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Induction Over subsets of Q

Anonymous Mon 18 Jan 12:52:28 2021 No.12596096 View Reply Original Report

Quoted By: >>12596104 >>12596268 >>12596378 >>12598148 >>12598228 >>12598248 >>12598707 >>12599042 >>12600867

Is this any good /sci/? I came up with this shit a while ago so I thought it'd be nice to write it down.

Made a mistake on a bit
>since we know every rational other than $b$
I meant other than $a$

Anonymous

Anonymous Mon 18 Jan 2021 12:54:36 No.12596104 Report

Quoted By: >>12596110

>>12596096
Give one example of a problem where such a method is useful. If you can't, then who cares?

Anonymous

Anonymous Mon 18 Jan 2021 12:56:43 No.12596110 Report

Quoted By: >>12596120

>>12596104
I don't know anon, I just wanted to make something useless

Anonymous

Anonymous Mon 18 Jan 2021 12:59:22 No.12596120 Report

Quoted By:

>>12596110
Ok but in all seriousness I don't have the slightest idea. Maybe you can use it when you can't think for some direct proof and would rather brute force your way through.

Anonymous

Anonymous Mon 18 Jan 2021 13:54:27 No.12596244 Report

Quoted By: >>12597686

In the abstract you mentioned thst your goal is to provide a method that is useful.
You need to provide more than one example where your method simplifies the more traditional proof.

Anonymous

Anonymous Mon 18 Jan 2021 14:06:14 No.12596268 Report

Quoted By: >>12597686

>>12596096
First check out some actual mathematical papers, and observe how to write properly.

Anonymous

Anonymous Mon 18 Jan 2021 14:48:32 No.12596378 Report

Quoted By: >>12597686

>>12596096
do not use i as a variable. Didn't read the rest, probably wouldn't understand it anyway.

Anonymous

Anonymous Mon 18 Jan 2021 20:46:55 No.12597686 Report

Quoted By:

>>12596244
I can't think of any at the moment, if something comes up I'll be sure to elaborate more on the method.

>>12596268
Fair enough anon, it's my first paper and I'm a junior so please take the it with agrain of salt anyways

>>12596378
Sorry, most of my profs in real analysis do, i guess it's not that used because you need a clearer context

Anonymous

Anonymous Mon 18 Jan 2021 22:29:34 No.12598125 Report

Quoted By:

bump

Anonymous

Anonymous Mon 18 Jan 2021 22:35:03 No.12598148 Report

Quoted By: >>12598162

>>12596096
This is absolute genius, how long did it take for you to come up with this?

Anonymous

Anonymous Mon 18 Jan 2021 22:38:04 No.12598162 Report

Quoted By: >>12598236

>>12598148
>Assuming this is not blatant sarcasm and you're actually interested
2-3 days, I had to polish it a little bit because it was written in spanish a month or so ago

Anonymous

Anonymous Mon 18 Jan 2021 22:55:27 No.12598228 Report

Quoted By: >>12598242

>>12596096
Pretty sure induction works for any countable set S.
Just use a bijection f: N --> S and use f(0) f(n) and f(n+1) instead of 0, n and n+1.

That's what you're doing, right?

Anonymous

Anonymous Mon 18 Jan 2021 22:57:23 No.12598236 Report

Quoted By:

>>12598162
If this is well recieved then I might make another paper using it to prove something we already know that works for $n \geq 0$ for the rationals via three inductions. Two for one interval and another for the arbitrary union of intervals of the same size.
If things go the right way from there, I'll come forward with my name and prove that it was really me who developed the thing.

Anonymous

Anonymous Mon 18 Jan 2021 22:58:26 No.12598242 Report

Quoted By:

>>12598228
Yeah, I'm only suggesting one way to go about doing it.

Anonymous

Anonymous Mon 18 Jan 2021 23:00:03 No.12598248 Report

Quoted By: >>12598257

>>12596096
can you prove r-a can be used to expressed all rational numbers less than |b-a|?

Anonymous

Anonymous Mon 18 Jan 2021 23:00:52 No.12598257 Report

Quoted By: >>12598306

>>12598248
I guess, I think it's already been proven.

Anonymous

Anonymous Mon 18 Jan 2021 23:09:27 No.12598306 Report

Quoted By: >>12598331

>>12598257
source?

Anonymous

Anonymous Mon 18 Jan 2021 23:16:43 No.12598331 Report

Quoted By:

>>12598306
it's easy to see that if you take a segment of length |b-a| and cut it it as two segments of length |a-r| and |b-r| you can find n and k such that r can be expressed like that anon, I don't know if someone else has already proven it but it's easy to see. Plus, I'm too lazy to make the proof right now.

Anonymous

Anonymous Tue 19 Jan 2021 00:21:36 No.12598559 Report

Quoted By:

bump

Anonymous

Anonymous Tue 19 Jan 2021 00:54:41 No.12598657 Report

Quoted By:

Does this merit a publication or is it of little importance? I was thinking about publishing on Acta Mathematica.

Anonymous

Anonymous Tue 19 Jan 2021 01:11:43 No.12598707 Report

Quoted By: >>12598840

>>12596096
> i in N

Anonymous

Anonymous Tue 19 Jan 2021 01:57:39 No.12598840 Report

Quoted By:

>>12598707
i as in index anon

Anonymous

Anonymous Tue 19 Jan 2021 02:23:18 No.12598927 Report

Quoted By: >>12600555

How long does it usually take for publications in Acta Mathematica to get approved?

Anonymous

Anonymous Tue 19 Jan 2021 03:10:08 No.12599042 Report

Quoted By: >>12599110

>>12596096
I have to say that this is a cool concept. I’m also a junior doing my own research in primitive groups, so this kinda gives me some motivation to see this. But on the other hand, I find it kinda incredulous that you are the very first person to discover this concept.

Anonymous

Anonymous Tue 19 Jan 2021 03:37:31 No.12599110 Report

Quoted By:

>>12599042
Thanks anon and good luck with your research! I don't really know what to say, i do know that proof methods aren't really the main topic of a great deal of math research, I guess I was just lucky to develop this first.

Anonymous

Anonymous Tue 19 Jan 2021 05:57:44 No.12599408 Report

Quoted By: >>12599454

Look up transfinite induction.

Anonymous

Anonymous Tue 19 Jan 2021 06:24:40 No.12599454 Report

Quoted By: >>12600511

>>12599408
I know of it, thats why I wrote this. It's just a way to organize stuff to make use of regular induction.

Anonymous

Anonymous Tue 19 Jan 2021 06:35:25 No.12599479 Report

Quoted By: >>12599522

OP don't listen to the retarded engieniggers taking about your grammatical prose and "utility" they have small cocks.

Anonymous

Anonymous Tue 19 Jan 2021 06:53:32 No.12599522 Report

Quoted By:

>>12599479
What do you think about it anon?

Anonymous

Anonymous Tue 19 Jan 2021 08:04:04 No.12599694 Report

Quoted By:

bump

Anonymous

Anonymous Tue 19 Jan 2021 10:33:40 No.12599965 Report

Quoted By:

bumpp

Anonymous

Anonymous Tue 19 Jan 2021 14:11:58 No.12600511 Report

Quoted By:

>>12599454
It's a generalization of regular induction.

Anonymous

Anonymous Tue 19 Jan 2021 14:24:50 No.12600555 Report

Quoted By:

>>12598927
Approved? I think you mean accepted.
Depends on how bad you were slaughtered in peer review.
If you sent your paper today, the best scenario is that your paper was accepted for publication in July or August.
However, your paper will be desk rejected by Acta, so expect a final decision in 72 hours.

Anonymous

Anonymous Tue 19 Jan 2021 14:26:58 No.12600566 Report

Quoted By:

Q has unlimited amount of shit.

Only finite sets are allowed thus finite subsets only.

t. radical finitist

Anonymous

Anonymous Tue 19 Jan 2021 16:09:04 No.12600867 Report

Quoted By:

>>12596096
this is just normal induction lmao

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