvious response

>>12028084
Like, would you describe comprehending your paper as the equivalent to becoming a trans-dimensional dolphin wizard rainbow unicorn mathematician and solve all the remaining symmetries and collect all that sweet millenium prize money?

>>12028087
I don't know. I wrote other papers with much more significant results in them.

>>12028093
I would not.

>>12028066
so what is "x+y" ?

>>12028094
Isn't it your duty to have rank ordered your papers that would prioritize maximum benefit to those that absorb it, all under the wise and succulent tutelage of you, Tooker-sama?

>>12028096
It's the pairwise sum of two Cauchy sequences of rationals. Why not just read the paper?

>>12028106
When number and when symbol, teh game!

This is one of the top three most important ones.

This is also one of the top three most important ones.

is this a number line ?

The other one of the top three most important ones.

>>12028112
>>12028113
>>12028115
Why are you the presenter of this past memory of self? It is as if you have pooped in your hands and shown me with pride the results.

>>12028114
If a parallel line construct by the parallel transport of a line, then that shape wouldn't satisfy the axiom that two parallel lines can never intersect.

>>12028116
You sound like you don't appreciate what I'm proud of.

>>12028121
Your interpretation is not what I asked for, I asked a question.

>>12028125
Indeed. It appears to be a rhetorical question.

>>12028126
So you are saying that your name is Pride?

>>12028117
but you wrote that "line" is "1D Hausdorff space extending infinitely far in both directions". is the picture not 1D Hausdorff space extending infinitely far in both directions?

>>12028131
so you mean its imagination. cool.

>>12028131
The thing you drew extends in more than two directions.

>>12028089
There isn't an obious response Tooker. You read all those math books without ever making the effort of learning basic mathematical rigor.

>>12028143
The obvious answer is that the things you drew aren't circles but things I drew are circles.

>>12028140
really ? elaborate.

>>12028143
For some reason I can really only imagine Tooker reading a math book with a raging erection, so turgid and strong that it looks like it is hurting the person it is attached to kind of erection.

>>12028145
It extends in the left and right directions and the up and down directions as well.

>>12028145
Maybe Tooker just has a fetish for being asked questions and having an audience willing to hear his explanations and expansions on the ideas present?

>>12028144
cool, now apply a x -> tan(x) transformation on that.

Maybe I enjoy discussing scholarly things.

>>12028149
Probably why he enjoys yelling at supermarket employees.

>>12028156
Oh, you big ol' sapiosexual you.

>>12028153
done. still two circles centered on A and B.

>>12028148
but it doesn't extend "infinitely far" in up and down right ?

>>12028159
Isn't that ultimately why we pay those people? Virtually every public space or place is essentially therapy for any given social subsection. Some people feed the pigeons, some people do street performance, etc.

People that get paid suffer the worst psychological abuse because they somehow have to suppress their own maturity and intelligence to accommodate a society where they being screamed at somehow makes fair sense, given the importance their existence should explain with not much predicate required.

>>12028164
So at which point in your head did it make sense to define "transformations" as operations that don't change anything?

>>12028176
BECAUSE INPUT AND OUTPUT ARE AS ONE, AS INSCRIBED ON THE ANCIENT SCRIPTURES OF TOOKER WHEN HE DESCRIBED ALL OF INFINITE ARGUMENTATION SPACE WITH HIS ONE FINAL DIVINE DECREE: "FEAR ME!"

>>12028166
yes but "both directions" limits the number of extending directions to two.

>>12028176
the operation changed the chart which is not featured in the figure.

>>12028180
This is true. That's the kernel of the wisdom which survives to infinity.

>>12028188
cool, so let's try to define what "extends into a direction" actually means

>>12028194
are you an ai programmed to sub-divide every point of potential inspection in Tooker's language, and he being the autistic monkey that he is can't help but engage?

:O ARE YOU TOOKER'S REWARD_FUNCTION A.I. COMPLEMENT!

>>12028194
pic

>>12028200
>thinking my life is so great that i have something better to do

>>12028188
You haven't defined a chart. Chart is a notion of analytic geometry. Plus it's not even defined on the whole segment. Your word salad doesn't make sense.

>>12028203
>thinking
why would buddha have need of this distraction or irritation to his bliss?

>>12028205
I didn't define "extend" or "direction" either. All of these words are already defined.

>>12028203
that's not a mathematical definition

based schizo owning math nerds

>>12028212
this definition of chart uses real numbers. you're using chart to define real numbers. nice try brainlet.

>>12028213
English is the official language of mathematics.

>>12028212
The objects you have drawn are not circles in the transformed chart.
Also, it's still something that only makes sense in analytic geometry. You can't claim you're doing something in pure geometry and invoke some chart nonsense.

>>12028216
This doesn't depend on real numbers:
>A coordinate chart is a way of expressing the points of a small neighborhood, usually on a manifold M, as coordinates in Euclidean space.

>>12028226
>The objects you have drawn are not circles in the transformed chart.
A circle is a circle by definition.

>>12028229
Yes and those are not circles in an analytical sense. Which is the only sense that matters as soon as you start invoking charts and conformal transformations.

>>12028234
What is an analytical sense?

>>12028237
Knowing when your butt is for sure getting eaten out by someone that really likes you would be an analytical moment or sense.

>>12028237
Jesus Christ, Tooker
https://en.wikipedia.org/wiki/Analytic_geometry

>>12028240
Yo have given an example of an analytical sense but you have not stated what an analytical sense is. Will you answer me?

>>12027596
Have you tried killing yourself for the betterment of humanity in general?

>>12028243
I see.

>>12028234
>Which is the only sense that matters as soon as you start invoking charts and conformal transformations.
This wrong.

>>12028246
no

>>12028245
Can I answer myself through this many degrees of abstraction if I really did prove a lot of mathematics as wrong and I the superior source teaching itself about itself as it describes and explores itself.

>>12028246
If his existence is that much a drain on the rest of us then when does it become an actual priority for us to kill Tooker to save the rest of us? Or are we allowed to be lazy forever and not care?

>>12028258
When he goes overboard and starts shitposting regularly to the point that /sci/ is filled with shit and it's no longer differentiable from /int/ or other boards. He currently does, albeit sporadically.

Is the total convergence of /sci/ and /x/ evidence of a declining standard of education?

>>12028249
>This wrong.
Cool thing buddy-oh, good look defining what the fuck is a conformal transformation without invoking coordinates.

>>12028277
I invoked the coordinates x and x'.

>>12028227
>manifold
>Euclidean space
>coordinates
all defined with real numbers

>>12028273
One could indeed argue that. Although I think that this argument is a bit narrow. One could also argue that the infiltration of newfags has reduced board quality and since oldfags are no longer there as 'moral' knights, newfags get to shit post whatever they wish to and also receive backup from other schizos.

>>12028285
Euclid definitely did not use real numbers as an ingredient for his construction of a Euclidean space. He didn't refer to them for his coordinates in that space either. He did all of it with pictures.

This is me paraphrasing you:
>Lies are true and the truth is a lie.

>>12028291
>Euclid definitely did not use real numbers as an ingredient for his construction of a Euclidean space. He didn't refer to them for his coordinates in that space either. He did all of it with pictures.
how is this relevant ?

>>12028291
>>Euclidean n-space, sometimes called Cartesian space or simply n-space, is the space of all n-tuples of real numbers, (x_1, x_2, ..., x_n). Such n-tuples are sometimes called points, although other nomenclature may be used (see below). The totality of n-space is commonly denoted R^n, although older literature uses the symbol E^n (or actually, its non-doublestruck variant E^n; O'Neill 1966, p. 3).
https://mathworld.wolfram.com/EuclideanSpace.html

>>12028294
It refutes pic related.

>>12028299
You have posted a definition which refers to R. Euclid's definition, which is the definition of record, and is an equivalent definition not mentioning R, appears here:
http://farside.ph.utexas.edu/Books/Euclid/Elements.pdf

>commonly denoted
Do you see the hole in the point you tried to make?

Tooker thinks, by trying to come up with shit, he's proving centuries of genius, precocious mathematicians wrong.
He seems to be an attention seeking whore.

>>12028305
>>Euclidean space was introduced by ancient Greeks as an abstraction of our physical space. Their great innovation, appearing in Euclid's Elements was to build and prove all geometry by starting from a few very basic properties, which are abstracted from the physical world, and cannot be mathematically proved because of the lack of more basic tools. These properties are called postulates, or axioms in modern language. This way of defining Euclidean space is still in use under the name of synthetic geometry.
>>In 1637, René Descartes introduced Cartesian coordinates and showed that this allows reducing geometric problems to algebraic computations with numbers. This reduction of geometry to algebra was a major change of point of view, as, until then, the real numbers—that is, rational numbers and non-rational numbers together–were defined in terms of geometry, as lengths and distance.

>>12028302
https://mathworld.wolfram.com/EuclideanSpace.html

>>12027596
We've been over this enlessly, Tooker. Inf-hat is provably (to be precise, for any well-defined definition you have thusfar provided) not an element of the real numbers, so you have not solved RH.

As for the proposition of extending the reals with inf-hat, note that the fact that the radius and circumference of the circle are related by a single constant does not depend on the introduction of the quantity pi. The introduction of pi is motivated by a fact that has been proven without using pi.

What fact have you proven that does not use inf-hat and motivates its introduction?

Euclid's definition of R was the one that existed for centuries, not the ones I oppose. Euclid's definition existed for so many centuries that it existed for millennia. Once mathematicians recently became more fixated on algebra than geometry, they said, "How can we come up with an algebraic definition of real numbers which we can use as a basis for algebraic rigor?" The best they could come up with had some conflicts with Euclid's geometric definition. Then those definitions were in use for about one single century before I showed how to create an algebraic definition which synthesizes perfectly with the pre-existing definition. What I came up with is better than what they came up with, and I was lucky to have a lot more experimental physics data than they had which guided my toward the truth about numbers. So, I have shown how to extend the old geometric definition to the algebraic sector without rejecting Euclid's principles of geometry, which is an undesirable feature of Cauchy equivalence classes, Dedekind cuts, and number fields, and then I also argue that it is better to extend Euclid than to scrap and replace him. It is the people who want to scrap and replace Euclid who are the ones that do what you say I do.
>come up with shit, he's proving centuries of genius, precocious mathematicians wrong.

>>12028330
>The best they could come up with had some conflicts with Euclid's geometric definition.
name one conflict
>What I came up with
you didn't come up with anything

>>12028311
I see you have posted one definition of Euclidean space relying on R. I have posted Euclid's own definition which does not depend on R, and it is Euclid's definition which I rely upon. Furthermore, my opinion is that no one knows what a Euclidean space is better than Euclid.

>>12028314
>not an element of the real numbers, so you have not solved RH.
I'm not following you. The number seven is not an element of S = {1,2,3,4,5} but x = 7-4 is an element of S. In the same way that 7 is not in S but 7-4 is in S, we have inf-hat not in R but inf-hat minus b is in R. Do you see? Seven isn't in S but a certain expressions containing seven are in S.

>the radius and circumference of the circle are related by a single constant
You haven't proven that.

>What fact have you proven.
In the OP image, I make a nice point about the symmetry of line segments under permutations of their endpoints. IMO, this sufficiently motivates the introduction of inf-hat.

>>12028342
>name one conflict
If every real number is a Cauchy equivalence class of rationals, then not every line segment has a midpoint.

>>12028351
prove it

>>12028351
Not every line has a midpoint? What line wouldn't have start, half-way, end markers? Otherwise it isn't a fucking line.

A line has to be subject to three units of measurement: length, ratio, minimal-height representation

>>12028369
I'm guessing his counter example would be a line segment with one endpoint inf hat - 1 or something

>>12028375
Then technically wouldn't that make the -1 the midpoint of the line being referenced? Also what is the point of this pedantic a level of accuracy or self-referentialism beyond our retarded deep level inspection of it here in this thread and on display to every lurker?

>>12028354
The gist of my argument is in the paper.

You asked me to name a contradiction with the Euclid definition of R. That definition gives numbers as cuts in a line. Every line segment can be cut at is midpoint. If the number at the left endpoint is zero, then the number at the midpoint has half the absolute value of the number at the right endpoint. For an infinitely long line segment, the number at the center has half the absolute value of infinity. Twice the absolute value of any rational number is less than infinity. Therefore, if every real number is a Cauchy equivalence class of rationals, either a number is not a cut in a line (contradicting Euclid) or not every line segment has a midpoint (contradicting geometry.)

In the scheme I came up with, real numbers are ordered pairs of Cauchy equivalence classes of rationals instead of singleton equivalence classes. It avoids these contradictions.

>>12028369
The implication was a problem with the equivalence definition. Every line segment certainly does have a midpoint.

>>12028389
>infinitely long line segment
Euclid implies existence of infinitely long line segments ?

>>12028382
He's desperate for attention.

>>12028403
And we feed him because?

>>12028405
We want to correct his fallacious theories. It seems to be in our blood to correct all the 'wrong'.

>>12028399
yes. they are implied.

>>12028409
I would never take an inspection so far as to need to be the one to label it with any judgment of quality or recommendation. Who am I to decide wrongness of a thing? What authority would ever gift me the right to correct something? How would it enshrine the knowledge that I am using to correct things in others so I can ensure I am doing the right job? Etc.

>>12028411
>What authority would ever gift me the right to correct something?
You, neither does anyone here, including me need an authority to correct some wrongness. What we choose to correct, can be widely different. But we as humans, voraciously correct only things that are near and dear to us.

>>12028415
>voraciously
*vociferously

>>12028410
??? how does this imply infinitely long line segments? what do you think "line segment" is?

>>12028415
Then boundary established and advertised.

>>12028410
According t you, a he implies infinitely long lines.
Then he says
>a line is a length
But length is the measurable property of a line. A line with 0 length 'cannot' be measured because it's length doesn't exist i.e measuring nothingness. In the same way, infinity cannot be measured in the sense of a line.
Length, therefore is a measurable property of a line, hence a line has to have a finite length.

He also says it right after
>extremities of a line are points

>>12028429
>says
*mentions

>>12028389
so what is the contradiction exactly? Euclid says that every line segment has a midpoint, but in the cauchy sequences definition not every line segment has a midpoint? can you give an explicit example of such line segment?

>>12028283
Yes, which makes you wrong when you claim you're just using non-analytic geometry, or Euclid's original framework. Do you understand?

>>12028419
>how does this imply infinitely long line segments?
a line being "a length" implies that any length will suffice

>what do you think "line segment" is?
A line with two end points. See pic in >>12028007
for the response to what I assume will be your next question.

>But length is the measurable property of a line.
Euclid's book was about measurable quantity but the implication of immeasurable quantity is clear to me. For instance, irrational lengths are obviously implied.

>Length, therefore is a measurable property of a line, hence a line has to have a finite length.
This seems to adress what wrote directly, and not that which is implied by his writing.

>>12028449
>the number at the midpoint has half the absolute value of the number at the right endpoint.
> For an infinitely long line segment, the number at the center has half the absolute value of infinity.
>Twice the absolute value of any rational number is less than infinity.
The contradiction is that there is no rational whose absolute value is half of the absolute value infinity.

>>12028455
>Do you understand?
No.

>you claim you're just using non-analytic geometry
I didn't claim that.

>>12028479
there are no infinitely long line segments in the cauchy sequence definitions

>>12028479
>irrational lengths
And you can cut a ruler to this length and hence approximate it. You, in the process of fine tuning your ruler's length, have tried to approximately measure a given irrational length. But infinity and 0 are truly immeasurable.

>>12028489
What is the cauchy sequence definition of a line segment?

>>12028493
A number which can only be approximated is "truly" immeasurable.

Have you all seen my treatise regarding planar geometry, pic related?

>>12028484
see
>>12028291
you claim to not use a coordinate system when talking about geometry
you change your mind halfway through

>>12028497
It's not truly immeasurable. You can still approximately measure and it can still be a good enough measurement.

>>12028496
[math][a,b] = \{ x \in \mathbb{R} \mid a \leq x \leq b\}[/math] for [math]a,b \in \mathbb{R}[/math]

>>12028500
Not interested.

'Member when the Catholics didn't like what Galileo Galilee wrote and then they made him go live at home for the rest of his life where he was segregated from ever speaking to the other educated people? At least they didn't build a fake version of Italy, stock it with Satanists and their slaves, kidnap him, take him there, and sexually torture him for the rest of his life. The anti-science climate sure did get worse since the good old days.

>>12028501
I still don't see how you get to your conclusion "a circle isn't a circle." I never made the claim you say I made and I think you're retarded for not making your point plain after a dozen or more tries. Maybe if you make a post with more than fifteen words in it?

>>12028506
I see. I agree with you then.

>>12028522
so how is the cauchy sequence construction not a model of the Euclid definition ?

>>12028510
There's difference between Galileo and you. I hope this is lucid as fuck to you.

>>12028527
It is "a model of it." Instead of using that model, however, I use the original object that Euclid made 2000 years before Cauchy was born.

>>12028529
Oh, I'm not the same as Galileo? Please tell me more about your keen insights.

>>12028536
What makes you say you're the same as Galileo?

>>12028542
What makes you imply that I said that?

>>12028532
there's no original object. it's defined axiomatically.

>>12028543
There was never a call to mention Galileo in this thread in the first place. His mention was definitely unwarranted.

>>12028545
There is an original object. It's the one Euclid writes about.

>>12028549
>His mention was definitely unwarranted.
Please tell me more about your opinion.

Is it possible that Tooker is just larping?

>>12028553
Why did you mention him here in the first place? How was his life history relevant to this discussion?

>>12028551
do you know anything else about this original object besides the axioms ?

>>12028557
I mentioned him because I felt like it. The thing I wrote was self-evidently relevant.

>>12028567
>I felt like it
Felt like what?

>relevant
In what way? Elucidate.

>>12028563
Am I correctly paraphrasing your question as "Do you know anything about the object of Euclid's analysis besides what was in the book Euclid wrote about it?" I want to make sure I understand you before I answer.

>>12028572
I felt like doing the thing you asked about. It was relevant in a self-evident way.

>>12028576
>asked
I never asked you about anything. This >>12028563 anon and me are not the same.

>>12028576
>It was relevant in a self-evident way.
You still haven't answered my question. How is the delineation of his life story relevant to this discussion in any way? You're beating around the bush.

>>12028574
there's no object such that Euclid's analysis is about "the object". do you not understand how axiomatic treatment works?

>>12028576
>>12028588
Let me posit it more simply
Why did you bring up Galileo?

>>12028519
For fuck's sake Tooker, in analytic geometry, a circle is defined by a parametric curve:
x=a*cos(s)+b
y=a*sin(s)+b
on the other hand
x=tan(a*cos(s)+b)
y=a*sin(s)+b
is NOT a circle
Your argument is so nonsensical. "Hey guys, what if I do a transformation on real coordinates, but then pretend I didn't do anything because actually I'm doing geometry independent of coordinate systems"

>>12028588
>I never asked you about anything.
>You still haven't answered my question.
I see. That is very interesting.

>How is the delineation of his life story relevant to this discussion in any way?
It's relevant in the way I stated.

>You're beating around the bush.
Please tell me more about your opinion.

>>12028599
>I see. That is very interesting.
My question about your Galileo reply steams from your reply. Do you not see that?

>>12028596
And then I remember that a person such as Ted Bundy actually existed.

Paradoxically, the closest I find in Euclid to the modern definition is his definition of a ratio, where a:b equals c:d if,
m*a < n*b for precisely those numbers m, n such that m*c < n*d; and
m*a > n*b for precisely those numbers m, n such that m*c > n*d; and
m*a = n*b for precisely those numbers m, n such that m*c = n*d.
(Here by number I mean positive integer.)
This looks a lot like Dedekind cuts.

>>12028591
I've never heard of "axiomatic treatment" so I don't know whether or not I understand it. The object I'm talking about is the straight line that appears in all the figures in Euclid's book, pic related.

>>12028595
I did it because I felt like the comparing the anti-science climate of antiquity to the anti-science climate we occupy now.

>>12028615
>I did it because I felt like the comparing the anti-science climate of antiquity to the anti-science climate we occupy now.
You are right. But I still fail to see how the anti science climate discussion is relevant to a scientific/mathematical discussion in this thread on a science board?

All of the line segments in the figures in Euclid are finite, for practical reasons if nothing else.

>>12028596
>in analytic geometry, a circle is defined by a parametric curve:
I am well aware of that. I used pic related definition.

>>12028602
I don't. In my eyes, your question stems from an unsavory part of your personality.

>>12028619
>I still fail to see
Please tell me more about how you fail.

>>12028620
yes, pic related from:
http://farside.ph.utexas.edu/Books/Euclid/Elements.pdf

>>12028633
Alright. So you state that an air of anti science is still present now as it was during Galileo's time. Which I thoroughly agree with you. But you bring this up in the middle of a scientific discussion. Why did you bring this up?

>inb4
>> did it because I felt like the comparing the anti-science climate of antiquity to the anti-science climate we occupy now.

Yes, yes I know. But that is not relevant to this discussion. Here we're talking about your theories but then you suddenly bring up Galileo's prosecution. Do you see how incoherent this is?

>>12027596
>infinity hat minus b
what is b? can it be anything? what if b just makes the solution an even negative number or a Re(z)=0.5?

>>12028639
Actually my point was that the anti-science climate now is much difference than it was in medieval Europe. I brought it up BECAUSE I FELT LIKE IT. If you didn't understand the first few times I said it and you still didn't understand it now, I don't think you will understand if I tell you again so I probably won't.

>Do you see how incoherent this is?
No.

>>12028648
If you're interested in the definitions of the symbols in the paper, you ought to read the paper which gives the definitions.

> what if b just makes the solution an even negative number or a Re(z)=0.5?
I don't know what would happen if b was like that.

>>12028536
>I'm not the same as Galileo?
So you disagree?

>>12028615
it means that notions are defined by properties and relations, not as concrete things. Euclid doesn't say what a point or a line is exactly, he only states the properties which characterize them. consequently any structure where points and lines are defined in such a way that these properties hold is a valid model of Euclidean geometry. there's no "original model".

>>12028669
Sometimes I agree and sometimes disagree. I guess it depends on what the topic is. When the topic is a question like your green text, it's not something I really agree or disagree with. How does one agree or disagree with a question?

>>12028670
>Euclid doesn't say what a point or a line is exactly
literally these are the first two lines of the entire 13 volumes of the Elements.

>not as concrete things.
In my opinion, all the points and lines in the dozens or hundreds of figures are 100% "concrete."

>there's no "original model".
You asked me if the Cauchy definition was a model of a Euclidean space, did you not? If there it is a model now, and there was no model 2000 years ago, then there must have been a first model. That is what I would call "the original model." Which "model" do you think was the first model? That will help me better understand hat your idea of a model is.

>>12027596
https://youtu.be/WO9ewCO7TYI