Solve

[Anonymous No.10554437]

[Anonymous No.10554452]

>>10554437
I would post my proof but I'd rather receive the 1 mil

[Anonymous No.10554462]

>>10554437
Niggers

[Anonymous No.10554520]

>>10554437
Dumbfuck that sum doesn't even converge for Re(s) <= 1

[Math Anon No.10554523]

>>10554437
I posted a proof of it 2-3 months ago. The thread was active for about 3 days. I'm sure you could find it in the archive if you're interested.

[Anonymous No.10554915]

>>10554452
You'd have to post it anyways. To receive the 1 million, it has to be published and accepted by the general community for 2 years prior to being eligible.

[Anonymous No.10555000]

I disproved RH more than two years ago
>On The Riemann Zeta Function
>http://www.vixra.org/abs/1703.0073

but since you all collude to act like I didn't, I can't get paid for it.
>>10554915
>accepted by the general community

[Anonymous No.10555021]

>>10554437
Can't into domain stretching.

[Anonymous No.10555026]

>>10555000
You're wrong and you know it. You're not even fooling people that you think you're right at this point. That part is an act. My question is, don't you even get tired of trolling with the same material? You're still having fun? Or maybe you do it just to generate conversation? Maybe you're just bored, hunh, no play friends?

[Anonymous No.10555035]

>>10555000
What the heck is that infinity with the hat over it mean?

[Anonymous No.10555049]

>>10554523
i fucking disproved it in original thread

[Anonymous No.10555050]

>>10555035
Infinity is usually afforded with some freedom to do the algebraic operations in any order one wishes or at any time one wishes. The hat is instruction for how to use that freedom.

I explain it here: where other pic is from:
>Real Numbers in the Neighborhood of Infinity
>http://www.vixra.org/abs/1811.0222

Pic related, this is how I disproved RH in 2017

[Anonymous No.10555084]

>>10555050
Are these all your papers?
http://www.vixra.org/author/jonathan_w_tooker

Are you a physicist or mathematician? Or do you consider yourself both?

[Anonymous No.10555087]

>>10555049
No you didn't, nobody did. A few people had some serious suggestions, and pointed out places where it could be cleaned up. The rest of the thread was some trolling. So what to meant to say was, "I trolled that in the original thread."

[Anonymous No.10555089]

>>10555084
I'm a physicist whose area is mathematical physics, so certainly I am also a mathematician. Yes, those are all my papers. There's a short book in there too.

[Anonymous No.10555090]

>>10555084
No, he's a troll, that hangs out on chan, just to get into conversations like this. Most of the pictures he posts are bait, just to get people to waste time.

[Anonymous No.10555092]

>>10555087
you reached contradictory conclusions retard

[Anonymous No.10555095]

>>10555050
>>10555084
I'm looking at https://en.wikipedia.org/wiki/ViXra

Looks like anyone can submit to ViXra without being part of an accredited institution. Do people take paper's seriously form ViXra? How creditable is it?

[Anonymous No.10555099]

>>10555089
He says you're a troll. >>10555090
Is this true?

[Anonymous No.10555101]

>>10555095
>Looks like anyone can submit to ViXra without being part of an accredited institution
same thing for arXiv

[Anonymous No.10555103]

>>10555092
So, sleepy. You're not even trying.

[Anonymous No.10555106]

>>10555000
-(inf-b)+iy0 is not in C so your argument fails.

>inb4 I define C differently
Then you're not solving the Riemann hypothesis.

[Anonymous No.10555111]

>>10555099
The troll face meme is based on my face, but I am a serious scientist. Pic related, I'm not trolling there. That's my regular face.

[Anonymous No.10555129]

>>10555106
I define C so that "z" is in C if and only if "x" and "y" are in R and

z = x + iy

This is the usual definition of C that appears in the first chapter of every complex analysis book that has ever been written. I have proven that (inf - b) is in R, and it is obvious that y0 is in R.

[Anonymous No.10555134]

>>10555103
link your fucking paper

[Anonymous No.10555141]

>>10555129
>I define C so that "z" is in C if and only if "x" and "y" are in R and z = x + iy
Yes, and -(inf-b) is not in R since it breaks the least upper bound property.

>inb4 I define R differently
Then you're not solving the Riemann hypothesis.

[Anonymous No.10555252]

>>10555141
> breaks the least upper bound property.
It does not and if you have a proof of this for me to refute then you should post it.

I don't define R differently. A real number is a cut in the real number line. What definition of reals do you use? (Please don't refer to a definition that didn't exist until after Riemann published his hypothesis.)

[Anonymous No.10555283]

>>10555252
>It does not and if you have a proof of this for me to refute then you should post it.
Assume inf-b is real. Let b be small enough that inf-b is a bound for the integers. But since the integers are a subset of the reals, the least upper bound principle means that the integers have a least upper bound a. a-1 is not an upper bound for the integers since it's less than a, the least upper bound. Therefore there is some integer n > a-1. But then n+1 > a. This contradicts that a is an upper bound for the integers. By contradiction, inf-b is not real.

[Anonymous No.10555291]

>>10555252
>A real number is a cut in the real number line.
This is not a definition. Do "cuts in the real number line" conform to the least upper bound principle? If not, then they are different from the definition of the reals and your argument fails. If yes, then inf-b is not real and your argument fails.

[Anonymous No.10555319]

>>10555283
>Assume inf-b is real.
x = ( inf - b ) & x in R

>Let b be small enough that inf-b is a bound for the integers.
b = 1 & ( inf - b ) greater than any integer

>But since the integers are a subset of the reals, the least upper bound principle means that the integers have a least upper bound a.
Here I think you are taking the property of the neighborhood origin that it is a connected set and applying to the entire set of real numbers. To apply that property thusly, you must first prove that R is a connect set. I am working on a proof that R is not connected, but rather is composed of an infinite number of discrete neighborhoods like "Cantor dust."

Please prove that R is a connected set and is, therefore, vested with the least upper bound property. I assume you will start with, "Let R be the set of reals in the nbhd of the origin," and let me tell you that the real definition of R is
x in R ---> x in ( -inf, inf )

[Anonymous No.10555323]

>>10555291
>different from the definition of the reals
You still haven't given that definition.

I agree that connected sets have this property, but I cannot at this time grant that R is a connected set. It might be. If you can prove it, I'd like to see the proof.

[Anonymous No.10555324]

>>10555252
>(Please don't refer to a definition that didn't exist until after Riemann published his hypothesis.)
Please show me where the "A real number is a cut in the real number line" was published before Riemann published his hypothesis.

[Anonymous No.10555343]

>>10555324
I asked you "Please show me the definition that predates RH."

You responded, "Please show me the definition that predates RH because otherwise RH depends on a definition that didn't exist at the time of RH."

All of the definitions you refer to indirectly as "THE" definition of the real came after RH, and therefore RH cannot depend on them. Please acknowledge that RH cannot depend on any definitions which did not exist at the time of RH, such as "number fields" and "Dedekind cuts."

To the contrary, the Archimedes property of real numbers predates RH. It says that given any real number, there is a larger real number and a smaller real number. The definition of cuts in a number line conforms to the Archimedes property which predates RH by very many centuries.

[Anonymous No.10555347]

>>10555319
>Here I think you are taking the property of the neighborhood origin that it is a connected set and applying to the entire set of real numbers.
No, I'm simply invoking the least upper bound principle, which states that every subset of R with an upper bound has a least upper bound. If your definition does not include this property then it's not a definition of the reals and you're not dealing with the Riemann hypothesis.

>Please prove that R is a connected set and is, therefore, vested with the least upper bound property.
There is no proof, it's axiomatic. Please show me where Riemann or his contemporaries ever treated R as disconnected. (Please don't refer to a definition that didn't exist until after Riemann published his hypothesis.)

[Anonymous No.10555357]

>>10555323
>You still haven't given that definition.
It's widely available and you should know it already.

Let R denote the set of all real numbers. Then:

1. The set R is a field
2. The field R is ordered
3. if x ≥ y then x + z ≥ y + z;
4. if x ≥ 0 and y ≥ 0 then xy ≥ 0.
5. every non-empty subset S of R with an upper bound in R has a least upper bound in R

[Anonymous No.10555360]

>>10555357
>R is a field
Number fields didn't exist in 1858 though you fucking imbecile

[Anonymous No.10555371]

>>10555343
>All of the definitions you refer to indirectly as "THE" definition of the real came after RH, and therefore RH cannot depend on them.
Then RH cannot depend on "cuts in the real number line" as a definition of the reals. Make up your mind already.

>It says that given any real number, there is a larger real number and a smaller real number.
No, the Archimedean property states that for any positive numbers x and y, there is a positive integer such that nx>y. If inf-b is real and positive then the Archimedean property states that there is an integer such that n*1 > inf-b. But you just said that inf-b can be greater than any integer. Thus by your own admission, inf-b is not a real number according to the conception of the reals at the time of Riemann!

[Anonymous No.10555373]

>>10555360
Neither did inf-b and "cut in the real number line" you fucking imbecile. Nice special pleading.

[Anonymous No.10555375]

>>10555343
>given any real number there is a larger real number and a smaller real number
Given any real number there is a larger integer and a smaller integer.

[Anonymous No.10555403]

>>10555347
That is further reflected here he uses different versions of infinity hat and says it means >>10532804 where he says

http://mathworld.wolfram.com/ComplexInfinity.htmlhttp://functions.wolfram.com/Constants/ComplexInfinity/introductions/Symbols/ShowAll.html

It's called complex infinity. A complex number z can be represented as |z| e^(i * theta). Theta is called the complex argument, and it is the "angle" that a vector directed at the point makes on the complex plane.

In real analysis, there is positive and negative infinity, but on the complex plane, there are an infinite number of infinities (that can be tended towards by picking a direction and travelling forever). Instead of naming them all, it's just called "complex infinity" and denoted by infinity-hat. The argument theta is unknown or undefined.

But then that premise breaks the conditions of the problem. By default complex infinity complex numbers have an unknown argument but the hypothesis is for complex numbers whose real portion is between 0 and 1 and whose complex portion is real valued, and thus has a known argument.

[Anonymous No.10555405]

>>10555371
I have proven that the "field" definition does not work for RH. You have been unable to prove the same for the "cut" definition. My claim which I cannot find evidence for is that the reals were defined as cuts in the number line before RH. My claim is that you have been unable to do so because Riemann himself defined reals as cuts in the real number line.
>Archimedean property states that for any positive numbers x and y, there is a positive integer such that nx>y.
I see you are attempting to paraphrase the Eudoxus statement of Archimedes' property as it appears appears in Euclid's Elements (You have not paraphrased it, but instead have paraphrased what you wish it said). There are very many statements of the Archimedes property that every real has a larger real, and the Eudoxus statement is only one of them. Furthermore, you have incorrectly paraphrased it!!! Neither Euclid, Eudodus, nor Archimedes say anything about positive numbers.

I suspect you have deliberately mischaracterized this property because you know good and well that real numbers in the neighborhood of positive infinity behave the under the Eudoxus criterion exactly like negative real numbers. Therefore, the real already contain the behavior which is seen in the neighborhood of infinity. I have added no behavior which does conform to the Eudoxus statement of Archimedes property.

If you want to be very strict about the property as it appears in Euclid's book, then negative numbers are not real numbers. If you want to add your own caveat, "Well, actually it's obvious that he was only talking about magnitudes as positive numbers," then I will also add a caveat, "It's obvious he was only talking about magnitudes as numbers in the neighborhood of the origin."

[Anonymous No.10555406]

>>10555347
That is further reflected here he uses different versions of infinity hat and says it means >>10532804 where he says

http://mathworld.wolfram.com/ComplexInfinity.htmlhttp://functions.wolfram.com/Constants/ComplexInfinity/introductions/Symbols/ShowAll.html

>It's called complex infinity. A complex number z can be represented as |z| e^(i * theta). Theta is called the complex argument, and it is the "angle" that a vector directed at the point makes on the complex plane.

>In real analysis, there is positive and negative infinity, but on the complex plane, there are an infinite number of infinities (that can be tended towards by picking a direction and travelling forever). Instead of naming them all, it's just called "complex infinity" and denoted by infinity-hat. The argument theta is unknown or undefined.

But then that premise breaks the conditions of the problem. By default complex infinity complex numbers have an unknown argument but the hypothesis is for complex numbers whose real portion is between 0 and 1 and whose complex portion is real valued, and thus has a known argument.

[Anonymous No.10555429]

>>10555373
In support of my claim that numbers are cuts in the line I will point out my opinion that Dedekind has a specific cut named after him because he was studying cuts, and it is my further opinion that Dedekind became interested in cuts because the definition of real he used was the same as mine. All of the definitions you guys give, I can prove they didn't exist in 1858.

>Neither did inf-b
This is a number not a definition. All cuts in the number line existed in 1858. No one had ever written down the number

62457457257257.948498387698873981787398682739568871388789718824588428806588904358948835808848848946898648684

in 1858 but did that mean it didn't exist? Call "inf - b" by the name "the crunchy number." No one had come up with a way to describe the crunchy number in 1858 but it still existed, even if no one had ever yet pondered it. In 2018, I introduced a definition which allow us to represent this number in the usual algebraic format. I did not redefine the reals, I introduced some useful notation.

>>10555375
Neither Euclid, Eudoxus, nor Archimedes wrote that. Who are you quoting? You didn't tweak it just so that it would support your argument did you?

[Anonymous No.10555472]

Gosh... maybe if I can just BTFO these guys one more time then I can get paid for my work and then use that money to improve my life!

[Anonymous No.10555870]

>>10555347
>There is no proof, it's axiomatic.
If you take that axiom for granted, then I agree with you. I, however, do not grant that axiom.

>Please show me where Riemann or his contemporaries ever treated R as disconnected.
This request is totally stupid. One defines a set and then proves whether or not is connected. It does matter how you "treat" it. It matters what you can prove (unless you start taking axioms).

[Anonymous No.10555876]

>>10555405
>I have proven that the "field" definition does not work for RH.
Where?

>You have been unable to prove the same for the "cut" definition.
I don't need to prove anything about arbitrary definitions you made up. Only you demanded that definitions conform to what Riemann knew about and by your own standards you failed.

>My claim which I cannot find evidence for is that the reals were defined as cuts in the number line before RH. My claim is that you have been unable to do so because Riemann himself defined reals as cuts in the real number line.
That which can be claimed without evidence can be dismissed without evidence.

>I see you are attempting to paraphrase the Eudoxus statement of Archimedes' property as it appears appears in Euclid's Elements
If you scroll down in the wikipedia page you took a picture of you'll see the various definitions. Notice that all of them say n is a natural number, not a real number. So the only one paraphrasing what you wish it to say is you.

>I suspect you have deliberately mischaracterized this property because you know good and well that real numbers in the neighborhood of positive infinity behave the under the Eudoxus criterion exactly like negative real numbers.
I didn't characterize it, I just looked up the definition. Again, the only one deliberately mischaracterizing various properties is you.

>If you want to be very strict about the property as it appears in Euclid's book, then negative numbers are not real numbers.
I want to use the actual definition of the real numbers. You're the only one playing semantic games. Either way you lose, since the idea that the natural numbers are bounded by a real is and always was contradictory with their conception. It's as simple as that.

[Anonymous No.10555887]

>>10555429
>In support of my claim that numbers are cuts in the line I will point out my opinion that Dedekind has a specific cut named after him because he was studying cuts, and it is my further opinion that Dedekind became interested in cuts because the definition of real he used was the same as mine.
I will point out that these are nothing but desperate figments of your imagination.

>This is a number
No it's not.

>not a definition.
I never said it was, I said it didn't exist in 1858.

>All cuts in the number line existed in 1858.
Cuts in the number line didn't exist 1858.

>in 1858 but did that mean it didn't exist?
Why are you arguing against yourself? The fact that real numbers were not rigorously defined until after 1858 does not mean that the real numbers (as they are defined, not as you arbitrarily re-define them) didn't exist in 1858 and that Riemann was not referring to them via the general understanding of them, such as the fact that they did not bound the naturals, which had been taken as fact for thousands of years.

>I did not redefine the reals, I introduced some useful notation.
Then why does your definition conflict with the definition currently in use and the fact that the naturals are not bounded by a real? Because you are redefining them and your definition is useless.

[Anonymous No.10555898]

>>10555870
>If you take that axiom for granted, then I agree with you. I, however, do not grant that axiom.
Too bad, the problem calls for it.

>This request is totally stupid.
Yes, because it's clear Riemann, and no one else who isn't mentally ill, ever did so.

>One defines a set and then proves whether or not is connected.
But that's wrong, Riemann didn't have a definition of the set, only an incomplete set of properties that allowed for the conclusions of the mathematics he created.

[Anonymous No.10555918]

>>10554437
The answer is 4 and everyone else is retarded

[Anonymous No.10555927]

>>10555876
>Where?
This is a good question because I have only proven via the citation of Dedekind's paper that Dedekind's cuts did not exist until the 1870's. To prove that all reals cannot be defined in terms of fields, please note that a number field is an extension of the rational numbers, and the rationals are only a subset of the reals. If you want to make a definition "the reals are the extension of a subset of the reals" then please do so and I will criticize you for circular reasoning.


>arbitrary definitions you made up.
I didn't make this up. This was the definition I was given when I studied real mathematical analysis at a university in 2007. In which year did you study real mathematical analysis at a university? If none, please take that as evidence of my subject matter superiority over you, you feeb.

>That which can be claimed without evidence can be dismissed without evidence.
This is false. A claim can only be dismissed when it is disproven. Your philosophical faculties are as pathetic as your analytical faculties.

>So the only one paraphrasing what you wish it to say is you.
I haven't paraphrased it all. I have given the most general statement of Archimedes principle, that which is encapsulated by any number of statements of the principle such as teh Eudoxus statement that you have bastardized by adding the word "positive." Notice that if you don't add the word "positive" but only use the original words, then negative numbers are not real numbers, and this tells the Eudoxus statement is not very rigorous int he modern sense.

> I just looked up the definition.
Citation needed.

>I want to use the actual definition of the real numbers.
If you want to claim, "The reals are an extension of a subset of the reals," then please do so. I have a nice rebuttal ready for that.

[Anonymous No.10555945]

>>10555887
>I said it didn't exist in 1858.
You're wrong and stupid then. Every number has always existed.

>Cuts in the number line didn't exist 1858.
This is patently stupid.

>real numbers were not rigorously defined until after 1858
You have outed yourself as a fool. You think Riemann wasn't using a rigorous definition of numbers? I bet you do think that, you idiot.

>why does your definition conflict with the definition currently in use
It's because I made a "discovery." All new discoveries always alter the existing knowledge base.

You're stupid. If you have other descendants besides me, I'm going to give them to the rapists and the monsters before I put you down. Haha, suck on that.

[Anonymous No.10555950]

>>10555898
>Riemann didn't have a definition of the set,
He did have the definition. The definition he used was that numbers are cuts int he real number line. Prove me wrong.

[Anonymous No.10556002]

>>10555927
>To prove that all reals cannot be defined in terms of fields, please note that a number field is an extension of the rational numbers, and the rationals are only a subset of the reals. If you want to make a definition "the reals are the extension of a subset of the reals" then please do so and I will criticize you for circular reasoning.
How is that circular reasoning?

>I didn't make this up. This was the definition I was given when I studied real mathematical analysis at a university in 2007.
No, it was a naive statement you misinterpreted by taking as a literal definition.

>In which year did you study real mathematical analysis at a university?
2009. If you did take such a real analysis course you would have been taught the rigorous definition. So either you are pretending not to know it or you failed to learn the material you were supposed to.

>This is false. A claim can only be dismissed when it is disproven.
Then I claim your claim is false and this cannot be dismissed until it's disproven. I've already disproven your claims by reference to the definitions of the real and natural numbers which you have yet to disprove. So I'll just take this is an admission of the failure of your argument.

>I haven't paraphrased it all. I have given the most general statement of Archimedes principle
What you gave is not a statement of the Archimedean principle at all, according to the definitions in the source you quoted from. Plus you keep ignoring that Riemann would be operating under the fact that the naturals have no least upper bound.

>Notice that if you don't add the word "positive" but only use the original words, then negative numbers are not real numbers
No it doesn't. It says "for any positive numbers x and y..." It says nothing about negative numbers, rather than saying negative numbers violate the principle. FYI, Archimedes had no conception of negative numbers.

[Anonymous No.10556007]

Are you all still here stroking each others brains off? You all need to get outside, get some play friends or something, lol. There's a good chance most of these posts are just him arguing with himself for practice, lol.

[Anonymous No.10556011]

>>10555927
>Citation needed.
I already told you, it's in the wikipedia page you took a picture of. The one you keep trying to pretend doesn't exist.

>If you want to claim, "The reals are an extension of a subset of the reals," then please do so.
The reals are an extension of a subset defined without reference to the reals. Are you really that stupid that you don't understand the difference between a definition and a description?

[Anonymous No.10556026]

>>10555945
>You're wrong and stupid then. Every number has always existed.
And inf-b is not a number. Congratulations on finally getting it!

>This is patently stupid.
Your claim, which you know is a pure figment of your imagination, is patently stupid.

>You have outed yourself as a fool. You think Riemann wasn't using a rigorous definition of numbers?
Riemann was not using a rigorous definition of the real numbers since such a definition was not yet invented. Also, he did not use "cuts in real number line" nor is that a rigorous definition. It's merely a handwave taken too literally by a mentally deranged individual in 2007.

>It's because I made a "discovery."
The only thing you "discovered" was that you never learned the definition of the reals even though you took a real analysis course. If your "discovery" leads to conclusions that contradict basic mathematical truths, such as the natural numbers being bounded, then this constitutes a discovery of a failure in your understanding of the concepts being used to reach that result. But because you are mentally ill, you are incapable of seeing your failures as failures and instead invent an alternate reality complete with it's own pseudohistory of mathematics.

>If you have other descendants besides me, I'm going to give them to the rapists and the monsters before I put you down. Haha, suck on that.
I can't imagine the pain you will feel when you are close to dying and the realization that none of these delusions of grandeur are coming true finally sinks in.

[Anonymous No.10556027]

>>10556007
No, I think this is my mother flinging in shit at me because nothing makes her feel better than to convince people that I'm the caliber of retard that she is.

>>10556011
Please confirm then that you are employing the definition, "The reals are a number field where number fields are an extension of the rational numbers which are themselves a subset of the reals."

>The reals are an extension of a subset
A subset of what? What is it that the rationals are a subset of you miserable fucking idiot who is almost surely going to prove to stupid even to kill yourself when faced with unimaginable torture at the hands of your enemies which I will gladly give you to, probably. Just kill yourself, please, I beg you. Just take responsibility for your life and end it. Take some pills or buy some vitamin H. Maybe jump in front of a train. Do you own a gun? Point it at your spine through your mouth.

[Anonymous No.10556031]

>>10556026
>Riemann was not using a rigorous definition of the real numbers

[Anonymous No.10556034]

>>10555950
>He did have the definition. The definition he used was that numbers are cuts int he real number line. Prove me wrong.
OK, this is very easy. Riemann knew that there were infinite primes. Since the primes are a subset of the natural numbers, this means the natural numbers cannot be bounded. But your definition of the real numbers means they are bounded. Thus Riemann did not hold your definition of the real numbers.

[Anonymous No.10556042]

>>10556027
>Please confirm then that you are employing the definition, "The reals are a number field where number fields are an extension of the rational numbers which are themselves a subset of the reals."
That's not a definition, that's just a description. The definition of the rational numbers does not refer to the reals. The rationals are only found to be a subset of the reals after the reals are defined. So there is nothing circular going on. You are barking up the wrong tree and making a fool of yourself.

[Anonymous No.10556047]

>>10556042
You should define a rational number without referencing real numbers then.

>>10556034
does not sequitur

[Anonymous No.10556048]

>>10556031
>Riemann was not using a rigorous definition of the real numbers
Yes, the first rigorous definition was created by Cantor in 1871. Are you still trying to creating pseudohistory to shore up your delusions?

[Anonymous No.10556052]

>>10556047
>You should define a rational number without referencing real numbers then.
Look up the definition in any textbook you want.

>does not sequitur
It's a very simple proof, you should be able to show me where it goes wrong. But we both know it's correct.

[Anonymous No.10556056]

>>10556048
Pythagoras was non-rigorous.
Euclid was non-rigorous.
Euler was non-rigorous.
Isaac Newton was non-rigorous.
James Clerk Maxwell was non-rigorous.

I think I see where you're going with this. You're going to hell.

[Anonymous No.10556060]

>>10556052
>It's a very simple proof
I put all my simple proofs in the thread.

[Anonymous No.10556066]

>>10556056
The first two had no conception of real numbers and the rest did not have a rigorous conception of the real numbers. The notions they used were good enough for what they used them for. What is your point?

[Anonymous No.10556072]

>>10556060
OK but I just proved your entire argument wrong and your only response is "does not sequitur." So clearly you have no counterargument and have nothing left but delusions. See you in the next thread when you get destroyed again.

[Anonymous No.10556073]

>>10556066
>good enough for what they used them for.
> What is your point?
This is the definition of rigorous

[Anonymous No.10556077]

>>10556073
No, it's essentially the opposite of rigorous. But this is all irrelevant. Riemann knew your definition of the reals is wrong. You lose, good day sir.

[Anonymous No.10556874]

>https://www.math.ucdavis.edu/~hunter/intro_analysis_pdf/intro_analysis.pdf
I was looking through some stuff. I found these nice chapters on real analysis. It says that
( R , +, · )

is a field. Therefore, R is not a field. Thus it demonstrated. Let it be known.

The contentious issue with R-hat not being a field is that it does not satisfy condition (f) related to the multiplicative inverse. Since we have added an exception for {0} and zero is still a real number, we may likewise add an exception for numbers in the neighborhood of infinity.

Detractors will say, "No, zero is the only exception because it is super special." I rebut that with, "The reason R-hat doesn't appear in the exceptions to (f) is because the author did not consider such numbers. If zero was an extra special super exception then the author would have written something like, 'Zero is the one and only exception to (f) and all other possible exceptions are ruled out by Theorem XXX.'"

In closing and without reference to my opinion about what the author would have done, take careful note that NOT all real numbers satisfy the field axioms. This is a fact. If you can add an exception for whomever came up with zero then you can add an exception for me. I'm not requesting a special exception. I am requesting the same exception afforded to the discoverer/inventor of the number/numeral zero.

[Anonymous No.10556885]

Infinity is a number. Let it be known.

[Anonymous No.10556910]

Obviously, I do not agree with this statement of the Archimedes property. I disagree because I have shown that R does not have this property, and the statement of the Archimedes property should be such that R does have it.

[Anonymous No.10556951]

>>10556910
Real numbers inherit that property because they're an extension.

Dude it is so blatantly obvious that if inf is not part of the reals so isn't inf-b or any finite combination with real numbers. You've wasted your time and ours. No go back and do something productive.

[Anonymous No.10557033]

>>10556951
"i" isn't part of the reals but "i^2" is. What's the difference with "inf" and "inf-b"?

[Anonymous No.10557190]

>>10556874
>Therefore, R is not a field. Thus it demonstrated. Let it be known.
R the field is R the set with addition, multiplication and ordering. What is the issue?

The rest is irrelevant as the problem is not about some field or set you made up, but about the field defined in your pic. Choose one: you failed to solve the RH as it's written or you solved some problem you made up that no one cares about.

[Anonymous No.10557204]

>>10556910
Where did you show that R direwolf not have this property? All you've shown is thai inf-b is not real since it does not allow for this property to be true. And Riemann's conception of the real numbers necessitates this since he knew the integers are not bounded. So by your own logic, you have failed to answer the RH.

[Anonymous No.10557210]

>>10556910

[Anonymous No.10557211]

>>10557033
The difference is that inf-b is not part of the reals by definition.

[Anonymous No.10557224]

>>10557190
>What is the issue?
R in the context of my argument is a set, as in "R is the set of all real numbers."

There are very many statements of the Archimedes property of real numbers. If you choose one that disallows my numbers then my numbers are disallowed. The main gist of the property that is encapsulated by EVERY statement of it is that every real has a larger real. My numbers conform to the main gist. Since neither Archimedes, Eudoxus, nor Euclid used what you are claiming to be the special ultimate statement of Archimedes' property, you will have a hard time convincing me that the statement you selected is the main gist of the property.

>>10557204
R direwolf is defined to be larger than every natural number. It's in the paper.

>>10557204
>he knew the integers are not bounded.
This was Riemann's opinion, one I have disproven.

[Anonymous No.10557229]

>>10557211
By definition, it is part of the reals. Therefore your claim is false. I have proven this in the paper. You have only made a claim without proof.

[Anonymous No.10557232]

Itt a bunch of retards arguing if some parts of math are valid only after a certain time after some dude died

[Anonymous No.10557241]

>>10557033
The reals are a subset of Z but nobody said shit about infinities

[Anonymous No.10557256]

>>10557241
>reals are a subset of Z
no

[Anonymous No.10557260]

>>10557224
>R in the context of my argument is a set, as in "R is the set of all real numbers."
So?

>There are very many statements of the Archimedes property of real numbers. If you choose one that disallows my numbers then my numbers are disallowed.
There are only a few for different contexts of real numbers and they all say that the naturals are not bounded. Riemann knew this. You demand that my arguments conform only to what Riemann knew but then that gets ignored whenever you make an argument. This is hypocriticlal special pleading.

>R direwolf is defined to be larger than every natural number. It's in the paper.
That sentence should read "where did you show R does not have this property?" If your define a number larger than every natural number then that number is not real.

>This was Riemann's opinion, one I have disproven.
Not an opinion, an axiom. Redefining numbers is not a proof of anything.

[Anonymous No.10557268]

>>10557229
>By definition, it is part of the reals.
Why are you lying?

>You have only made a claim without proof.
I proved it easily here >>10556034
and you failed to provide a counterargument.

[Anonymous No.10557279]

>>10557232
Actually my point is inf-b is not and never was able top be considered a real number. Only the schizo pretended to care about what Riemann knew but then of course that gets abandoned as soon as the schizo starts talking about his made up numbers. Unfortunately, mental illness often leads to such logical failures.

[Anonymous No.10557541]

>>10557260
>they all say that the naturals are not bounded
The statement, "There are no infinite or infinitesimal real numbers," doesn't say anything about naturals.

>You demand that my arguments conform only to what Riemann knew
I don't demand that at all. My issue is that you are claiming that the domain of zeta is restricted by a definition that didn't exist until almost 20 years after RH was published. This is completely stupid.

>This is hypocriticlal special pleading.
No, that's you raising a straw man to argue against by attributing to me words that are not my own.

>Not an opinion, an axiom.
It was his opinion that this axiom is universally valid.

[Anonymous No.10557764]

>>10557541
>The statement, "There are no infinite or infinitesimal real numbers," doesn't say anything about naturals.
This statement is only equivalent to the Archimedean principle if by "infinite real number" one means a real number that bounds the naturals.

>I don't demand that at all.
You did that here >>10555252

"I don't define R differently. A real number is a cut in the real number line. What definition of reals do you use? (Please don't refer to a definition that didn't exist until after Riemann published his hypothesis.)"

>My issue is that you are claiming that the domain of zeta is restricted by a definition that didn't exist until almost 20 years after RH was published. This is completely stupid.
No, my claim is that the domain of zeta is restricted by properties of the reals that Riemann knew of (and that were known for thousands of years before Riemann). Your definition contradicts the properties inherent to the problem, which is completely stupid.

>No, that's you raising a straw man to argue against by attributing to me words that are not my own.
They are your own words, you literally demanded that the definition of the reals conform to what existed before the RH was published.

>It was his opinion that this axiom is universally valid.
It is universally valid in the reals, since it's axiomatic. If you could show that this axiom was contradicted by any other axiomatic property then you would have done so by now. Instead you just show that your assumption that inf-b can be a real is contradicted by it. This does not constitute a disproof of the axiom, it constitutes a disproof of your assumption. You're basically admitting that you know your argument is wrong, but your delusional state prevents you from doing so explicitly. So you behave as if your assumption takes precedence over an axiom forming the basis of the problem. It's quite pathetic.

[Anonymous No.10557942]

>>10557764
nah

[Anonymous No.10557997]

>>10557942
Thanks for admitting defeat.