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10155745 No.10155745 [Reply] [Original] [archived.moe]

Some real numbers are larger than every real number.

>Real Numbers in the Neighborhood of Infinity

>> No.10155753

Why have you abandoned the Archimedean property that has been accepted for more than two thousand years?

>> No.10155755


>> No.10155768

Maybe if you described the property instead of name dropping it I could give you a better answer. I googled it last time you made this comment and it told me something about number fields.
>Why have you abandoned descriptions of things in favor of their labels?

>> No.10155785

How could you possibly not know what the Archimedean property is?

It is the first thing you're told in baby analysis 1.

If you don't even know baby analysis, why the fuck are you writing about math you schizo.

>> No.10155790
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Actually, I looked it up again since I made the thread for discussions. I found pic. I think the Archimedian property must be the lower statement which I preserve and not the middle statement since the notation in the middle statement was known to Archimedes.

>> No.10155798

>How could you possibly not know what the Archimedean property is?
Probably for same reason you don't know the name of 53rd closest star to Sol.

The first thing I learned in my single semester of a two semester undergraduate course in real analysis was that a real number is a cut in a real number line. Baby analysis must not be very good if starts assigning properties to numbers before it defines numbers.

>> No.10155813

The statement you didn't preserve is true by definition of the real numbers, so you're wrong.

>> No.10155819
File: 31 KB, 624x218, TIMESAND___762++16bwddbf7de614rfde17tfre45t6547tfre45t654345tytre8er17t8634ct76c834yt7.png [View same] [iqdb] [saucenao] [google] [report]

What definition is that? Why do you guys "the definition" without including the definition, and cite "the Fart property" without describing what the fart property is?

>> No.10155823

The way it was formulated by Eudoxus, which I posted in a previous thread fyi, was that for any positive numbers x and y, with x < y, you can find an integer n such that n x > y

Again, this is babby level analysis, and if you're not using this property, you're going against thousands of years of mathematical knowledge for no reason.

>> No.10155830

Real numbers are the completion of the rationals under the absolute value norm. Nobody disputes this definition but you.

>> No.10155831

The definition of the real numbers is as the completion of the rationals with respect to the standard absolute value.

In number theory, that absolute value is genrally called an "Archimedean place" of the rationals because it satisfies the Archimedean property.

There are Non-Archimedean places of the rationals, they are the p-adic absolute values and completing with respect to them gives the p-adic numbers. But the real numbers are Archimedean.

>> No.10155841

I think this formulation of the property is superior to Eudoxus' formulation:
>The set of real number is unbounded above.

However, I can almost accommodate Eudoxus' formulation if I change it to:
>for any positive numbers x and y, with x < y, you can find a rational number q such that q x > y

Indeed, although
inf - 1

is as large as "integer-looking numbers" get in the neighborhood of infinity, you can multiply it by 1/2 to get
0.5 (inf - 1 ) = inf - 0.5

inf - 0.5 > inf -1

Likewise, I could adapt Eudoxus' version of the property to say
> for any positive numbers x and y, with x < y, you can find an integer n such that n x > y or x/n > y

In that case I can take
inf - 1

and divide by two to get
(inf - 1) / 2 = inf - 0.5

where, again,
inf - 0.5 > inf -1.

I think the main thing in the principle is that the reals are not bounded above, and that is something I have preserved.

>> No.10155842

Let x = 1 and y = infinity minus 1. Find n.

>> No.10155853

I understand what you mean "completion of the rationals" but could you say precisely what you mean "with respect to absolute value?"

>Nobody disputes this definition but you.
I think the definition that no one disputes is that the reals may be represented in interval notation as
R = (-inf,inf)

Does anyone dispute this definition? I dispute your definition about the completion of the rationals on the basis that it is impossible to fill the interval (-inf,inf) with rationals and the irrationals which squeeze between them if you don't include the number in the neighborhood of infinity.

HOWEVER, if one acknowledges that "completion of the rationals" does indeed fill the interval (-inf,inf) then I will be happy to agree that numbers in the neighborhood of infinity are irrational, or that they conform to whatever the specifics of "completed rationals" are.

So... does the completion of the rationals with respect to absolute value fill the interval (-inf,inf)???

>> No.10155857

Good counterpoint. "n" would have to be something like (inf - 0.5) but it is trivial to adapt Eudoxus' definition. I don't see a need anyhow since the main principle of the unboundedness remains even while the statement of the principle gains added nuance.

>> No.10155867

>I understand what you mean "completion of the rationals" but could you say precisely what you mean "with respect to absolute value?"

I mean completion of the rationals as a metric space with metric d(x,y)=|x-y| where |.| is an absolute value.

>> No.10155879

Then let the numbers in the neighborhood of infinity be irrationals. I don't think this even stretches the definition of irrational does it? Irration means simply "not rational" where rationals are quotients of naturals iirc. Certainly we have a metric space

Let x = inf - 5 and let y = -7. Then
d(x,y) = | inf + 2 |

You can say that this is (inf + 2) or (inf) depending on what works better.

>> No.10155887

>Then let the numbers in the neighborhood of infinity be irrationals.
That's not how completions work.

>> No.10155890

>I think the definition that no one disputes is that the reals may be represented in interval notation as
>R = (-inf,inf)
>Does anyone dispute this definition?
That's not a definition, it's just notation.

>> No.10155893

Any irrational is a limit of a sequence of rationals by density of Q in R.

So no you can't just choose irrationals.

>> No.10155900
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Why do you make this comment without stating how completions work? What does it mean "completion of rationals" if not "union of rationals and irrationals?"

Ok. I have the definition in my picture. The notation no one disputes is that
R = (-inf,inf)

I dispute the definition which precludes numbers in the neighborhood of infinity because such a definition cannot be used to describe all elements of set defined by the interval notation.

>> No.10155906

Wolfram, a reputable source, disagrees with you and agrees with me.
>An irrational number is a number that cannot be expressed as a fraction p/q for any integers p and q.

>> No.10155910

That doesn't disagree with what he said.

>> No.10155914

The definition you listed is right. An irrational is defined as a real number which isn't rational.

But the rationals are dense in the reals, i.e. the topological closure of Q is = R. This means, that any real number is a limit of a sequence of rational numbers.

Thus an irrational number is a limit of a sequence of rational numbers.

Seriously, pick up any standard text on introductory analysis and read the first few chapters. You will see all of this.

>> No.10155932
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>if you described the property
>without including the definition
>could you say precisely
>not a definition
>stating how completions work
Perhaps if you dweebs studied Mathematics as diligently
as you study disputation, then you would learn something.

>> No.10155986

>Ok. I have the definition in my picture.
You mean YOUR definition, which nobody else in mathematics agrees with.

>> No.10155988
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Yes it does. He implied that my numbers don't conform to the definition of irrationals but the real definition says anything that isn't a rational is an irrational.

consider the obvious number:
inf - 1

This isn't rational and it isn't a limit of a sequence of rationals.

My high stress gangstalking environment and condition of homeless indigence is not conducive to study. Even then, if I thought there was any amount of merit that could overcome the real criticism against me, namely that I don't like to suck dick while everyone inside the temple today is a giant faggot, then I would do it. However, there is no amount of math that I could learn which would override the faggot's criticisms of me, and everything I could glean now is something that I could glean 10,000x faster later when I can get into a structured collaborative study environment.

>> No.10155990

Is the square root of negative one irrational?

>> No.10156015

I suppose it must be since it does not conform to the definition of a rational but there are caveats to made about what constitutes a rational imaginary number. I think the definition in question pertains to the 1D case implicitly.

>> No.10156021

Seriously though... all those 10,000 reports out there about how bad I suck would have said I was great if I was gay. That's the real issue.

>> No.10156024

Also from the reputable source you cited:
Irrational numbers have decimal expansions that neither terminate nor become periodic.

>> No.10156044

>consider the obvious number:
>inf - 1

That is also not an irrational number. It is not a real number.

R := Completion of Q w.r.t |.|

{Irrationals} := R\Q

Infinity is not a real number and nothing you say makes sense.

>> No.10156078

Yes but at some point I get to interject a statement, "If they knew about the thing I discovered then I wouldn't be the one who discovered it."

>> No.10156083
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>It is not a real number.
it is a real number.

>> No.10156092


>> No.10156109
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>Affirmative Ghost Rider. You are cleared to buzz the tower.

>> No.10156174

It's not called a discovery when you change a definition.

>> No.10156181

You just cited definitions you made up. Are you really this fucking stupid or just a troll?

>> No.10156190
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I didn't change a definition. Real numbers existed long before anyone came up with a statement, "Reals are the completion of the rationals."

>> No.10156193

numbers are a social construct.

>> No.10156194
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This is the definition of real numbers that I learned when i studied real analysis in college. I didn't make it up. I learned it from a tenured PhD professor.

>> No.10156196

Thats dumb

>> No.10156198
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I'm detecting a highly intelligent person behind this ironic post

>> No.10156202

Should have said, "larger than every natural number"


>> No.10156203

thanks. but im not hitting the link.

>> No.10156204

link hits you

>> No.10156209

ok. I hit the link. I read the abstract. I have come to the only conclusion possible - that the author of that paper is an autistic window licker.

>> No.10156227


>> No.10156241

you should stop leaving sequitor in your toothpaste, anon.

>> No.10156248

>Some real numbers are larger than every real number.
does this mean that some real numbers are bigger than themselves?

>> No.10156291

I meant to write "than every natural number"

>> No.10156302

>something about number fields

>> No.10156314

which i disregarded as needlessly complicated

>> No.10156318

Here's some advice I learned in second grade while doing arithmetic
Just because you don't like something because it's hard or because it doesn't make sense, doesn't mean you can just ignore it.

>> No.10156326
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Ignoring the things that seem needlessly complicated is basically the thesis of my entire research program. I'm a pretty good judge of what is and is not irrelevant

>> No.10156329

Buddy, ignoring the outright autism of that, what you're describing is an ethos, not a thesis

>> No.10156341

yes, that ethos is basically the thesis

>> No.10156355

>research program
you don't have a research program Jon. You have a laptop, free wifi (probably nearby library) and a tent. Please get help. You obviously are very talented and passionate but your mental state is severely affecting the way you rationalise things.

>> No.10156359
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>> No.10156368

You can do arithmetic on numbers in the neighborhood of infinity but it doesn’t have commutivity and some other properties I forget. Omega. It doesn’t do this stuff.

>> No.10156401

>Some real numbers are larger than every real number.
This statement alone is a contradiction. A real number cannot be larger than every real number since it cannot be larger than itself. Furthermore, if there are some (more than one) real numbers, only one can be larger than every other real number, being the max of that some

>> No.10156420

Jon my brain tells me you're wrong, but deep down I want you to be right about everything somehow get vindicated in the future like George Cantor. However I want you to take it easy cause you dont wanna end up in an asylum like George Cantor

>> No.10156422

Idk I came up with the same conclusion, must be a trend

>> No.10156427

Me one real that is bigger than every natural number. I'll assume you can and call that x. Then there exists a natural number y=floor(x+1), which is bigger than x and is a natural number. Since y>x, there is a contradiction, meaning some assumption was wrong. Therefore, by contradiction, there cannot be a real number greater than every natural number. Q.E.D.

Try formulating a proof at least as rigorous as that one.

>> No.10157576

>that pic
my stocks reached the highest they've ever been at 350 on november 7th, and through some inexplicable cruel turn of fate or bogdanoff meddling, they're now at 300, which is the lowest they've been in 5 months. all news about the company is positive, i have no idea what caused this extremely sudden decline.

>> No.10157803
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I recommend reallocation to cash but also know that I like it when the market goes down. Hopefully they'll stop lying about my research soon

>> No.10157856

You're fuckin retarded, I'm out

>> No.10157951

takes one of ur Rs
adds 1 to it
U are reaction?

>> No.10157955
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>> No.10157961

math is gay shit for npcs anyway

>> No.10158160

Only if you're a user of math, but if you're an inventor of math like I am then you're no longer an NPC

>> No.10158173


>> No.10159556
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happy thanksgiving

>> No.10159911


>> No.10159920

Looks like marinara to me

>> No.10159923

some Russian guy got irradiated and they spent a couple of months keeping him alive against his wishes

>> No.10159927

>tfw you realize el arcon has another pdf which is 71 pages

>> No.10159949


>> No.10159972


Into the trash

>> No.10160029

I don't even know how somebody assumed that function result in something different than 0

>> No.10160131

Can you imagine the scientific principles involved if that happened to you and you wanted to find the long rest of peace but the person who could choose to sustain you or let you pass away was the target of extensive gangstalking activities perpetrated by your organization, or even kidnapping, torture and rendition activities? You would be like, "Does the scientific method allow you to let my misery end?," to which the counterparty might respond, "It does... but because of what you did and the actions of those close to you, I don't want to. Instead, I want to keep you alive to do worse things to you later," and then they would be like, "Damn, I wish the organization to which I have pledged myself made more of an effort to treat others the way they would like to be treated because now I'm on the other side of it and I don't like it!"

>> No.10160150
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>Jonathon W. Tooker is a guy who has no formal math or physics training
I have a BS (magna cum laude) and an MS in physics, and I was probably within a year of getting my PhD when I got expelled from college for being a serial rapist.
Pic related: you can see my formal math training in the tiny font there.
>Jonathan != Jonathon

>> No.10160159
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I wrote a book summarizing the foundations my research program. It's almost 300 pages.
>The General Relevance of the Modified Cosmological Model

>> No.10160195
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If a real number is larger than every real number, wouldn't it be larger than itself?

>> No.10160211
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Yes, this was a typo in the OP post and was basically the same issue I corrected in v1 of this paper. You know... even while the Torah is said to be "perfect" it has several typos in it, typos which have been replicated in every version of the Torah for centuries or millennia, and that makes a lot when you think about the number of typos in my posts. I used to make an effort not to make posts that were biordeline unintelligible due to typos but after I filmed typos getting inserted into my FB posts my desire to avoid them has been on a long wane.

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