/sci/ - Science & Math

>>12021885
>criticism that your definition of the reals does not follow current conventional definition?
I introduced my definition specifically to show the relative inferiority of the conventions which I do not follow. I assume you're talking about the field axioms. My neighborhood of the origin is an explicit number field in the usual way but then there is a neighborhood of infinity as well. My definition does everything the field axioms do, and more. Furthermore, I respond with a criticism of my own that numbers were geometric in nature for thousands of years until this current trend of algebraic definition materialized in the last century or so. In that way, my definition is the one that follows the thousands of years of accepted convention and it is these algebraic definitions which are the odd ones.

> it does restate the original hypothesis in a way that diverges from its original intention, does it not?
absolutely it does NOT!!! Anything that can be called "current conventional definition" was published at least years after Riemann published and none of it came into common usage until at least decades after. In 1859 when Riemann published, real numbers were still geometric in nature.

>>11925987
Yes, Brian, that's one way to say it though I would probably like to introduce new jargon to differentiate finite numbers having "0% fractional distance with respect to infinity" from other finite numbers in the neighborhood of infinity which have "greater than 0% fractional distance with respect to infinity."

Sometimes I hope the people who rebel against me kill themselves to avoid succumbing to my wrath, but I do hope you remain alive for me to pour it out on you. I hate you with passion and zeal, Brian, and not in a general way at all, but you specifically are a person that I hate, and I desire to see you humbled and to hear your lamentations.

>>11925897
>>11925715
> let's say that I define a rule
If he does go ahead and define that rule instead of simply proposing that he might, then I will check it for contradictions so as to evaluate whether or not the rule is mathematical, which is to say that it is "mathematically valid."

>one invents arithmetic rules that depart from common convention
It was the arithmetic rules for number fields which departed from the common convention many years ago. The arithmetic rules I introduced support the convention that existed for thousands of years before the community erred in adopting the algebraic number field definition of R at the expense of its geometric definition. The geometric definition was in use from the time before Euclid until decades after Riemann published his hypothesis in 1859, and your criticism of my arithmetic scheme is rightly levied against the scheme given by the field axioms.

Also, I call you an asshole for suggesting in a roundabout way that Riemann's hypothesis from 1859 can only be analyzed in a framework of arithmetic (the complete ordered field axioms) which were a generalization of something Hilbert put together 1899. Since 1859 minus 1899 is a negative number, it is quite stupid to propose that RH depends on the field axioms.

>>11561185
>What I did say, however, is that your proof is not a proof of the RH.
And what you most certainly did imply, for the 900th time, is that the Riemann hypothesis from 1859 depends on some other definition from the 1870s or later.

Do you fail to realize how abso-fucking-lutely stupid it is to say that the Riemann hypothesis from 1859 can only be decided in terms of definitions of R that didn't exist or weren't published until many years later? Do you really not see how fucking stupid it is, ir did you see it just fine the first 50 times I explained the chronology to you and you are just getting paid to fling shit at my research because you were never smart enough to do anything original on your own?

If you are so smart, (((based poster))), then you should tell us all which definition of R is an acceptable one for the Riemann hypothesis. My conjecture is that every definition you might give did not exist in 1859, and therefore you are wrong and stupid.

Do you see how I already had pic related stock image ready to go because you have been making this same, "1859 hypothesis asks a question about something that didn't exist in 1872 or 1898," over and over and over, and you've getting BTFOed by me all along?

>>10780575
>We care about the "tarded" real field
Ok, well... like Riemann, I don't give a shit about the real number field. Like Riemann, I'm here to analyze numbers. Fields are cool, I guess, if you're into that sort of thing, but I'm not.

Field axioms can be traced to Dedekind in 1872. RH can be traced to Riemann in 1858.

>>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.)

>>10481127
Yes this is what people did to the historical definition of real numbers as cuts in the real number line. You can see in this paper that if you don't change the definition to something that's been put together in the last few hundred years then it is easy to show that RH is false.

>>10207909
>>10207912
Dedekind cuts are needlessly specific and the reason there is a variety of cut named after Dedekind is because everyone knows that the real definition of real numbers is as a "cut" in the real number line. This is definition Dedekind was working with that he added to but I reject his additions and I myself work with the same simple definition "cut" that Dedekind himself used.

>>10176538
I do know what it is. It's something Dedkind published many years after Riemann published his hypothesis.

>>10177255
Yes, but how far into the future do you think my ignorance will extend? Do you think it will exceed the natural life of all of you descendants, and theirs, and theirs, and on and on, such that I will never catch up with you and never take away your share in the tree of life? Maybe you tell yourself that, but do you honestly believe it? Maybe you do.

>>10136723

>>10108496
>Yes, but what _IS_ a cut?
A cut separates a line into two pieces.

>but what kind of object is it?
It's a number

>all the definition anyone requires.
Certainly I don't need more definition that what Riemann himself was working with.