/sci/ - Science & Math

>changing definition of real numbers

>>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.

>>10481133
We've been over this before with the Archimedean property.

>>10481141
Yeah, I know. I was bored so I wanted to BTFO you faggots again before I give you, your friends, and your loved ones to some third world barbarians that don't speak your language. Pic related, the real numbers in the paper respect the Archimedean property.
>inb4 you post someone's statement of the property who failed to account for all real numbers when they were putting together the statement that you guys all failed to notice was wrong 200 years until I came along and showed you how brains are supposed to work.

>>10481158
>Pic related

>>10481158
>the real numbers in the paper respect the Archimedean property.
Only when you change the definition of the Archimedean property...

>>inb4 you post someone's statement of the property who failed to account for all real numbers when they were putting together the statement that you guys all failed to notice was wrong 200 years until I came along and showed you how brains are supposed to work.
... which you admit to.

>>10481167
I didn't change the property. Archimedes (transalted) wrote:
>Magnitudes are said to have a ratio to one another which can, when multiplied, exceed one another.

There is no violation of this statement in the paper. More importantly, the main thing about Archimedes' principle is that real numbers are neither infinite nor infinitesimal, and the numbers in the paper respect that principle.

>>10481188
Alright, so what is a number in the neighborhood of infinity multiplied by a number in the neighborhood of zero?

Do some math with your useless definitions

>>10481167
>which you admit to.
I admit to using complete sentences, and I also admit that pic related is the only formulation of the Archimedes that matters. All other formulations are intended to restate this general principle for specific application.

Real numbers in the neighborhood of infinity respect this principle! Who will deny it?!?!?!? Who will give an example of a number which I call a real number and yet that number does not conform to pic related property? (Nobody is the answer.)

>>10481188
Of course, in the context of Euclid's Elements, "multiply" here refers to multiplying by an integer.

>>10481195
Name one integer larger than infinity hat minus 0.1

>>10481205
Infinity hat plus one

JK Tooker needs meds

>>10481195
wrong pic, oops.

>>10481193
What does multiplication have to do with the Archimedes property? I think you are getting the property confused with someone's statement of the property.

>>10481204
>"multiply" here refers to multiplying by an integer.
Multiply 0.5 by an integer. (It comes out smaller than the integer.)

>>10481216
But not smaller than 0.5

>>10481212
So you can't do math with the numbers you made up? Interesting. I'd like to declare a previously unnamed and unexplored interger between 10 and 11 called eleventy. It has all of the properties you would expect for an interger between 10 and 11

>>10481204
To be more accurate: multiply by a positive integer.

>>10481220
Here's some math for you. The Archimedes property of real numbers requires that for every real number X there is a large real number Y, this is to say: there are no infinite or infinitesimal elements of the real number system.

Consider any number in the neighborhood infinity (inf - b), and any other real number such that 0 < a < b. Then we find that for any real number (inf - b) there exists another real number (inf - b - a) which is larger than (inf - b). Therefore, all real numbers in the neighborhood of infinity have the Archimedes property.

>>10481241
I like how you always use a different statement of the Archimedean property when it suits your needs.

>>10481220
Let X be an integer between 10 and 11. That is
10 < X <11

Every integer may be obtained by adding one to the supremum of all smaller integers. 11 is greater than X so 10 is this supremum.
10 + 1 = X

This is a contradiction because 10 + 1 =11 but we have already required that X < 11.

Your example is totally stupid.

>>10481246
I only use the one definition: For every X in R there exists a Y in R such that X<Y.

I dislike how you say things happen but then don't cite a case of that thing happening because it did not ever, actually, happen.

>>10481252
You just aren't adding it right

>>10481259
Come on now.
First: >>10481162
Second: >>10481188
Third: >>10481195
And now fourth: >>10481259

>vixra
utterly embarrassing

>/sci/ is still falling for this b8

>>10481265
For the third one:
>>10481212
>wrong pic, oops.

Those other three are all the same.

In my own words, "The Archimedes principle states than for every real number X, there is a larger real number Y, namely there are no infinite or infinitesimal real numbers."

>>10481195
Infinity is a property not a number

>>10481307
I think that thing you wrote is totally stupid but it is only a matter of semantics. I agree, however, that infinity isn't a real number.

>>10481300
Well gee, what is the right pic then?

>Those other three are all the same.
Uh huh.
>It is the property of having no infinitely large or infinitely small elements
>Magnitudes are said to have a ratio to one another which can, when multiplied, exceed one another.
>The Archimedes property of real numbers requires that for every real number X there is a large real number Y

The last one, the one you made up, is not the same as the other two. A number being infinite means it is larger than any integer. What is an integer that is larger than infinity hat minus 0.1?

>>10481316
I was not counting Archimedes words as my own. This is the definition I use, the one at the top of the Wikipedia page: "The Archimedes principle states than for every real number X, there is a larger real number Y, namely there are no infinite or infinitesimal real numbers."

>What is an integer that is larger than infinity hat minus 0.1?
Why are you restricting to integers? It is sufficient for there to be a greater number and there is:
(inf - 0.00001) > (inf - 0.1)

>>10481337
>Why are you restricting to integers?
Because that's the definition of being infinitely large, no matter how much you'd like to change it.

>>10481352
"Hurr durr, restricting to integers is the definition of being infinitely large."
You almost made a coherent statement there! Nice! Try using more words and you will get there.

PIC: Independent, original proof that some real numbers are larger than every natural number.

>>10481374
no, you can't call that a proof
cuz its wrong

>>10481374
A number is infinitely large if and only if it is larger than every natural number. This definition dates back to Archimedes. You insist that you aren't changing definitions, but then you raise a fit every time I call you out on using different definitions.

>>10481119
>modded infinity is exactly the same as infinity unless there’s a logical contradiction, in which case it’s magically not the same
holy shit this is stupid

>>10481408
hes been at it for years

>>10481408

>>10481419
1=2 is an established contradiction though, and the assumption that an object like 0hat exists led to it, so therefore 0hat does not exist.

>>10481404
I dispute the "if and only if" condition there. I can provably demonstrate the existence of finite numbers larger than every natural number. These numbers are not infinitely large.

>>10481408
yeah, with all these consistent definitions that ~always~ work in ~every~ case you can tell its not even real math

>>10481434
>I dispute the "if and only if" condition there.
Then you're using a different definition of infinite.

>>10481434
Give me a number then. I can find another natural that is bigger. This is a contradiction that your number is bigger than every natural.

You have to do away with this neighborhood of origin and infinity stuff.

This thread is stupid.

Real numbers are not the same as hyperreal numbers.

https://en.m.wikipedia.org/wiki/Hyperreal_number

>>10481436
You are the one using a different definition to:
>A number is infinitely large if and only if it larger than every REAL number.

>>10481459
Yeah, because that's nobody's definition but your own.

>>10481434
>I can provably demonstrate the existence of finite numbers larger than every natural number.
you haven't done that tho
in fact its trivial to disprove

>>10481444
>do away with this neighborhood of origin and infinity stuff.
NO PROBLEM

>Give me a number then. I can find another natural that is bigger.
OK HERE YOU GO

(1) Every line segment has a midpoint.

(2) If C is a midpoint of AB then
AC = CB = 0.5*AB.

(3) A line segment AB is a real line segment if the endpoints A and B bound some subset of the real line (-inf,inf).

(4) Let AB be [0,inf].

(5) Every point of AB is a real number except B=inf.

(6) The midpoint C of AB is a real number.

Please tell me which natural number is larger than the number at the midpoint of [0,inf].

>>10481470
I disagree with your proposition that have a unique definition for "infinitely large" or even that there is one such definition generally accepted to be better than all others.

>>10481472
I did. Here it is in the pic right here. Without reference to widehat infinity, I prove that there are elements of R greater than every element of N

>>10481485
You go from talking about real line segments to suddenly discussing half of the extended real line. That's a nice sleight of hand, but it's not a proof.

>>10481511
> from talking about real line segments to suddenly discussing
Yes, I define line segments and then I discuss a particular line segment. Did you fail to notice that half the extended real line conforms to the definition of a line segment?

>>10481485
Yeah, uhhh, half of the extended real line is not a line segment. Nice try.

>>10481485
given any real number n, n can be written as a largest integer less than n, and the fractional part of n
the largest integer less than n +1 is an integer larger than n

your construction of D_ab is contradictory
"Dab is bijective"
"Dab also sends all naturals to 0"
"No that doesn't mean it fails to be injective"

>>10481524
A line segment is a line with two endpoints. You are, uhhh, retarded.

>>10481536
infinity isnt an endpoint

>>10481536
Yeah, real number endpoints.

>>10481529
Domain of Dab isn't numbers. Domain is line segments. Please read first, then make counterarguments.

>>10481542
that isnt a counter argument
you take in numerous different line segments to the same output

>>10481539
It is.

>>10481540
No. A line segment is a real line segment if the endpoints bound some subset of the real line.

>>10481546
And so now, on top of different definitions of real numbers and Archimedean principle, we have a different definition of line segment.

>>10481553
*property

>>10481545
No. If two line segments are such that
Dab(AC) = Dab(AD) then the two line segments are equal
AC = AD

Every line segment within AB has a unique Dab

>>10481553
No, this is the usual definition of a line segment and conforms to the most general statement of the Archimedes property.

>>10481563
>No, this is the usual definition of a line segment,
So you're saying that rays are line segments. Nice try.

>and conforms to the most general statement of the Archimedes property.
By "most general statement" you mean "the one I made up out of desperation because the actual statements of the Archimedean property don't work for my numbers".

>>10481569
A ray is a line with one end point. An example is the interval [0,inf).

A line segment is a line with two endpoints. An example is [0,inf] != [0,inf).

>By "most general statement"
I mean I'm using the one in the first paragraph of the Wikipedia article.

>don't work for my numbers
They don't work for numbers less than one or negative numbers, and you have no problem rationalizing those exceptions because preserve the predicate that every real number X is such that there exists a greater real number Y

>>10481477
I'm only in calc 2 and even I know you're just bending the definition and misusing infinity. It isn't an arbitrarily large number duder, you can't just get half of infinity.

>>10481558
that is not true
1 to 10
is not
1 to 11

and yet D(1,10) = 0 = D(1,11)
also D(1,1) = 0
you are wrong

You also haven't proven that D is continuous for the ray "line segment" [0,inf)
ps, its not continuous

So this is the power of \widehat. I always knew this day would come.

>>10481582
none of that post is accurate

>>10481582
>I mean I'm using the one in the first paragraph of the Wikipedia article.
You mean the one that says "roughly speaking"? And the one where I told you what infinitely large means and you covered your ears and said it doesn't have an accepted definition? That definition?

>They don't work for numbers less than one or negative numbers
One is an integer larger than all of those. And negative numbers aren't magnitudes as formulated in Euclid's Elements, so of course the formulation in terms of magnitudes doesn't cover negative numbers. But it does cover positive numbers smaller than one.

You just don't know basic mathematics.

>>10481589
rofl

>>10481582
The Archimedean property on the reals is equivalent to

for any x in the real numbers, the set of integers greater than x has a least element.
Also equivalent to,
every real number is less than some natural number.
Both of which prove the negation of your statement.

those equivalences are on the very same wiki page for the Archimedean Property
Maybe if you could read past the first paragraph you'd learn something.

if you want to use a consistent form of mathematics
and thus give us a reason to listen to you
i recommend you figure out why we all have issues with your "proofs" as you call them

>>10481589
640 by 480, that's what God said, VGA.

oh no he's sulking now

>>10481586
1 to 10 is an algebraic interval, not a geometric line segment.
>you are wrong

>>10481597
Those are two different definitions, so no, not that definition. I like the "roughly" speaking def of Archimedes' principle because because it tells you the important point that has to be made by any rigorous statement of Archimedes' property. Without the "rough" definition, people like you might want to argue that Archimedes' property is about the properties of real numbers under multiplication but that is not right. The multiplication is only there to show a rigorous case of the "rough" definition.

>And negative numbers aren't magnitudes as formulated in Euclid's Elements
AHA!!! Then it easy for me to make the same claim about real numbers in the neighborhood of infinity because Euclid's elements only considers positive numbers in the nbhd of the origin.

>>10481623
I think your definition is less fundamental than mine because my definition only makes reference to real numbers but you have to make an ancillary construction "integers." I think AP is not equivalent to what you wrote but rather is equivalent to:
for any x in the real numbers, the set of real numbers greater than x has a least element.

>i recommend you figure out why we all have issues
You're not going to like it when that happens!!!

>>10481683

>>10481683
>1 to 10 is an algebraic interval, not a geometric line segment.
>he doesnt know what coordinates are
cope

>I think AP is not equivalent to what you wrote but rather is equivalent to:
you can think it as hard as possible
but youre still wrong

I dont give a shit what property you're using and then naming the Archimedean Property
because it isn't the Archimedean Property, I don't care that your property works for your numbers
The Archimedean Property doesn't hold, therefore your numbers are useless

>>10481700
>Archimedean Property
It's that every real number is smaller than some other real number. Archimedes property as written by Archimedes doesn't hold for negative numbers and we still find that they are plenty useful and REAL

>>10481728
holy shit
>an ordering is the archimedean property now
way to totally miss the point, thats not at all what it is
thats not even close

>>10481485
D_ab maps to R as defined in 4.7.
Yet in the Proof of 4.25 you claim to have found a number X such that D_ab(AX)>D_ab(AX). In other words, you have found a real number that is strictly greater than itself. Explain how this is not a contradiction.

>>10481119
I hope for your own sake that you legitimately have a serious mental issue because that is the shittiest, most pseudo mathematical paper, if we can even call it that, i've ever seen.

>>10481119
>tfw tooker broke into ga tech so he could shitpost from a non-banned ip

>>10481792
>D_ab(AX)>D_ab(AX)
typo should say
D_ab(AX)>D_ab(AN)=0

who let tooker out of prison

>>10482325
I was in jail, not prison. Unless you meant space jail... that might be prison. I'm not familiar with space law.

>>10482369
Put on your \widehat for the next picture. I think that will help.

>>10482991

>>10483010
what is the true powerlevel of widehat?

So you're out of jail finally?

>>10481291
Fuck off these are the only interesting threads we have anymore

>>10483031
It's hard to tell if you mean meme jail or real jail. I was locked in a real small concrete box for about 50 days there, but they unchained me and I can walk around outside the box now.

>based tooker is back
nice thread as always my man

Shhhh Shhhh let it die already.

>>10483071
Real jail. I didnt expect you back for a while, it looked like some of the stuff they charged you with had mandatory minimums

>>10481477
3 and 4 are contradictory. The results do not follow.

>>10484052
>3 and 4 are contradictory.
What do they contradict? Let 0 and inf be two points that are endpoints of a subset of (-inf , inf). A line segment is a line with two end points. A line segment is a real line segment if the two endpoints bound some subset of the real line R = (-inf , inf). I don't see a contradiction. Where is the contradiction?

>>10484645
The contradiction is that you stated a real line segment exists in (-inf,inf) but then claimed AB is [0,inf]

In case you didnt know, [] is inclusive, and () is exclusive. Therefore [0,inf] does not meet the definition in 3.

Also, including infinity in the first place is circular to your argument and I suspect you actually do know this and are just trying to sneak in your infinity hat shenenagins hence my first statement about needing to abandon it.

>>10484645
> [0, inf] is a subset of (-inf, inf)
> "Where do they contradict?"

>>10481683
>AHA!!! Then it easy for me to make the same claim about real numbers in the neighborhood of infinity because Euclid's elements only considers positive numbers in the nbhd of the origin.
Sure, just ignore the thousands of years of history in mathematics.

>>10484666
>does not meet the definition in 3.
[0,inf] is two endpoints "0" and "inf" together with a subset of the real line: (0,inf). You are totally stupid.

>>10484677
>[0, inf] is a subset of (-inf, inf)
I see you are using greentext to quote yourself, and then you criticism of me to your own comment. I never claimed [0, inf] is a subset of (-inf, inf). What I claimed is that [0, inf] is a subset of (-inf, inf) bounded by two endpoints.

>>10485261
>thousands of years of history in mathematics.
I'm not ignoring the thousands of years wherein people understood that the Archimedes property as stated in Euclid's book only refers to a subset of all real numbers.

>>10481431
whoosh

>>10485985
>What I claimed is that [0, inf] is a subset of (-inf, inf)
jon, dude, think about what you just said for a minute

>>10483071
Wait I don't come on /sci/ much these days I just thought this was a run of the mill meme thread, what the actual fuck is going on in here??

>>10486026
it’s a Jon Tooker thread, he’s our jolly resident schizo and he gets into high-level math arguments about nonsense math ideas and /sci/ mathbros tagteam him for shits and giggles until he edits his vixra articles and then repeats the cycle (except for when he went to jail)

>>10486026
iirc he went to jail for squating in an abandoned house, don’t know how long he was there tho

The Reals don't exist

>>10486032
Ahh, I thought it was just someone memeing, but in hindsight nobody can imitate a schizoposter this well

>>10481477
Points 1, 2, 3 here are a good example of what is wrong with most of the supposed mathematics you are writing.

>(1) Every line segment has a midpoint.
>(2) If C is a midpoint of AB then AC = CB = 0.5*AB.
Okay -- this is true for (a particular version of) what most mathematicians understand to be a line segment.

>(3) A line segment AB is a real line segment if the endpoints A and B bound some subset of the real line (-inf,inf).
This is NOT what most mathematicians understand to be a line segment. A bound on the subset of the real line is not, in general, what most mathematicians would call a "line segment", nevermind a "real line segment".

This is fine. You are totally allowed to define your own extended notion of a line segment, that is different from what people are used to.

But if you do that, then statements (1) and (2) don't follow anymore. Statements (1) and (2) hold for what most mathematicians would call a "line segment", so you can state these properties without argument and move on. But you are not using that notion -- you are using a different, extended concept of "line segment". Which means you need to prove, independently, that statements (1) and (2) hold for your notion of "line segment". It holds for the standard notion, but you are not using that, so you'll have to show that it holds for YOUR notion.

To avoid issues like this, a rule followed in most mathematics is to never define a concept after having assumed properties about it. Always define first, list properties later:

>(1a) A line segment AB is a real line segment if the endpoints A and B bound some subset of the real line (-inf,inf).
>(2a) Every line segment has a midpoint.
>(3a) If C is a midpoint of AB then AC = CB = 0.5*AB.

Suddenly, it is now obvious that points (2a) and (3a) need proofs. In this notation, it is immediately obvious that I don't actually know what (3a) means, if applied to B = infinity.

>>10486011
...is a subset of (-inf, inf) bounded by two endpoints"

>>10485985
>What I claimed is that [0, inf] is a subset of (-inf, inf) bounded by two endpoints.

>>10486087
>This is fine. You are totally allowed to define your own extended notion of a line segment
I agree.

>>10486087
>To avoid issues like this
The ones where you make a word salad?

>never define a concept after having assumed properties about it
This general rule is a good general rule.

>>10486009
ok I’ll bite. what’s the problem with that statement, schizo poster?

>>10487477
Slapping is a capital offense.

>>10481193
you're talking about indeterminate forms, which is what l'hopital's rule is all about

>>10487495
???

>>10481119
>Neighborhood of Infinity
compared to inf,
TREE(TREE(3)) and 1 might as well be the same number

>>10486087
Pointless rant. According to his definition, there is no subset of (-inf,inf) that contains inf. Assuming B=inf automatically implies it's the largest number, which is what he was originally trying to prove.

>>10487498
>Multiplication by two itegers yeilds 0/0
Are you feeling okay?

>>10488726
>Pointless rant. According to his definition, there is no subset of (-inf,inf) that contains inf. Assuming B=inf automatically implies it's the largest number, which is what he was originally trying to prove.