/sci/ - Science & Math

>>15434492
It's false because it's a shitty mathematical circlejerk with no real life applications, aka you shouldn't waste your time on this shit

>>15434527
It's even more useless than you can imagine. Libraries of papers have already been written assuming RH. Proving or disproving it would add nothing of value to our current understanding of number theory and could only impoverish our future understanding.

Partially updated version this.

>>15434492
Proposition 1.8 doesn't appear to actually be claiming anything

>>15434600
The proposition is that the object defined by the supposition can exist. I could have written "We propose that the absorptive properties of infinity might by inhibited by the hat..." and the meaning would be the same. I think a non-obtuse reader can connect the dot that article labelled "Proposition" has a proposition in it. That's not you, I guess.

>>15434611
Does infinity hat plus x exist for positive real x, or only for negative?

Euclid didn't believe 1 was a number, much less [math]\sqrt{2}[/math] or infinity-hat.

>>15434492
>RH is false because there is a zero at [math]z = -(\hat{\infty} - b) + 1[/math] which is not on the critical strip
do I have that right?

>>15434642
Well, in addition to not being on the critical *LINE*, there are at least some "b" which make that "z" not a trivial zero, and RH is false due to both of those reason being taken together. In pic related (and here >>15434597) I show that there are also non-trivial zeros off the critical line yet still within the critical strip.

>>15434630
>Euclid didn't believe
What Euclid called "numbers" are what we call natural numbers today, and I am pretty sure that he believed the single unit was a number. If you can disprove me, please post corroborating evidence. Other than that, what Euclid called "magnitudes" are what we call real numbers today. The Elements was a treatise on constructible numbers, of which the square root of two is one, so I am pretty sure Euclid believed in it. Again, if you can disprove me, please post corroborating evidence.

>>15434628
Such numbers are only (positive) real numbers when x is finite and negative, but INF-0 is a well known extended real number, and INF+x for positive x would be a transfinitely continued real number.

>>15434659
>I show that there are also non-trivial zeros off the critical line yet still within the critical strip.
I'm not seeing how 5.5 follows from 5.4 and 5.3, neither of those results mention anything about zeroes off the critical line

That's a great proof of the Riemann hypothesis over the Tooker numbers. But does it hold over the real numbers?

>>15435062
Axiom 5.3 says that the zeros of a holomorphic function within a small disc are totally disconnected or the function is zero everywhere on the disc. Theorem 5.4 shows that the zeros are not disconnected along the critical line in the neighborhood of infinity. Main Theorem 5.5 hopes the reader will use the reference to Axiom 5.3 and Theorem 5.4 to imagine a small disc containing a portion of the critical line in the neighborhood of infinity. Since RZF's zeros in that disc are not totally disconnected (proven in Theorem 5.4), RZF is zero everywhere on the disc. Parts of the disc lay to the left and right of the critical line, so, therefore, RZF has non-trivial zeros off the critical line.

>>15435118
You're going to regret your foolish wickedness.

>>15435139
>Theorem 5.4 shows that the zeros are not disconnected along the critical line in the neighborhood of infinity.
No it doesn't, it just shows that their imaginary parts get closer and closer. The sequence of zeroes can still be disconnected. As an analogy, both the sets {1, 1/2, 1/3, 1/4, ...} and {1, 1/2, 1/3, 1/4, ... 0} are totally disconnected despite having this same property.

>>15435684
>>15435139
Also wouldn't that imply the existence of some open disk of zeroes in the Archimedean part of the critical strip? The zeta function is analytic on the entire strip, so that would imply it is zero everywhere by basic complex analysis

>>15435684
>>15435684
>No it doesn't
If you think you can identify a flaw in the proof of the theorem, then I encourage you to do so. If I have an error, which I don't believe I do, then I will be eager to correct it. My point is that if the distance between points is zero, not approaching zero but literally zero, then the points are not disconnected. What is your counterpoint?
>As an analogy,
I think your analogy is as retarded as I think you are. A non-retarded analogy is the spectrum of energy eigenvalues for a hydrogenic electron. Below the ionization energy, there are a countable infinity of totally disconnected bound states, but above the ionization energy the energy states form a continuum. That's like the RZF zeros getting closer and closer together in the neighborhood of the origin (bound states) until a transition occurs at some finite value where the neighborhood of infinity starts (~13.6eV ionization energy) after which the RZF zeros form a continuum (free particle states). Since the energetic separation of the states approaches the limit of "Delta E=0" at the ionization energy, the states are no longer discrete above that energy. Perhaps you dispute the accepted fact that the spectrum of the Hamiltonian operator for a free particle is continuous?

Tooker I'd written you up to last month about an error with theorem 1.9 - proposition 1.8endowed with definition 1.1 and you still haven't addressed that.

In fact in no axiomatic system is your proof consistent because of those 3 statements

>>15435800
>If you think you can identify a flaw in the proof of the theorem, then I encourage you to do so. If I have an error, which I don't believe I do, then I will be eager to correct it. My point is that if the distance between points is zero, not approaching zero but literally zero, then the points are not disconnected. What is your counterpoint?
My counterpoint is that you did not claim the distance between some two points is literally zero, you're claiming that the successive differences approaches zero. If your claim is that some continuous patch of zeroes occurs high enough on the critical strip then >>15435716 applies

>>15435822
I think you're lying.

>>15435823
>you did not claim the distance between some two points is literally zero, you're claiming that the successive differences approaches zero.
If a non-negative, monotonic sequence approaches a limit L at x (gamma_n in the theorem), them it has already reached the limit beyond x. Beyond x, it is constant. I have shown that the space between successive zeros is zero beyond a number in the neighborhood of infinity. If the space between the zeros of a holomorphic function is zero on some disk, then the function takes a constant value "zero" everywhere on the disc. I have entertained you, but I think you are being obtuse artificially.

>>15435875
Well I think you are a schizo

>>15435875
>If a non-negative, monotonic sequence approaches a limit L at x (gamma_n in the theorem), them it has already reached the limit beyond x. Beyond x, it is constant.
Then it is also constant below x on any region containing x, correct?

>>15435887
No, due to the refutation of Proposition 5.2.

>>15435934
Is there a complex x on the critical strip which is archimedean (x = a + bi with both a, b < n for some natural n) for which zeta is constant beyond x, or is your x a nonstandard complex?

>>15435944
I think you have presented a false dichotomy with your word choice. Since your pitfall is poorly hidden, I think I will not throw myself into it. Also, while I can see your meaning plainly, your parenthetical definition allows "Archimedean" complex x in the critical strip with imaginary parts in the neighborhood of minus imaginary infinity because all negative numbers are less than every natural number.

Also, I might add that the false dichotomy is as follows. He presents a choice between numbers being either "Archimedean" (as he has defined them) or being "nonstandard." However, the main result of my program, even more so than the RH result, is that there are numbers in standard analysis which do not have the property he associates with the word "Archimedean." Section 6.3 in my long paper (>>15434597, also pic) shows that he is not using the word "Archimedean" properly, and that all of the numbers I included in my standard analysis do have the Archimedes property according to Euclid's statement of the property. If you use Rudin's bastardized statement of the Archimedes property of real numbers, or some similarly bastardized statement as my counterparty has, then the numbers I use do not have the Archimedes property. According to Euclid, however, who is the author of the statement of that property, the numbers I use are Archimedean.

>>15436055
Sneed.

>>15434492
Infinityhatbros...

>>15436060
>>15436060

>>15435986
>I think you have presented a false dichotomy with your word choice
I wasn't intending to, but let me rephrase it if that bothers you. The complex x for which zeta is constant beyond x, is there such an x = a + bi for -n < a, b < n for some natural number n?

>>15434492
But he does not prove infinity hat is in the complex plane.

>>15436460
I don't prove that because it isn't. That doesn't stop INF-b from being in it though. For instance, consider the set {1,2,3,4}. the number 5 is not in this set, but 5-2 is in it, and it's the same for the set (0,INF) and INF-b given appropriate b.

>>15436549
He does not prove -(infinity hat - b) + 1 is in the complex plane , for whatever b he’s using

>>15436575
I definitely did prove that numbers in the nbhd of infinity, such as the one you mention, are on the complex plane.

>>15436549
Okay but the number 7 is not in that set and neither is 7 -2

>>15434492
This has to be a bot. No way a human could still be posting this shit for years on end

>>15436813
Yes, but if we look at the set (0,10) then 10-x is in the set for any 0<x<10 because 10 is the supremum or least upper bound. It works the same for (0,INF) and INF-x for 0<x<INF because INF is the least upper bound. In fact, we have defined INF to be the LUB. Your example with 7 doesn't work because 7 isn't the LUB.

>>15436834
My trade requires that I communicate results to complete a work unit. I seem to have some trouble getting that work done, and I have been working on it for a long time.

>no way a human would work hard for a long time

>>15436844
You've worked hard because you believed you were on to something but many people have shown you that you're just wrong. Time to move on

>>15434492

>>15436846
>but many people have shown you that you're just wrong.
I think I corrected the few errata that were brought to my attention.

>>15436083
gonna answer this >>15436439 bub?

>>15436837
what's INF + 4?

Tooker's proof is correct but unwieldy. I have an elegant simplification
>adjoin to the complex plane a new element D defined to be off the critical line
>extend the riemann zeta function by letting Z(D) = 0
>since the riemann zeta function has zeroes off the critical line, RH is false

>>15434492
>true to billions of examples
>wrong because some poorly argued reason, like saying the definition of infinity - something that cannot be defined at all - is the limit of some other shit, which has nothing to do with limits at all
>"the real number line is a 1D space extending infinitely far in both directions"
>doesn't define far, both, or directions\
>attempts to define reals numbers as cuts
>does not define cut
>attempts to define the extended real numbers in terms of being 'affine" - doesn't define affine in regards to numbers or first principles whatsoever
>introduce infinity hat without defining it
>proposition 1.8 reads, in essence, "suppose that this thing I just said is axiomatic isn't actually an axiom"
>the definition of infinity hat proceeds circularly from the supposition that the axioms we've established aren't axioms
>claims "we" when it's literally a single author
>expects me to take this seriously
It's really easy to prove anything when you just say some shit without any rigor whatsoever.

>>15434611
>I think a non-obtuse reader
It's very convenient to write off all your criticism as people being obtuse, but what's actually happened is you've stated some axioms prior to proposition 1.8 and then said "suppose none of those axioms are actually axioms".

>>15436937
It sounds like you're asking if RZF has non-trivial zeros of the critical line with real and imaginary parts both in the neighborhood of the origin. I don't know and my feeling is probably not. The zeros I used to negate RH all had either a real or imaginary part in the neighborhood of infinity. Numbers in the neighborhood of infinity are greater than every natural number.

>>15436940
INF + 4 = 4 + INF, for example. It equals INF + 2x2, etc. Seems like if you have a poignant question, you didn't use enough words to state it.

>>15436977
In your terminology, RH is actually the hypothesis that the Riemann zeta function has non-trivial zeroes off the critical line with real and imaginary parts in the neighborhood of the origin

>>15436978
is it different from INF?

>>15436954
>true to billions of examples
Even 10^1000000000000000000000000 has 0% fractional distance with respect to infinity. Those numbers are teeny weeny.
>doesn't define far, both, or directions
In the absence of contextual definitions intended to create jargon, all words take their meaning as given in the English dictionary.
>does not define cut
I do define it in Definition 1.3, shit cunt.
>proposition 1.8 reads, in essence
The proposition is that the object can exist. In other work, work which is not written explicitly to be "quick," I prove that it can exist.
>claims "we" when it's literally a single author
That is the author and the reader together: we. It is also known as "the royal we" and it is a canonical tense in academic writing.

>>15436958
I don't think I'm pushing the limits of reasonable rhetoric when I claim that one would have to be obtuse not to understand that the article labeled "Proposition 1.8" has a proposition in it.

>>15436986
you're pushing the limits of mathematical writing by having a proposition environment consisting of "Suppose [x] and further suppose [y]" without any subsequent "Then [z]"

>>15436980
>In your terminology, RH is actually the hypothesis that the Riemann zeta function has non-trivial zeroes off the critical line with real and imaginary parts in the neighborhood of the origin
You are 100% full of shit. I am posting the official problem description from Clay which shows that you are lying. Riemann's paper is on the internet too and you can see that he does not restrict to the neighborhood of the origin. Furthermore, the only thing that matters is if my solution sheds sufficient light on the prime number application which made RH so interesting to begin with. All of these people trying to redefine real numbers as only the neighborhood of the origin are completely stupid. It's like they're saying they don't want to know about the prime number application if the analysis of the question involves numbers that are larger than any natural number. Obviously, I haven't looked at the prime number application yet but I heard from three different frog memes that my solution does everything that is expected.
>It's like they're saying they don't want to know about the prime number application if the analysis of the question involves numbers that are larger than any natural number.

>>15436981
You'd need to post your definition of INF before I could tell you, and should probably post the axioms of your analytical framework too.

>>15436990
I disagree. The "then z" statement is implicit: Suppose this object can exist with these properties and then **not entail contradictions that make it useless for mathematics.** Basically everything written speculatively in math has this implicit "and then" statement on it. Most people don't write it and I didn't either.

>>15436992
The object [math]\mathbb{C}[/math] which that PDF refers to has the property that every element can be written as x = a + bi with |a|, |b| < n for some natural number n. You can ree about that and complain that [math]\mathbb{C}[/math] actually refers to something different, but then your argument is basically >>15436944.

Would be interesting to know if your argument actually does shed some light on prime number distributions, but if the frog emotes didn't elaborate on how this is true then I'm sorry to inform you they were shitposting

>>15436993
INF is the number [math]+\infty[/math] as constructed in Definition 1.4, under the same axiomatic framework you are working under in your paper.

>>15436998
>Most people don't write it and I didn't either.
You are unable to provide a single example of a published mathematical paper which contains a proposition written that way.

As usual he disappears when he can no longer insult his way out of having to answer questions

>>15437002
>The object C which that PDF refers to has the property that every element can be written as x = a + bi with |a|, |b| < n for some natural number n.
It doesn't. You're referring to C having the Archimedean property which wasn't bastardized into something other than what Euclid said it was until many decades or maybe a century after Riemann published his hypothesis. I refer you to my earlier post: >>15436055. You are stupid and I undermined the castle of your argument before you even started building it. What you're saying is the Archimedes property using a condition for natural numbers wasn't invented until the 20th century. Back in Riemann's day, scholars still studied The Elements in their primary education. Riemann's program of Riemannian geometry as an extension of Euclidean geometry emphasizes the well known fact that Riemann's program was based on Euclid's program. When the modern statement of the Archimedes property got adopted, they thought it was equivalent to Euclid but it actually truncates the possibility of a neighborhood of infinity. The way Euclid made the statement, the neighborhood of infinity is allowed and you are trying to conjure an anachronism by saying that Riemann was bound by the restatement of the Archimedes property that didn't exist until after he was dead. In fact, there was an error in mathematics when they said that your statement is the Archimedes property.

If you intend to continue insisting that Riemann used Rudin's statement of the Archimedes property rather than Euclid's please cite the material Section 6.3: >>15436055. I have already addressed every point you might raise. Furthermore, your preoccupation with the Archimedes property rather than the prime number application that makes RH interesting shows that you are a troll.
>It's like they're saying they don't want to know about the prime number application if the analysis of the question involves numbers that are larger than any natural number.

>>15437038
The [math]/mathbb{C}[/math] that Riemann studied has the property that for any analytic function defined on a region, if the set of zeroes has a limit point then the function is constant. Your complex plane does not have this property. Am I correct about both of these statements?

>>15437002
To say that numbers in the neighborhood of infinity aren't real numbers, you'd have to reject R=(-INF,INF). A number slightly less than infinity is in that set in the same way that a number slight less than 5 is in S=(-5,5). You're saying (liberal paraphrasing with foresight), "The modern restatement of the Archimedes property is the law of the land now and if that means we have to get rid of R=(-INF,INF) then it's gone." I'm saying, "What your calling the Archimedes property didn't exist in Riemann's lifetime and the Archimedes property recorded by Euclid does allow a neighborhood of infinity. On top of that R=(-INF,INF) is the fundamental, immutable property of R, not the Archimedes property."

You have no self-awareness at all that the real numbers existed for thousands of years possessing the Archimedes property as it was written by Euclid. That only changed at the cusp of history and it was an error when people though the new statement was exactly equal to Euclid's statement. The wrong idea that the new statement was the same as the old on is why they adopted the new statement but if they had known that Euclid allowed a neighborhood of infinity as a corner case which they failed to consider, then they never would have started calling it the Archimedes of property of real numbers in the first place. Now everyone has been working with an error in their axioms for 100 years and no one wants to say, "Oops, we have an embarrassing error here."

You also have no self-awareness that what you are calling the Archimedes property of real number did not exist while Riemann was alive.

>>15437049
>Am I correct about both of these statements?
No.

>>15437055
Which one(s) am I wrong about?

>>15437051
in order to throw INF into the real numbers you must either make addition a partial function or make it non-associative, neither of which seems like a more intuitive choice than the modern restatement of the archimedean property

>>15437056
I don't have a complex plane and you're ignoring the refutation of Prop 5.2 to which I already referred you, or to which I already referred someone earlier. Why are you criticizing my work with referring to what I wrote? The answer is obvious: you're trying to build a parallel environment apart from my research articles into which you can drop your unsupported but bombastic zingers. In other words, you are a troll.

I will continue to entertain your trolling only if you inquire about the enumerated articles in my papers. I will not entertain your intention to construct a parallel environment.

>>15437058
I don't throw INF into the real numbers. INF and INF-HAT are ****not**** real numbers.

I don't need to throw 5 into S=(-5,5) to know that x=5-1 is in S, and, likewise, I don't need to throw INF into R=(-INF,INF) to know that x=INF-1 is in R.

INFINITY IS NOT A REAL NUMBER!!! NOT WITH A HAT!!! NOY WITHOUT A HAT!!! NOT EVER!!!

>>15437067
in order to throw infinity hat into the real numbers you still must either make addition a partial function or make it non-associative

>>15437063
You have a mathematical structure which includes an element infinity-hat and an instance of a Riemann zeta function, sorry to trigger you with incorrect pronouns

>>15437069
I don't throw it into the real numbers. Infinity hat is not a fucking real number. Are you retarded.

Suppose the set S is the interval S=(-5,5). Now suppose x=5-1. Clearly, 5 is not in S, and, yet, somehow, x is in S. What about that is too hard for you to understand? I don't need to put 5 into S to know that x=5-1 is in S.

>>15437070
It's your innumerate language that's triggering me. I use infinity in my analysis but I do not put infinity into the domain of the RZF. Your "inability" to differentiate (1) infinity and RZF being discussed in the same paper from (2) infinity being put into the domain the RZF is so stupid that I must conclude it is a carefully crafted ruse you intend to perpetrate while understanding perfectly well that I have not put INF into the domain of the RZF.

>>15437072
>infinity hat is not a real number
>infinity hat minus b is a real number
then either (infinity hat minus b) + b does not equal infinity hat, and addition is not associative, or (infinity hat minus b) + b is not a real number and the real numbers are not closed under addition

>>15437082
>then either (infinity hat minus b) + b does not equal infinity hat, and addition is not associative, or (infinity hat minus b) + b is not a real number and the real numbers are not closed under addition
I agree.

>>15437080
you put 1/2 + (infinity hat - b)i into the domain of RZF

>>15437085
Is addition on the real numbers associative?

>>15437086
I agree.

>>15437087
If you're not going to read my paper, I'm not going to answer your questions.

>>15437088
And one of the functions
>f(x) = x - 1/2
>f(x) = x + b
>f(x) = x / i
is not a total function on the complex numbers

>>15437091
Do you think the complex numbers as Riemann perceived them also had non-associative addition?

>>15437094
>>15437096
>inb4 two different red herrings

>>15437103
I'm gonna take that as a no, Riemann was studying a structure with associative addition. In which case the criticism in >>15437002 applies again. The object [math]\mathbb{C}[/math] which the RH is about is a field, in particular a structure with associative addition. You have disproven RH in a structure with a non-associative addition. Which is very cool and you should be very impressed with yourself but unfortunately is not a refutation of RH by the standards of the Clay institute.

>>15437063
Took a relook at proposition 5.2 by the way. It's a lot easier to refute the statement "if f is a holomorphic function defined on a region and f(z) = 0 for more than one z, then f is constant 0" than you're making it, just consider sine.

>>15437117
>>15437103
lol wait, that was me being a retard about reading comprehension. I have a more substantial criticism: the union of your neighborhood of infinity hat with the set {a + bi : 0 < a < 1} is a connected open set, so by Axiom 5.3 and Theorem 5.4, the Riemann zeta function is constant 0 on this set.
Surely I'm getting some detail wrong here, please help me figure out what it is. Genuinely trying to figure out what you're doing here mathematically.

>>15437008
I went to arXiv to check if you were right since I don't read a lot of math papers. I found this kind of proposition in the very first paper I looked at: the newest paper in algebraic geometry:
https://arxiv.org/abs/2305.06411

It's implicitly proposed that this equality doesn't entail any contradictions which make the proposition useless for mathematics.

>>15437536
No, that equality is presented as a conclusion from the hypothesis of having a variety and an integer. See the word "Then"?

>>15437815
Prop 3.7 in the same paper then. "Every module has a basis ***without the basis causing any problems that make it useless for mathematics.***"

>>15438099
Once again this has an explicitly stated conclusion and assumptions. You would have written
>Proposition 3.7 (Proposition A.4). Suppose every submodule M of F has a unique reduced Grobner basis.
leaving the reader confused and annoyed

>>15436589
Nope. Where?

>>15438106
I can concede your counterpoint in the case of Prop 2.1 and agree that the proposition does contain a "then" statement. However, I cannot concede regarding Prop 3.7. There is no "then" condition. You have moved the goalpost from including a "then" statement. Now you say the problem is that I asked the reader to suppose the proposition was valid rather than merely stating the proposition while letting the article type "Proposition" convey to the reader that I wanted to suppose the condition stated in the article. This issue reflects nothing but a choice of prose. It's like your criticism is that I called it a proposition rather than a supposition.

>>15438133
Here: >>15434597, as excerpted in pic related.

>>15438188
Also, I have started playing semantics by distinguishing between a "then" statement and an "as a result" statement. Therefore, I should not insist continuing to debate this point. Still, I maintain that my proposition is ordinary and I refer to my proposition as following the template of Prop 3.7, which is a random Proposition from the first math paper I could find on arXiv.

>>15438188
My goalpost was never "you must include the word then", my goalpost was always that a proposition should have assumptions and a conclusion. Your picture is dishonest because you are comparing a proposition from OP's meme image to a proposition plus additional remarks from the mathematical paper. Remake your image without "as a result [...] in handling the conditions (b)(c)" and still see if you can make the same equivalence

>>15438218
>taking for granted that x does not have any infinitesimal part, which is obvious
No it's not, and since x with an infinitesimal part are by definition dense in the complex plane, the neighborhood of infinity must include some

>>15438255
Then I rephrase my previous statement as follows: The conclusion of Prop 1.8 is that there exists a number with the given ordering (and it doesn't entail any contradictions which make it useless for mathematics.) We "further suppose" the conclusion because we started by "supposing" the motivating condition. Telling the reader to suppose it is close enough to telling the reader that I propose it that the two directions have essentially the same meaning.

>>15438267
And I rephrase my previous statement as follows: a proposition consisting solely of sentences of the form "suppose [x]" with no conclusion is unusual mathematical writing.

>>15438255
I think if you remove the remarks from the italicized Proposition, then that strengthens my point. I thought you were including these words in the Proposition with your "this has an explicitly stated conclusion and assumptions" comment. I feel like I have sufficiently shown that my proposition is ordinary despite my failed attempt to find a perfect one-to-one correspondence in a sample of one random math paper.

>>15438270
>a proposition consisting solely of sentences of the form "suppose [x]" with no conclusion is unusual mathematical writing.
>>15438267
>Telling the reader to suppose it is close enough to telling the reader that I propose it that the two directions have essentially the same meaning.

>>15438273
Assumptions: M is a submodule of F
Conclusion: M has a unique reduced Grobner basis

Assumptions: Suppose the additive absorptive blah blah blah
Conclusion: [none]

>>15438274
Are these two points supposed to contradict each other? Obviously you think what you wrote has the same meaning as what you intended to wrote, doesn't mean the average reader is there with you

>>15438273
>I think if you remove the remarks from the italicized Proposition, then that strengthens my point.

>>15438287
>Proposition 3.7 (Proposition A.4). Every submodule M of F has a unique reduced Grobner basis.
>Proposition 3.7 (Proposition A.4). Suppose every submodule M of F has a unique reduced Grobner basis.

>>15438282
I think the average reader knows that supposing and proposing are about the same.

>>15438279
>Assumptions: M is a submodule of F
No. It is already established as a fact that M is submodule of F.

I think this person's argument that I have supposed rather proposed is very weak. Unfortunately, I did not present my countercase as efficiently as possible.

>>15438306
>I was never born.
>Suppose I was never born.
>The average reader sees the previous two sentences as saying the same thing.

Your second point is beyond retarded.
Take the L on this one, Took. I'm not even criticizing your math, I'm just telling you that you're writing in an unconventional way.

I think this person's argument that I have supposed rather than proposed is very weak. Unfortunately, I did not present my countercase as efficiently as possible.

>>15438311
>Proposition: I was never born.
>Suppose I was never born.
>The average reader sees the previous two sentences as saying the same thing.

>>15438311
>Take the L on this one
You are the one who has lost. These two sentences do mean the same thing.

Ugh fine I'll point out the mistake myself.

In proposition 1.8 one gets [math] \lim_{x\rightarrow0^\pm}{\frac{1}{x}}<\lim_{x\rightarrow0^\pm}{\frac{1}{x}} [/math] due to the first definition and theorem 1.9

Do you see the error yet?

>>15438326
Correction, left side of the inequality is rather [math] \lim_{x\rightarrow0^\pm}{\fract{1}{x}-a} [/math]

>>15438324
What about these two sentences
>Suppose I was never born.
>Imagine I was never born.
Do they mean the same thing?

>>15438326
>Do you see the error yet?
No.

>>15438330
I do not wish to engage in these extended matters of semantics. I am not fascinated by the point you raise.
>>15438306
>I think the average reader knows that supposing and proposing are about the same.

What we have done here is to construct a parallel environment apart from my research articles.

>>15438337
once again the point I raise is that your writing is unconventional and that the average reader would not treat those sentences as the same thing.

If you'd like to discuss your research, here's something I'm curious about. Presumably the argument
>infinity hat - b is a real number
>infinity hat = infinity hat - b + b is a real number, since the real numbers are closed under addition
is invalid because addition is not actually associative in the neighborhood of infinity hat.
The question: is there a standard real a (a < n for some natural number n) so that (infinity hat - b) + b = infinity hat - a?

>>15438350
>the average reader would not treat those sentences as the same thing.
Your opinion is different than mine. I think most people use "suppose" and "propose" as loose synonyms.

>>15438350
>Presumably the argument is invalid
I suggest that you don't presume that then. This should resolve the issue.

>>15438368
>I suggest that you don't presume that then. This should resolve the issue.
Then why is the argument invalid?

found another contradiction in your work, Took.
>if x =/= y are real numbers then there is a natural number 1/n such that |x - y| > 1/n
>tangent function bijectively maps [0,infinity] to [0,1]
>there is a midpoint between 0 and infinity
do you see the contradiction?

>>15438375
I don't concede that you have made an argument. You have made a statement: "I presume this is invalid."

>>15438387
The argument
>b is a real number
>infinity hat - b is a real number
>infinity hat = infinity hat - b + b is a real number, since the real numbers are closed under addition
valid, or invalid?

>>15434492
Have sex

Infinityhatbros

WE
WON!

>>15438390
If you're not going to read my paper, I'm not going to answer your questions.

>>15438652
Suppose I did read it. Will you answer my question then?

>>15438333
You are denying here that 2+2=5

Fucking schizo stop wasting time

>>15438691
If you read and demonstrate with your questions that you have read the material, and your questions pertain to the material, then it is likely that I will answer your questions.

>>15434597
fucking hell, imagine wasting time out of your life on 143 pages of nothing

>>15438710
Time one could spend on good food and cold brews, a good movie for good time.
:)

>>15438702
Just finished it, my question is still relevant. Is my argument mathematically valid or not? If you can't give me a yes or no I will have to conclude that you don't know

>>15438652
oof here's another Tooker contradiction
>subsets of R_0 have the least upper bound property (remark 5.4.12)
>there is a bijective fractional distance function from [0,infinity-hat] to [0,1]
can you spot the contradiction Tooker? You 100% do not address it in this paper

>>15436954
The use of "we" is commonly used in research, is this your first time?

Hell even Perelman's proof was done in this manner, yet it was correct (I don't know)

You should've given citations in axiom 8.2.3 since the new readers would not understand all the references, citations would help establish that this axiom can indeed be taken as a reasonable axiom.
If anything I would guess that somewhere in the main theorem 8.2.5 you dod a mistake

>>15438740
>If you can't give me a yes or no I will have to conclude that you don't know
I disagree and I don't think you could prove that claim with symbolic logic.

>>15438771
>can you spot the contradiction Tooker?
I think the reason I'm not spotting it is because you're not stating it.

>>15438867
>there is a bijective fractional distance
Higgs' famous paper about the scalar boson is also a good example of the "we" tense.

>>15438874
least upper bound of the set [math]\{r \in [0,1] : \mathcal{D}_{0 \hat{\infty}}([0,0] [0,x])(x) = r \mbox{ for some }x \in \mathbb{R} \mbox{ with } x < n \mbox{ for some natural }n\}[/math]

>>15438870
Yes, I was thinking about converting 8.2.3 and 8.2.4 into a theorem with a proof like, "Proof can be found in any complex analysis book." Thank you. It really ought to be a theorem but I made it an axiom to forego giving such a well known proof.

>>15438885
When I was in like first grade or so, I learned about this thing called "a complete sentence." You might want to study them. I think you could benefit from learning about them. Other than that, I don't know how I'm supposed to read the notation you put in your post.

>>15438891
I think a non-obtuse reader would interpret my post as saying that the contradiction follows from that least upper bound. And can't read your own notation, top kek, I was using it as a sign of respect. You know how the (number corresponding to the) midpoint X of 0 and infinity hat exists, and is the point for which D([0,X]) = 1/2? If that number is < n for some natural n, then 1/2 is in that set.

>>15438932
You're definitely not using my notation. I certainly understand that you're saying the contradiction follows from the LUB. However, this is the third post you've made about it following without saying what follows, and I still don't know what you're getting at. Instead of making three different posts saying that a contradiction follows, why not just state the contradiction?

>>15438960
Contradiction is that the least upper bound can't exist. If r is in that set, then we can extend the line segment [0,x] a bit farther by a natural number amount and obtain a bigger r. If r is not in that set, we can shorten the line segment [0,x] downwards by a natural number amount and obtain a smaller r. Ultimately a consequence of the fact that the real numbers as you have constructed them are not a connected set.

>>15438975
What was your opinion on Section 7.5 whose topic was "the least upper bound problem?"

>>15438980
I thought it was great but did not actually address my contradiction.

>>15438975
>If r is in that set,
Which set? This is at least the fourth post where you have dropped ambiguous references without just stating the thing you think is a contradiction? If you think there is contradiction, please state it is a self-contained post with complete sentences, as if it was a 3rd grade writing assignment and you were going to get graded on your ability to put together a coherent and cohesive paragraph.

>>15438983
For example, I told you "I cannot understand the notation you used," and then you said, "If r is in the set whose definition you don't understand, then there is a contradiction." It's like you're being unserious.

>>15438998
Once again, I think an non-obtuse reader would interpret that post as referring to the set in >>15438885. Some of those clues are as follows
>the previous sentence talking about finding a least upper bound
>the letter r being used in the set-builder notation
>being the one and only one set in this conversation.
Now that I have fully stated the contradiction, please state it as a self-contained posts with mathematical explanations, as if were a 1st grade book report and you would get an F if you turned in the sentence "just look at section 7.5"

>>15439003
And in the post between me saying those things I paraphrased the notation I used, and since you had no objections in your following post I assumed you then understood what I meant.

>>15439005
I know you're referring to that set. That's the set about which I told you, "I cannot understand your notations."

I told you, "I cannot understand your notation," and instead of defining the set with sentences, you pretend like I can't understand which set you're talking about. I know which set you mean. What I don't know is the definition of that set or how I'm supposed to read the TeX you used to define it.

>>15439030
I was using notation from Fractional Distance, but forget about it, we have already established that I used confusing notation. Surely you find this topic tiresome. Let's get back to mathematical matters. Am I correct about all of these things
Real numbers are cuts on a real number line (Definition 2.1.5)
There is a particular line segment AB = [0, infinity] (Definition 2.3.8)
For any real line segment AB, there is a continuous bijective map [math]\mathcal{D}_{AB}[/math] from initial segments AX of AB to real numbers in [0,1]

Inb4 "just make your argument in one post". I'm making sure we're axiomatially on the same page, and you should be happy I'm bumping your thread.

>>15439054
>Real numbers are cuts on a real number line (Definition 2.1.5)
>There is a particular line segment AB = [0, infinity] (Definition 2.3.8)
>For any real line segment AB, there is a continuous bijective map DAB
> from initial segments AX of AB to real numbers in [0,1]
yes.

>>15439054
>I'm bumping you
Is that you putting this shit on my face then?

>>15439070
How about this
>There is a midpoint X of AB, where D(AX) = 1/2
>X is (or can be thought of) as a cut of the line segment AB
>X is a real number

>>15439082
>>There is a midpoint X of AB, where D(AX) = 1/2
Yes.
>X is (or can be thought of) as a cut of the line segment AB
No, X is a point, not a cut
>X is a real number
No, X is a point. Numbers are written with lower case Latin letters: x.

>>15439087
Does there exist a real number x corresponding to the point X, which is the unique real number halfway between zero and infinity given in Theorem 3.2.2?

>>15439796
You still haven't posted what you say is a contradiction.

>>15440639
No I haven't, because like I said before, I want to make sure we're on the same page axiomatically. Do you agree with >>15439796?

>>15440864
I think you are lying when you indicate the reason for your failure to state the contradiction. I think the reason is that the contradiction does not exist.

>>15440990
Let's find out. Am I correct in >>15439796 or not? Literally no reason for you not to answer.

>>15441001
based

>>15441001
There's no reason for you not to post what you think is a contradiction, other than the obvious fact that it doesn't exist.

>>15441418
lmao dude why don't you agree or disagree with post of that anon? it's that easy

>>15441507
It's because he won't post the contradiction that he has been alluding to.

>>15441695
i think he'll post his concerns when you answer

>>15441697
Your opinion is much different than mine then.

>>15441418
Okay I'll try a different angle. I'm going to repeat the same claim, and if you do not disagree with it, I will take that as tacit agreement and procee.
>There exists a real number x corresponding to the point X, which is the unique real number halfway between zero and infinity given in Theorem 3.2.2.
Do you disagree?

To be a math crank like tooker requires extreme mental gymnastics. I feel bad for him.

>>15442093
>gymnastics
What do you know of Gymanistics?

https://youtu.be/8ES6YSmmRgA

>>15434492
B A S E D

and

R E D P I L L E D

>>15436954
>claims "we" when it's literally a single author

mfw scared Tooker out of his own thread