/sci/ - Science & Math » Thread #14146782

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/mg/ - maths general

Anonymous Tue 25 Jan 11:28:55 2022 No.14146782 View Reply Original Report

Quoted By: >>14146945 >>14147100 >>14147200 >>14147438 >>14151925 >>14161154 >>14167696 >>14175772

Formerly >>14146730

Yet another Floer homology edition.

Talk maths.

Anonymous

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Anonymous Tue 25 Jan 2022 12:25:51 No.14146945 Report

Quoted By: >>14148154 >>14180100

>>14146782
>for once, no faggy reddit reading list

Anonymous

Anonymous Tue 25 Jan 2022 13:16:39 No.14147079 Report

Quoted By: >>14160049

Any good books on Linear Programming?

Anonymous

Anonymous Tue 25 Jan 2022 13:26:46 No.14147100 Report

Quoted By:

>>14146782
mathematics is a hoax. It doesn't exist.

Anonymous

Anonymous Tue 25 Jan 2022 13:30:48 No.14147111 Report

Quoted By: >>14147163 >>14147195 >>14149378 >>14149587 >>14167841

What does Linear Programming cover? What does Numerical Analysis cover? Are these 2 just Optimization? Why do I need these as a Pure Mathematics major?

Anonymous

Anonymous Tue 25 Jan 2022 13:55:45 No.14147163 Report

Quoted By:

>>14147111
>Pure without numerical analysis

Anonymous

Anonymous Tue 25 Jan 2022 14:06:43 No.14147195 Report

Quoted By:

>>14147111
Numerical analysis is essentially the broad area of numerical methods to solve analysis problems and linear programming is essentially optimization over linear functions and constraints.

Anonymous

Anonymous Tue 25 Jan 2022 14:08:27 No.14147200 Report

Quoted By:

>>14146782
Based OP. This is the real /mg/.

Anonymous

Anonymous Tue 25 Jan 2022 15:00:37 No.14147339 Report

Quoted By: >>14147393 >>14159779

There are lots of ways to enumerate all k-tuples of nonnegative integers, but which one is the best?

Anonymous

Anonymous Tue 25 Jan 2022 15:19:38 No.14147393 Report

Quoted By: >>14147500

>>14147339
{{0,0...0},{0,0...1}...{0,0...k},{0,1...0},{0,1...1}...{0,1...k}...{0,k...0},{0,k...1}...{0,k...k},{1,0...0},{1,0...1}...{1,0...k},{1,1...0},{1,1...1}...{1,1...k}...{1,k...0},{1,k...1}...{1,k...k}...{k,0...0},{k,0...1}...{k,0...k},{k,1...0},{k,1...1}...{k,1...k}...{k,k...0},{k,k...1}...{k,k...k}}

Anonymous

Anonymous Tue 25 Jan 2022 15:40:36 No.14147438 Report

Quoted By: >>14147483

>>14146782
>Floer homology
Why are there so many trans women in this area? I know they love algebraic topology, but still.

Anonymous

Anonymous Tue 25 Jan 2022 15:57:21 No.14147483 Report

Quoted By: >>14147909

>>14147438
It's in the thin territory of having complicated category theory but not completely filtering trannies like Lurie's autism.

Anonymous

Anonymous Tue 25 Jan 2022 16:04:43 No.14147500 Report

Quoted By: >>14147585

>>14147393
What about for all k in N?

Anonymous

Anonymous Tue 25 Jan 2022 16:29:41 No.14147585 Report

Quoted By: >>14147628

>>14147500
by k-composition
{{1},{2},{1,1},{3},{2,1},{1,2},{1,1,1}...}

Anonymous

Anonymous Tue 25 Jan 2022 16:46:38 No.14147628 Report

Quoted By: >>14147735

>>14147585
i don't think that's what he meant

Anonymous

Anonymous Tue 25 Jan 2022 17:25:11 No.14147735 Report

Quoted By:

>>14147628
what do you think he meant

Anonymous

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Anonymous Tue 25 Jan 2022 17:32:47 No.14147761 Report

Quoted By: >>14147826

i need a clear and readable source on simplicial (co)homology and related stuff - i'll be taking part in an undergrad seminar on manifolds (continuation of our current course) and i'll probably be picking this and/or de Rham's theorem as my topic. the professor listed Lee's Smooth Manifolds as a recommended source, but i'd like to have a couple sources on hand, in case i don't understand the presentation in one. took a brief look at Hatcher and i think it was too much, anything simpler/more elementary?

Anonymous

Anonymous Tue 25 Jan 2022 17:51:24 No.14147826 Report

Quoted By: >>14147856

>>14147761
Lee doesn't cover simplicial homology.
Lee covers singular homology.
The difference is, essentially, that simplicial homology is a combinatorial construction on simplicial complexes and singular homology is a topological construction on topological spaces.
Anyhow, assuming you mean singular homology, Fuchs Fomenko.

Anonymous

Anonymous Tue 25 Jan 2022 18:01:07 No.14147856 Report

Quoted By:

>>14147826
idk what the difference between simplicial/singular is, i just need to learn what pertains to de Rham's theorem (i had understood it as having to do to simplices and simplicial complexes, hence why i assumed it's the simplicial homology)
thanks, i'll take a look at it

Anonymous

Anonymous Tue 25 Jan 2022 18:16:52 No.14147909 Report

Quoted By: >>14148907 >>14149550

>>14147483
So only lesbians can handle Lurie's autism? Does that make them TERFs?

Anonymous

Anonymous Tue 25 Jan 2022 19:22:27 No.14148154 Report

Quoted By: >>14148242

>>14146945
>I heard redditors breathe
>I'm gonna stop breathing because I don't wanna be a redditor

Anonymous

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Anonymous Tue 25 Jan 2022 19:53:27 No.14148242 Report

Quoted By:

>>14148154
>redditors breathe hence breathing is reddit

Anonymous

Anonymous Tue 25 Jan 2022 23:47:40 No.14148907 Report

Quoted By: >>14149048 >>14149550

>>14147909
There are women out there who can read Lurie's autism?

Anonymous

Anonymous Wed 26 Jan 2022 00:29:17 No.14149048 Report

Quoted By: >>14151023 >>14179027

>>14148907
Presumably Emily Riehl can.

Anonymous

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Anonymous Wed 26 Jan 2022 02:10:00 No.14149378 Report

Quoted By: >>14149587

>>14147111
Linear programming a.k.a linear optimization is a pretty cool topic, with a well-defined start and finish. The really cool thing that's worth seeing is the duality theorem. When a linear programming problem is presented in economics, they call its dual program the "shadow cost" which makes it sound even cooler.

Numerical analysis at the introductory level usually means things like: You know Newton's Method, right? Now make a MATLAB program that actually carries it out to find the roots of f(x). You may view it as drudgery now, but it's a really useful skill set to practise and you will be glad you did it.

Anonymous

Anonymous Wed 26 Jan 2022 03:07:27 No.14149550 Report

Quoted By:

>>14147909
>>14148907
It makes them trans men I guess

Anonymous

Anonymous Wed 26 Jan 2022 03:19:23 No.14149587 Report

Quoted By:

>>14149378
>>14147111
I was gonna say exactly this. Both very worthwhile and edifying courses for a pure math major to take.
Imagine graduating a 4y uni and only knowing group theory and Heine-Borel and shit lmao

Anonymous

Anonymous Wed 26 Jan 2022 13:37:06 No.14151023 Report

Quoted By: >>14151127

>>14149048
You're really tempting me to cold email her asking this.

Anonymous

Anonymous Wed 26 Jan 2022 14:19:41 No.14151127 Report

Quoted By: >>14151743

>>14151023
Haha well good luck if you do. I've met her before and we know some of the same people so I think that would be a very dumb thing for me to do.

Anonymous

Anonymous Wed 26 Jan 2022 17:34:04 No.14151743 Report

Quoted By: >>14151758 >>14151828

>>14151127
OK I'm going to email her saying I know her, specifically referring to Lurie's work as autism and linking this thread.

Anonymous

Anonymous Wed 26 Jan 2022 17:41:47 No.14151758 Report

Quoted By:

>>14151743
Scary stuff mate.

Anonymous

Anonymous Wed 26 Jan 2022 17:42:23 No.14151759 Report

Quoted By:

Put me in the screen cap lads

Anonymous

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Anonymous Wed 26 Jan 2022 18:05:57 No.14151828 Report

Quoted By: >>14151842

>>14151743
Using your university email.

Anonymous

Anonymous Wed 26 Jan 2022 18:09:42 No.14151842 Report

Quoted By: >>14151902

>>14151828
Nothing ensures your place in academia like publicly linking yourself to a /mg/ thread discussing trans women.

Anonymous

Anonymous Wed 26 Jan 2022 18:29:00 No.14151902 Report

Quoted By: >>14151954

>>14151842
Academia is an anti-white racism shithole anyway. We should start publishing papers on /sci/.

Anonymous

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Anonymous Wed 26 Jan 2022 18:36:25 No.14151925 Report

Quoted By: >>14151964 >>14151968

>>14146782
Is there anything special about the pattern that on ZxZ that eliminates a/b that is not in simplest form

Anonymous

Anonymous Wed 26 Jan 2022 18:45:07 No.14151954 Report

Quoted By: >>14151977

>>14151902
I'll publish on /sci/ if you pay me. I'm not some rich NEET who can post solutions to anime puzzles for free.

Anonymous

Anonymous Wed 26 Jan 2022 18:50:17 No.14151964 Report

Quoted By:

>>14151925
Yes, it's called the totient function.

Anonymous

Anonymous Wed 26 Jan 2022 18:51:58 No.14151968 Report

Quoted By: >>14152020

>>14151925
You fucked up eliminating

Anonymous

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Anonymous Wed 26 Jan 2022 18:55:04 No.14151977 Report

Quoted By: >>14152005 >>14152069

>>14151954
Every business requires an initial high-risk investment. Nobody wants to make that investment but it's the kind of action required to dethrone the journal moneylenders. An anon on 4chan is already known for solving the Haruhi problem. Anons could do it again.

Anonymous

Anonymous Wed 26 Jan 2022 19:03:12 No.14152005 Report

Quoted By: >>14153314

>>14151977
I'm glad that your boypussy gets wet at the thought of eliminating the old journal system, but that's going to happen by people forming open-source journals on a volunteer basis and conducting themselves in a professional manner. No serious academic wants their shiny new theorem right next to schizo posters, Nazi propaganda, and discussions of the relationship between subfields of homotopy theory and cross-sex horomone regimens.

Anonymous

Anonymous Wed 26 Jan 2022 19:10:52 No.14152020 Report

Quoted By: >>14152041

>>14151968
I wouldnt be surprised lol

Anonymous

Anonymous Wed 26 Jan 2022 19:19:06 No.14152041 Report

Quoted By: >>14152046

>>14152020
Find the square

Anonymous

Anonymous Wed 26 Jan 2022 19:21:02 No.14152046 Report

Quoted By: >>14152055

>>14152041
10/5

Anonymous

Anonymous Wed 26 Jan 2022 19:24:35 No.14152055 Report

Quoted By:

>>14152046
we did it /mg/

Anonymous

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Anonymous Wed 26 Jan 2022 19:29:23 No.14152069 Report

Quoted By:

>>14151977
>solving the Haruhi problem
He didn't solve it.
Can you guys at least have some basic knowledge about the things you're posting?

Anonymous

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Anonymous Wed 26 Jan 2022 19:54:19 No.14152168 Report

Quoted By: >>14152204 >>14152308 >>14152660 >>14152705 >>14162997 >>14163032

Is there a mathematician more based than Moore?

Anonymous

Anonymous Wed 26 Jan 2022 20:00:37 No.14152204 Report

Quoted By: >>14152308 >>14152660 >>14153006

>>14152168
Did he hate black people or did he just dislike integration?

Anonymous

Anonymous Wed 26 Jan 2022 20:26:02 No.14152308 Report

Quoted By:

>>14152168
>>14152204
>t. eurafricasiaoid incest babies

Anonymous

Anonymous Wed 26 Jan 2022 22:09:00 No.14152660 Report

Quoted By: >>14152681

>>14152168
>moore's record as a teacher has been tarnished
jewpedia is getting worse and worse it seems, soon even the mathematics pages will be ruined by the queer ideologues.

If anything I respect Moore more now. It is his body and his choice what crowd he will teach to. Somebody who does not have his preference, is not somehow morally superior in any way. In my experience, blacks and women are loud and stupid and rarely hold any wisdom to warrant it.

>>14152204
if a woman refuses to date me, does she hate me?

Anonymous

Anonymous Wed 26 Jan 2022 22:16:04 No.14152681 Report

Quoted By: >>14152689

>>14152660
>if a woman refuses to date me, does she hate me?
Is not wanting to have your retarded babies equivalent to hate? If so, then probably yes.

Anonymous

Anonymous Wed 26 Jan 2022 22:20:17 No.14152689 Report

Quoted By:

>>14152681
you are thinking of "dating" in the most crude way possible, but even in that case I dont think its really hate, just preference and choice. if she does not want to bear my children, does that really mean she hates me? maybe she just thinks im ugly, or has her eyes on another better looking guy. None of this is hateful, just choice.

and believe me, in this case I like any other guy would prefer it if were illegal for women to deny me :)

Anonymous

Anonymous Wed 26 Jan 2022 22:24:57 No.14152700 Report

Quoted By: >>14168632

Anyone know of some good measure theory/probability theory notes/lectures I'm trying to rectify my horseshit undergrad education before I start my PhD.

Anonymous

Anonymous Wed 26 Jan 2022 22:27:30 No.14152705 Report

Quoted By: >>14152835

>>14152168
this seems like false information with an agenda.
they are implying there were black people able to do math to make them look smarter

Anonymous

Anonymous Wed 26 Jan 2022 23:19:11 No.14152832 Report

Quoted By:

the relationship between the division and multiplication symbols, and their associated matrix transformations, suggests the meaning of the positive and negative signs should be inverted

Anonymous

Anonymous Wed 26 Jan 2022 23:20:50 No.14152835 Report

Quoted By:

>>14152705
Agreed
He refused to let black people into classes, but he also told black students they can take his classes but won't get higher than a C?
the article that quote is cited in cites this website
http://www.math.buffalo.edu/mad/special/RLMoore-racist-math.html
where it just kinda appears

Anonymous

Anonymous Thu 27 Jan 2022 00:22:38 No.14153006 Report

Quoted By:

>>14152204
>did he just dislike integration?
heh

Anonymous

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Anonymous Thu 27 Jan 2022 02:09:08 No.14153314 Report

Quoted By: >>14153336 >>14154055 >>14161611 >>14169734

>>14152005
>No serious academic wants their shiny new theorem right next to schizo posters, Nazi propaganda, and discussions of the relationship between subfields of homotopy theory and cross-sex horomone regimens.
That sounds like current academia anon. They're literally inventing a million genders and saying math is racist.
There's no in between, it's either 4chan or literally the pit of hell.
Anyway maybe we can pool together money for excellent papers and we can also give free peer review. We never get paid for peer review as academics anyway.

I actually think a 4chan journal would be an amazing idea and would make /sci/ a non-shit board for a change. It would actually allow us to explore things that would get you beheaded as an academic once we expand beyond math as well.

I for one am all for it.

Anonymous

Anonymous Thu 27 Jan 2022 02:17:36 No.14153336 Report

Quoted By: >>14153346

>>14153314
There's a lot of stupid PC bullshit for sure, but it sounds like you don't have much experience with real academia and I am doubtful /sci/ could ever manage to actually peer review and post anything approaching an issue of an actual mathematics journal. Outside of anime tranny, the Riemann hypothesis guy, some undergrads, and some /pol/ transplants no one would even contribute anything and basically no one has the ability to judge mathematics at a graduate level here.

Anonymous

Anonymous Thu 27 Jan 2022 02:19:33 No.14153346 Report

Quoted By: >>14153371

>>14153336
>sounds like you don't have much experience with real academia
I literally have a PhD, I stopped reading the rest of your post when I encountered this retarded projection.
I left academia to pursue actual work instead of appeasing grant reviewers.

Anonymous

Anonymous Thu 27 Jan 2022 02:27:54 No.14153371 Report

Quoted By: >>14153390

>>14153346
My mistake, but I also have a PhD and stayed in academia, so maybe I'm just one of the people you detest and that's why I thought your perspective was unrealistic.

Anonymous

Anonymous Thu 27 Jan 2022 02:34:31 No.14153390 Report

Quoted By:

>>14153371
Don't tell me you fell for the post-doc scam...

Anonymous

Anonymous Thu 27 Jan 2022 02:48:49 No.14153434 Report

Quoted By: >>14153458

reals are a 2D matrix composed of two members of the surreals

Anonymous

Anonymous Thu 27 Jan 2022 02:55:36 No.14153458 Report

Quoted By:

>>14153434
What is an example of this construction?

Anonymous

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Anonymous Thu 27 Jan 2022 02:59:18 No.14153469 Report

Quoted By: >>14153485 >>14153496

I've become retarded and need help. A college student is asking me for help on this braindead question and I'm talking myself in circles around it.
I've got that cos(x) is -2/3 from the dot product, and my brain is dying trying to relate it together for the vector sums because they're just a scalene triangle.
Imagine getting a bachelor in mathematics and physics and forgetting week 1 calc 3, this is embarrassing.
It would be far easier if I just had the vectors so there must be some relation I'm missing out on.

Anonymous

Anonymous Thu 27 Jan 2022 03:03:44 No.14153485 Report

Quoted By: >>14153499

>>14153469
It was the law of cosines.
I knew I was retarded.

Anonymous

Anonymous Thu 27 Jan 2022 03:08:38 No.14153496 Report

Quoted By: >>14153503

>>14153469
v=(-2,+-sqrt(5)) do the rest by hand don't be dumb

Anonymous

Anonymous Thu 27 Jan 2022 03:09:39 No.14153499 Report

Quoted By: >>14153503

>>14153485
Don't even have to go that far, just define u=(1,0) and find v via the dot product and length constraint.

Anonymous

Anonymous Thu 27 Jan 2022 03:11:14 No.14153503 Report

Quoted By: >>14153504

>>14153499
Reorienting the vectors does seem a lot smarter in retrospect, this is what happens when you talk yourself in circles.
>>14153496
I was trying to do it by hand but when you start working with angles outside some pi/6 or pi/4 multiple it's not as easy.

Anonymous

Anonymous Thu 27 Jan 2022 03:11:38 No.14153504 Report

Quoted By:

>>14153503
>this is what happens when you talk yourself in circles.
nice

Anonymous

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Anonymous Thu 27 Jan 2022 03:54:37 No.14153618 Report

Quoted By: >>14153709 >>14153771 >>14153784

Explain to me how the second equation becomes the third-- I've been pushing this around as phasors with no results.

Anonymous

Anonymous Thu 27 Jan 2022 04:20:26 No.14153709 Report

Quoted By:

>>14153618
I don't know how they expect you to do it, but you can apply the formula for cosine of a difference, evaluate sine and cosine of some constants, and gather terms, to get an expression of the form a*sin(3 pi n/4) + b*cos(3 pi n/4), and then reverse the process to return to the form c * cos(3 pi n/4 - d).

Anonymous

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Anonymous Thu 27 Jan 2022 04:40:04 No.14153752 Report

Quoted By: >>14153781 >>14167868

anyone here knows backward prediction?
i have a dataset of values increasing over time but its missing the first three months. Is there a way to use math and predict the missing value?

Anonymous

Anonymous Thu 27 Jan 2022 04:59:58 No.14153771 Report

Quoted By:

>>14153618
Apply the cos(a+b) = cos(a)cos(b) + sin(a)sin(b) identity. you get
$8.6\cos\left(\frac{3\pi x}{4}-2.1\right)+5.2\cos\left(\frac{3\pi x}{4}-0.8\right) = \cos\left(\frac{3\pi x}{4}\right)\left(8.6\cos\left(2.1\right)+5.2\cos\left(0.8\right)\right)+\sin\left(\frac{3\pi x}{4}\right)\left(8.6\sin\left(2.1\right)+5.2\sin\left(0.8\right)\right)$
The idea is that we need the to find $A$ and $\theta$ such that
$A\cos \theta = 8.6\cos\left(2.1\right)+5.2\cos\left(0.8\right)$
and
$A \sin \theta = 8.6\sin\left(2.1\right)+5.2\sin\left(0.8\right)$
Squaring both we get that $A^2 \approx 124.9$ , so $A \approx 11.18$ .
From there, we solve for $\theta$ .

Anonymous

Anonymous Thu 27 Jan 2022 05:01:34 No.14153781 Report

Quoted By: >>14153782

>>14153752
If they oscillate, just use Fourier.

Anonymous

Anonymous Thu 27 Jan 2022 05:02:36 No.14153782 Report

Quoted By:

>>14153781
nvm. Just approximate by a polynomial or something, and then plug in to the first three months.

Anonymous

Anonymous Thu 27 Jan 2022 05:03:19 No.14153784 Report

Quoted By: >>14153815

>>14153618
how did you go from the first to the second

Anonymous

Anonymous Thu 27 Jan 2022 05:17:07 No.14153815 Report

Quoted By:

>>14153784
cosine is an even function

Anonymous

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Anonymous Thu 27 Jan 2022 07:18:57 No.14154030 Report

Quoted By: >>14154210 >>14160954

Where do you buy your books? I've been trying to find a hardcover copy of a textbook and I can't find it anywhere, not even a used copy. Softcover is annoying because the book keeps closing itself when reading.

Anonymous

Anonymous Thu 27 Jan 2022 07:29:34 No.14154055 Report

Quoted By:

>>14153314
kys tranny

El Arcón

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El Arcón Thu 27 Jan 2022 07:37:38 No.14154075 Report

Quoted By:

Anonymous

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Anonymous Thu 27 Jan 2022 08:07:32 No.14154137 Report

Quoted By: >>14154189 >>14156564

i'm trying to understand the multilinear map and basis-free formulation of tensors.
the tensor product of vectorspaces $U$ and $V$ is defined in terms of a bilinear equivalence relation on the free basis of the Cartesian product of $U$ and $V$ , that is $U \otimes V \equiv F(U \times V) / \sim$ where
$ \begin{split} (\vec{u} \alpha + \vec{u}' \alpha', \vec{v}) \sim (\vec{u}, \vec{v}) \alpha + (\vec{u}', \vec{v}) \alpha' \\ (\vec{u}, \vec{v} \beta + \vec{v}' \beta') \sim (\vec{u}, \vec{v}) \beta + (\vec{u}, \vec{v}') \beta' \end{split} $

the outer product maps pairs of vectors to elements of $U \otimes V$ . but in the abstract this is left undefined.

can any bilinear map serve as an outer product? it seems like any bilinear function will do, and once in hand, the expansion of any other bilinear map is uniquely defined

Anonymous

Anonymous Thu 27 Jan 2022 08:37:23 No.14154189 Report

Quoted By: >>14158146

>>14154137
The outer product yields an element of the tensor product of U and V. Since there is only one unique tensor product, you’re always in the same one if you’ve got the bilinear map.

Anonymous

Anonymous Thu 27 Jan 2022 08:50:36 No.14154210 Report

Quoted By:

>>14154030
Try bookfinder

Anonymous

Anonymous Thu 27 Jan 2022 19:44:05 No.14155884 Report

Quoted By: >>14155945

>Bernoulli's inequality for natural numberes ( $(1+k)^n \geq 1+nk$ ) can be proven through combinatorial means, that is, constructing the proper injections

Holy fuck this totally blew my mind. What are some books that delve in these topics? I'm in love with bijective proofs (and I'm absolutely fed up with "intuitive-informal-choosing" counting techniques)

Anonymous

Anonymous Thu 27 Jan 2022 20:02:12 No.14155945 Report

Quoted By:

>>14155884
Check out Euler's pentagonal function and how it relates to partitions, divisor sums, etc.

Anonymous

Anonymous Thu 27 Jan 2022 20:28:59 No.14156033 Report

Quoted By: >>14156876

division is just a matrix rotation

Anonymous

Anonymous Thu 27 Jan 2022 22:52:40 No.14156564 Report

Quoted By: >>14158146

>>14154137
There is a cannonical bilinear map $U \times V \to U \otimes V$ sending $(u,v)$ to its equivalence class $[(u,v)]$ . This class is denoted $u \otimes v$ .

Anonymous

Anonymous Fri 28 Jan 2022 00:12:23 No.14156876 Report

Quoted By: >>14158308

>>14156033
explain

Anonymous

Anonymous Fri 28 Jan 2022 09:33:53 No.14158146 Report

Quoted By:

>>14154189
>>14156564
i've been thinking about this hard all day and it's almost clicked. i need to sleep on it another day. thanks

Anonymous

Anonymous Fri 28 Jan 2022 10:53:36 No.14158246 Report

Quoted By: >>14158301 >>14158870 >>14158887

Let's say (G, ×) is a group. Is there an infinite sequence G, Aut(G), Aut(Aut(G)), Aut(Aut(Aut(G)))... with increasing orders?

Anonymous

Anonymous Fri 28 Jan 2022 11:26:29 No.14158301 Report

Quoted By: >>14158322

>>14158246
yep
aut[g] is a group -> aut[aut[g]] is a group

Anonymous

Anonymous Fri 28 Jan 2022 11:32:19 No.14158308 Report

Quoted By:

>>14156876
if you keep your algebraic values in fractional form, including integers, it becomes self-evident
i'd go as far as to say that focusing early maths education on reals will, decades from now, be seen as a stupendously damaging approach to numeracy

Anonymous

Anonymous Fri 28 Jan 2022 11:46:15 No.14158322 Report

Quoted By:

>>14158301
I mean an infinite sequence that |G| < |Aut(G)| < |Aut(Aut(G))| < |Aut(Aut(Aut(G)))| ...

Anonymous

Anonymous Fri 28 Jan 2022 15:40:02 No.14158870 Report

Quoted By:

>>14158246
This is a homework problem, I think. You should start by checking simple examples.

Anonymous

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Anonymous Fri 28 Jan 2022 15:45:30 No.14158887 Report

Quoted By: >>14158907

>>14158246
Nah.
http://jdh.hamkins.org/wp-content/uploads/2012/04/AutoTowers-Bristol-2012.pdf

Anonymous

Anonymous Fri 28 Jan 2022 15:52:54 No.14158907 Report

Quoted By:

>>14158887
Well that clearly says groups may have infinite automorphism towers so it depends on what you mean by "terminates".

Anonymous

Anonymous Fri 28 Jan 2022 18:12:08 No.14159362 Report

Quoted By: >>14159383 >>14159408 >>14159436 >>14159473

Is it possible to prove that there are infinitely many prime numbers without resorting to $reductio\space ad\space absurdum$ ?

Anonymous

Anonymous Fri 28 Jan 2022 18:19:15 No.14159383 Report

Quoted By: >>14159392 >>14159421 >>14159543 >>14159545

>>14159362
suppose the primes are finite.
multiply all the primes together and add 1.
this new number is not divisible by any primes in your finite set, and is thus prime.
this violates the assumption that the primes are finite.
thus, there are infinite primes.

Anonymous

Anonymous Fri 28 Jan 2022 18:21:53 No.14159392 Report

Quoted By:

>>14159383
oops, i thought reductio involved recursion. sorry, that's not a line of logic you are interested in.

how about prime decomposition of numbers?

Anonymous

Anonymous Fri 28 Jan 2022 18:26:25 No.14159408 Report

Quoted By:

>>14159362
Yes. For example, Euclid's proof.

Anonymous

Anonymous Fri 28 Jan 2022 18:29:54 No.14159421 Report

Quoted By: >>14159432 >>14160086 >>14160714

>>14159383
>suppose the primes are finite
This is true by definition of a prime. Primes are just natural numbers like 5,7,11, and as such, they are finite. To prove me wrong, feel free to point to an infinite prime.

Anonymous

Anonymous Fri 28 Jan 2022 18:32:07 No.14159432 Report

Quoted By: >>14159442

>>14159421
jesus you pedantic fuck. suppose the cardinality of the set of all primes is finite.

Anonymous

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Anonymous Fri 28 Jan 2022 18:32:46 No.14159436 Report

Quoted By: >>14159494 >>14180474 >>14181020

>>14159362

Anonymous

Anonymous Fri 28 Jan 2022 18:33:39 No.14159442 Report

Quoted By: >>14160086

>>14159432
>suppose the cardinality of the set of all primes is finite
Or you could say suppose there are finitely many primes (as opposed to "suppose there are finite primes", which would be useless as we already know that there are primes and all primes are finite).

Anonymous

Anonymous Fri 28 Jan 2022 18:39:37 No.14159473 Report

Quoted By: >>14159521

>>14159362
Euclid's proof is NOT reductio ad absurdum. It inputs a finite collection of primes and finds a prime outside of this collection. This is exactly what it MEANS for a collection of natural numbers to be infinite. As such, the proof is direct and is NOT a proof by contradiction.
You could also think of it as follows. The definition of an infinite set is a set that is finite. To demonstrate that some set is infinite, we assume it's finite and and demonstrate a contradiction. Because the negation of a proposition P is defined as P=> (contradiction). In this case, P = "the set of primes is finite" and P=>(contradiction) means "the set of primes is not finite /the set of primes is infinite".
A proof by contradiction is when you try to prove P for some property P by proving (P=>(contradiction)) => (contradiction).

Anonymous

Anonymous Fri 28 Jan 2022 18:44:02 No.14159494 Report

Quoted By: >>14159521 >>14180474

>>14159436
Filip Saidak is a fucking retard.
>unlike most other proofs of the theorem, it does not require p|ab => p|a or p|b
Neither does Euclid's proof, dumbass.
>moreover, our proof is constructive
So is Euclid's proof.
The "new proof" he presents contains absolutely no new ideas from Euclid's proof. It's trivial to translate from one proof to another.

Anonymous

Anonymous Fri 28 Jan 2022 18:49:48 No.14159521 Report

Quoted By:

>>14159473
>>14159494
dilate

Anonymous

Anonymous Fri 28 Jan 2022 18:50:08 No.14159525 Report

Quoted By: >>14159532 >>14181029

Here is the actual proof of Euclid's translated to english for you retards.
http://aleph0.clarku.edu/~djoyce/java/elements/bookIX/propIX20.html
Completely constructive, completely clear. NOT a proof by contradiction.

Anonymous

Anonymous Fri 28 Jan 2022 18:51:36 No.14159532 Report

Quoted By: >>14181052 >>14181215

>>14159525
>Therefore G, being a number, measures the remainder, the unit DF, which is absurd.

Anonymous

Anonymous Fri 28 Jan 2022 18:54:23 No.14159543 Report

Quoted By: >>14159647 >>14159675

>>14159383
then why can't it be divisible by a prime not in that set?

Anonymous

Anonymous Fri 28 Jan 2022 18:54:35 No.14159545 Report

Quoted By: >>14159562

>>14159383
The number you get is not necessarily prime you ding dong. It is just a number that has a different prime factors than any of the primes in the list. For instance 2,3,5,7,11,13 multiplied together and adding 1 give you 30031 which is not prime.

Anonymous

Anonymous Fri 28 Jan 2022 18:59:59 No.14159562 Report

Quoted By:

>>14159545
it was a sloppy proof from memory. i suppose the correct statement would have been "relatively prime"

Anonymous

Anonymous Fri 28 Jan 2022 19:21:56 No.14159647 Report

Quoted By: >>14159668

>>14159543
the new number is a multiple of that prime p1(p2p3p4...pn)+1, i.e. not a multiple

Anonymous

Anonymous Fri 28 Jan 2022 19:28:43 No.14159668 Report

Quoted By: >>14159674 >>14159965

>>14159647
probably not asking correctly since I'm not a math person. say you have (2.3)+1 = 7, that does not generate the prime 5, there's a gap. in the more general case why can't one of these 'gap primes' not divide the generated one?

Anonymous

Anonymous Fri 28 Jan 2022 19:30:59 No.14159674 Report

Quoted By: >>14159696

>>14159668
If a>1, then ab+1 is not divisible by a for any b.
Assume it is. ab is divisible by a. Since the difference of numbers divisible by a is divisible by a, so is (ab+1) - ab=1. But that means a is +-1, contrary to our assumption.

Anonymous

Anonymous Fri 28 Jan 2022 19:31:30 No.14159675 Report

Quoted By:

>>14159543
divide by any number in the set and you get remainder 1

Anonymous

Anonymous Fri 28 Jan 2022 19:36:55 No.14159696 Report

Quoted By: >>14159711 >>14159712

>>14159674
that I understand but I still can't get my head around the fact there will also be cases where there is also a prime c such that a,b < c < (ab)+1

so why can't c divide (ab)+1 ?

Anonymous

Anonymous Fri 28 Jan 2022 19:41:27 No.14159711 Report

Quoted By:

>>14159696
Not him, but it can. For example 7*11+1 = 78 and 13|78

Anonymous

Anonymous Fri 28 Jan 2022 19:41:36 No.14159712 Report

Quoted By: >>14159733

>>14159696
there absolutely will be cases where such a number c exists, but c wasn't on the original list under consideration.

Anonymous

Anonymous Fri 28 Jan 2022 19:47:24 No.14159733 Report

Quoted By: >>14159763 >>14159859

>>14159712
that's what confuses me. it's a method to generate endless primes but it doesn't generate every prime so why doesn't the proof include them?

Anonymous

Anonymous Fri 28 Jan 2022 19:52:29 No.14159763 Report

Quoted By: >>14159773 >>14159784

>>14159733
the proof is about how many primes there are, not how to generate all those primes.
consider some other example: there are infinite whole numbers, and i can generate an infinite sequence of even numbers, but that sequence misses the odd numbers. yet i could still deduce there are infinite whole numbers because there are infinite even numbers

Anonymous

Anonymous Fri 28 Jan 2022 19:53:48 No.14159773 Report

Quoted By: >>14159781 >>14160086

>>14159763
>there are infinite whole numbers
Bullshit. Give me a single example of an infinite whole number.

Anonymous

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Anonymous Fri 28 Jan 2022 19:55:08 No.14159779 Report

Quoted By: >>14159805

>>14147339
I like this: Split a number in an even and uneven part via
2^x * (2 * y + 1)
(maximizing and reading out the exponent x) and then iterate this procedure on the factor y.
This can be generalized to any base (2 above)
https://gist.github.com/Nikolaj-K/5df0a93b2eb65bbc2658929ed48f6c81

The first 20 result for base 2 resp 3, mapping an n to a tuple of x's, are

0:
[]
[]
1:
[0]
[0]
2:
[1]
[0, 0]
3:
[0, 0]
[1]
4:
[2]
[0, 0, 0]
5:
[0, 1]
[0, 1]
6:
[1, 0]
[1, 0]
7:
[0, 0, 0]
[0, 0, 0, 0]
8:
[3]
[0, 0, 1]
9:
[0, 2]
[2]
10:
[1, 1]
[0, 1, 0]
11:
[0, 0, 1]
[0, 0, 0, 0, 0]
12:
[2, 0]
[1, 0, 0]
13:
[0, 1, 0]
[0, 0, 0, 1]
14:
[1, 0, 0]
[0, 2]
15:
[0, 0, 0, 0]
[1, 1]
16:
[4]
[0, 0, 1, 0]
17:
[0, 3]
[0, 0, 0, 0, 0, 0]
18:
[1, 2]
[2, 0]
19:
[0, 0, 2]
[0, 1, 0, 0]
20:
[2, 1]
[0, 0, 0, 0, 1]
...

Anonymous

Anonymous Fri 28 Jan 2022 19:55:26 No.14159781 Report

Quoted By: >>14159794

>>14159773
jesus dude, fuck off, everyone knows what that means

Anonymous

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Anonymous Fri 28 Jan 2022 19:56:06 No.14159784 Report

Quoted By: >>14160086

>>14159763
>there are infinite whole numbers

Anonymous

Anonymous Fri 28 Jan 2022 19:57:22 No.14159794 Report

Quoted By: >>14159803 >>14160086

>>14159781
I know that there are finite ordinals, and that there are also infinite ordinals. Now you say that there are also infinite whole numbers. Could you explain?

Anonymous

Anonymous Fri 28 Jan 2022 19:59:20 No.14159803 Report

Quoted By: >>14159816

>>14159794
>there are [insert quantity] things
>there are 100 things
>there are infinite things
that's how english works. i'd latex out math if i was being autistic

Anonymous

Anonymous Fri 28 Jan 2022 20:00:13 No.14159805 Report

Quoted By:

>>14159779
One million becomes
[6, 2, 4, 1, 0, 0, 0]
for base 2 and
[0, 0, 0, 0, 0, 0, 0, 0, 2, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0]
for base 3

Anonymous

Anonymous Fri 28 Jan 2022 20:03:08 No.14159816 Report

Quoted By: >>14159837 >>14160086

>>14159803
That's not how English works you idiot.
"There are infinite things" means there are things that are infinite. The word infinite is a property, not a number. There is an infinity of X means there are infinitely many X.
The difference between "There are dozenal number systems" and "There are a dozen number systems", or between "There are finite cardinalities" and "There are finitely many cardinalities".
You're a retard, so shut up and learn English.

Anonymous

Anonymous Fri 28 Jan 2022 20:06:55 No.14159837 Report

Quoted By: >>14159839

>>14159816
i have no idea if you are talking about countable or uncountable infinities. please specify.

Anonymous

Anonymous Fri 28 Jan 2022 20:07:20 No.14159839 Report

Quoted By: >>14159884

>>14159837
Irrelevant.

Anonymous

Anonymous Fri 28 Jan 2022 20:11:40 No.14159859 Report

Quoted By: >>14159873

>>14159733
>why doesn't the proof include them
Because they don't matter to the proof.

Anonymous

Anonymous Fri 28 Jan 2022 20:14:06 No.14159873 Report

Quoted By: >>14159907

>>14159859
why? what's the proof those other primes can't divide the number that was generated?

Anonymous

Anonymous Fri 28 Jan 2022 20:15:40 No.14159884 Report

Quoted By: >>14159912 >>14159917

>>14159839
learn context. i can define "infinity" as an element of the riemann sphere and construct usable math.
that has nothing to do with "how many primes are there?" and the answer "there are infinite primes". if in this context you were to interpret the phrase "there are infinite primes" as trying to attribute a "value" of infinity to some prime numbers, that doesn't follow from the question.

"how many apples are there?"
"there are 5 apples"
"how can apples be 5?"
"are you a robot?"

Anonymous

Anonymous Fri 28 Jan 2022 20:21:38 No.14159907 Report

Quoted By:

>>14159873
Are we talking about the same proof? The reduction to absurdity by Euclid and/or the algorithmic restatement of it in terms of coprimality?

Anonymous

Anonymous Fri 28 Jan 2022 20:23:53 No.14159912 Report

Quoted By: >>14159982

>>14159884
>i can define "infinity" as an element of the riemann sphere and construct usable math.
Correct but irrelevant to the argument.
>and the answer "there are infinite primes".
That's not the answer. That's a completely unrelated assertion that is false.
>if in this context you were to interpret the phrase "there are infinite primes" as trying to attribute a "value" of infinity to some prime numbers
That's literally what the expression means. If you meant to say there are infinitely many primes, you should've said so, or something equivalent to it.
>that doesn't follow from the question
Which is why your assertion was nonsense.
>"how many apples are there?"
>"there are 5 apples"
5 is not a property applicable to an apple, in contrast to the word "infinite". 5 is a quantity applicable to groups of objects. "infinite" is a property applicable to any object. Thus you could say "infinite love", or "infinite ordinal", but it doesn't make sense to speak of "5 love" or "5 ordinal".
In conclusion, you're retarded, and you should sit the fuck down.

Anonymous

Anonymous Fri 28 Jan 2022 20:25:37 No.14159917 Report

Quoted By: >>14160086

>>14159884
What's your native language?

Anonymous

Anonymous Fri 28 Jan 2022 20:37:20 No.14159965 Report

Quoted By: >>14159975 >>14160036

>>14159668
no worries,the argument doesnt create the next largest prime, its not an algorithm
the idea was that 2 and 3 were the only primes, and that cant be the case because 7 isnt in the 2 or 3 times table, so there must be more than just 2 and 3
there are cases where the abcde...+1 isnt even prime, just that it has prime factors arent in your original list

Anonymous

Anonymous Fri 28 Jan 2022 20:39:58 No.14159975 Report

Quoted By: >>14160036

>>14159965
2*3*5*7*11*13+1 = 30031
30031 is 59 × 509
i think this is the smallest one where it happens

Anonymous

Anonymous Fri 28 Jan 2022 20:41:25 No.14159982 Report

Quoted By: >>14160002

>>14159912
>"there are infinitely many primes"
in what sense? countable, uncountable? if you say it's clear by context, i'll say that's my line

Anonymous

Anonymous Fri 28 Jan 2022 20:44:19 No.14159988 Report

Quoted By: >>14160002

"infinite series" or "infinitely many termed series"?

Anonymous

Anonymous Fri 28 Jan 2022 20:47:56 No.14160002 Report

Quoted By:

>>14159982
It's not clear by context. It's irrelevant.
>>14159988
A series has the property of being infinite if it has infinitely many terms.

Anonymous

Anonymous Fri 28 Jan 2022 20:59:07 No.14160036 Report

Quoted By: >>14160044 >>14160046 >>14160061

>>14159965
>>14159975
> there are cases where the abcde...+1 isnt even prime
> 2*3*5*7*11*13+1 = 30031 = 59 × 509

erm. say what now?! how is that not a contradiction to Euclid's Proof?

Anonymous

Anonymous Fri 28 Jan 2022 21:01:47 No.14160044 Report

Quoted By:

>>14160036
because neither 59 or 509 were part of the original set of {2, 3, 5, 7, 11, 13} that supposedly formed all the primes

Anonymous

Anonymous Fri 28 Jan 2022 21:02:05 No.14160046 Report

Quoted By:

>>14160036
Not him, but this is the proof you're looking for. a is coprime to a+1 for any a > 1. So the recursion a_{1} = 2 ; a_{n} = a_{n-1} * (a_{n-1} + 1) gives you a number with at least n prime factors for any n. It doesn't matter to the proof how many more primes exist either in a_{n} or not in a_{n}, just that you have at least n primes for any n.

Anonymous

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Anonymous Fri 28 Jan 2022 21:03:11 No.14160049 Report

Quoted By:

>>14147079
>Linear Programming

Anonymous

Anonymous Fri 28 Jan 2022 21:08:13 No.14160061 Report

Quoted By:

>>14160036
the idea was that 2,3,5,7,11,13 were the only primes that exist, and there are no primes bigger than 13
but 30031 isnt a multiple of 2,3,5,7,11 or 13, and must be a product of primes that arent 2,3,5,7,11 or 13

Anonymous

Anonymous Fri 28 Jan 2022 21:19:11 No.14160086 Report

Quoted By:

>>14159421
>>14159442
>>14159773
>>14159784
>>14159794
>>14159816
>>14159917
What is this reddit shit doing in this thread. Jannies on strike?

Anonymous

Anonymous Fri 28 Jan 2022 21:54:56 No.14160230 Report

Quoted By: >>14160239 >>14160243 >>14160257

How does one publish as an enthusiast ? How do I approach academics for possible co-author without looking like a schizo ?

Anonymous

Anonymous Fri 28 Jan 2022 21:57:10 No.14160239 Report

Quoted By: >>14160491

>>14160230
what do you want to publish
where do you want to publish it
do you have a result, or are close to it

Anonymous

Anonymous Fri 28 Jan 2022 21:58:06 No.14160243 Report

Quoted By: >>14160491 >>14162979

>>14160230
If you think you have something interesting to say that you need someone else's help to write properly, just email them or something. Profs often reply even to emails from schizi let alone nonschizi.

Anonymous

Anonymous Fri 28 Jan 2022 22:01:43 No.14160257 Report

Quoted By: >>14160291 >>14160301

>>14160230
>co-author
you gonna do any of the work, like research or typesetting?
if not, there are journals that publish anything, so long as you pay "publication fee"
all you need to is hire a typist to type some garbage, then pay the journal to publish it
lots of people do that
have you heard of "Wildberger"?

Anonymous

Anonymous Fri 28 Jan 2022 22:08:27 No.14160291 Report

Quoted By: >>14160334 >>14160348

>>14160257
Norman Wildberger is an actual PhD mathematician who published in analysis before going insane. Probably not the best example of someone who uses a pay-to-publish journal.

Anonymous

Anonymous Fri 28 Jan 2022 22:09:28 No.14160301 Report

Quoted By: >>14160386

>>14160257
Can you point to any specific issues with Wildberger's papers on Lie thoery, or are you just making things up because you don't like his philosophical views on the foundations of mathematics?

Anonymous

Anonymous Fri 28 Jan 2022 22:14:20 No.14160334 Report

Quoted By: >>14160345

>>14160291
How has he gone insane? Can you point out your reasons for thinking he is insane?

Anonymous

Anonymous Fri 28 Jan 2022 22:16:32 No.14160345 Report

Quoted By: >>14160445

>>14160334
He denies the reals and rejects the consensus of math experts.

Anonymous

Anonymous Fri 28 Jan 2022 22:16:59 No.14160348 Report

Quoted By: >>14160374

>>14160291
Wildberger made his publication list public at some point. If you would mind to look at it,
you will observe whether he is a good example of someone who has used pay-to-publish.
And let the graduate student "co-authors" do the work and the typesetting.
Pretty sure that you have not bothered to do so until now, dear unbiased anon?

Anonymous

Anonymous Fri 28 Jan 2022 22:20:31 No.14160374 Report

Quoted By: >>14160426

>>14160348
He has a list of his papers here:
https://web.maths.unsw.edu.au/~norman/papers.htm
Which one was pay-to-publish?

Anonymous

Anonymous Fri 28 Jan 2022 22:22:56 No.14160386 Report

Quoted By: >>14160419

>>14160301
Firstly, it is not possible to have "philosophical views" of something about which you are entirely clueless.
Wildberger never contributed to the theory of Lie Algebras anyway.

Anonymous

Anonymous Fri 28 Jan 2022 22:27:12 No.14160419 Report

Quoted By: >>14160441

>>14160386
>Wildberger never contributed to the theory of Lie Algebras anyway
How is the paper below not a contribution?
https://web.maths.unsw.edu.au/~norman/papers/CombinatorialLieAlgebras.pdf

Anonymous

Anonymous Fri 28 Jan 2022 22:29:04 No.14160426 Report

Quoted By: >>14160437

>>14160374
That is nice.
His own carefully edited list omits publication dates, journal names and "co-author" names.
Good work anon, you essentially proved my point.

Anonymous

Anonymous Fri 28 Jan 2022 22:32:11 No.14160437 Report

Quoted By: >>14160481 >>14160523

>>14160426
>carefully edited list
As opposed to a carelessly edited list, which would be better somehow?
>omits publication dates
All his papers as far as I've checked have publication dates.
>avoids journal names
But he doesn't. Did you even read the list? E.g.
"Characters, bi-modules and representations in Lie group harmonic analysis in Harmonic Analysis and Hypergroups Trends in Mathematics Eds. K. A. Ross et al Proceedings Delhi 1995 Birkhauser 1998"
>and "co-author" names
He doesn't. E.g. "(with N. Obata) Generalized hypergroups and orthogonal polynomials". No offense but you come across as the schizo here. Is everything ok?

Anonymous

Anonymous Fri 28 Jan 2022 22:32:28 No.14160441 Report

Quoted By:

>>14160419
A "construction" does not add to a theory.
Anyway the paper is just basic graph theory.
And no, it does not add to graph theory either.

Anonymous

Anonymous Fri 28 Jan 2022 22:33:46 No.14160445 Report

Quoted By:

>>14160345
I've yet to hear a good explanation for how Cauchy equivalence classes aren't rigorous. It appears to be a circular logic whereby a sequence can be properly defined in ZF to be e.g. either {0,0...} or {1,1...} but of course not both at the same time. However, the existence of two possible convergences is also irrelevant by ZF standards because the false "paradox" can't be quantified by first order logic and so the fact that the sequence always converges, regardless of where it converges to, is enough for the Cauchy equivalence class definition to be rigorous as is.

Anonymous

Anonymous Fri 28 Jan 2022 22:41:12 No.14160481 Report

Quoted By:

>>14160437
Then let us take this little excerpt from the published articles of an obscure Croatian journal:
https://hrcak.srce.hr/en/pretraga?q=Wildberger
These are not really articles which he wants the general public to know of, are they?

Anonymous

Anonymous Fri 28 Jan 2022 22:43:30 No.14160491 Report

Quoted By: >>14160509 >>14160665

>>14160243
>>14160239
Thanks.When I think about it I have an old econ prof that was also a math prof at another university. Its just a cool sequence I found thats not in OEIS.
Cheers

Anonymous

Anonymous Fri 28 Jan 2022 22:46:38 No.14160509 Report

Quoted By:

>>14160491
I love the OEIS, you should just make an account and submit the sequence along with any cool descriptions, relationships, or proofs you've written about it.

Anonymous

Anonymous Fri 28 Jan 2022 22:49:55 No.14160523 Report

Quoted By:

>>14160437
The webpage that I was pointed to did not show any of that kind of information.
Which I assumed was on purpose.

Anonymous

Anonymous Fri 28 Jan 2022 23:17:33 No.14160665 Report

Quoted By:

>>14160491
neat
you have the right idea, people you know can at the very least put you in contact with the people you need
gl anon

Anonymous

Anonymous Fri 28 Jan 2022 23:20:21 No.14160676 Report

Quoted By: >>14160962 >>14163486 >>14163785

honestly why the fuck are there so many trannies studying type theory?

Anonymous

Anonymous Fri 28 Jan 2022 23:31:23 No.14160714 Report

Quoted By: >>14161004 >>14162212

>>14159421
>feel free to point to an infinite prime
$\omega, \omega + 1, \omega^2 + 1, \omega^3 + 1, ..., \omega^\omega, \omega^\omega + 1, ...$

Anonymous

Anonymous Sat 29 Jan 2022 00:44:43 No.14160954 Report

Quoted By:

>>14154030
Thriftbooks

Anonymous

Anonymous Sat 29 Jan 2022 00:46:25 No.14160962 Report

Quoted By:

>>14160676
A: they are whatever these days passes as a computer scientists

Anonymous

Anonymous Sat 29 Jan 2022 01:04:38 No.14161004 Report

Quoted By:

>>14160714
pw equiv w -> plw
w equiv w¬{1,..,p-1} -> pw equiv w equiv w¬{1,..,p-1}
-> w+1 equiv p[w¬{1,...,p-1}+1]

Anonymous

Anonymous Sat 29 Jan 2022 01:57:43 No.14161154 Report

Quoted By: >>14161337 >>14161636

>>14146782
can this actually be done?
>pythagorean theorem
$a = x \\ b = \frac{12x}{9} \\ c = 5 \\$
or in other words
$x^2 + \left(\frac{12x}{9}\right)^2 = 5^2$
I tried to use quadratic formula, but doesn't seem to satisfy the quadratic equation ( ${ax}^2 + bx + c = 0$ )
$x^2 + \left(\frac{12x}{9}\right)^2 = 5^2 \\ x^2 + \frac{12^2x^2}{9^2} = 5^2 \\ x^2 + x^2 \frac{12^2}{9^2} - 5^2 = 0$
the $bx$ in this case is $bx^2$

Anonymous

Anonymous Sat 29 Jan 2022 03:11:42 No.14161337 Report

Quoted By: >>14161830

>>14161154
>the bx in this case is bx^2
no, it's 0. you have 25/9*x^2 = 25.

Anonymous

Anonymous Sat 29 Jan 2022 04:10:04 No.14161491 Report

Quoted By:

does the euclidean algorithm have any practical use?

Anonymous

Anonymous Sat 29 Jan 2022 04:48:13 No.14161611 Report

Quoted By:

>>14153314
stop avatarfagging and I might consider reading your posts you fucking nigger

Anonymous

Anonymous Sat 29 Jan 2022 05:01:23 No.14161636 Report

Quoted By: >>14161830

>>14161154
Try $a = x^2$

$(x^2)^2 + (\frac{12x}{9})^2 = 5^2$
$x^4 + \frac{144x^2}{81} -25 = 0$
$x = \frac{-\frac{144}{81}-\sqrt{(\frac{144}{81})^2 - 4(-25)}{2}$

Anonymous

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Anonymous Sat 29 Jan 2022 05:56:35 No.14161749 Report

Quoted By: >>14164979

hello. i am not very smart yet. i am trying to learn. i have picked up a book to try to learn. can anyone explain to me what the subscript n represents here?

Anonymous

Anonymous Sat 29 Jan 2022 06:33:31 No.14161830 Report

Quoted By:

>>14161636
gives me
$\left(x^2\right)^{2} + {\left(\frac{12x}{9}\right)}^{2} = 5^2 \\ x^4 + \frac{144x^2}{81} - 25 = 0 \\ x = \frac{-\frac{144}{81}-\sqrt{\left(\frac{144}{81}\right)^2 - 4(-25)}}{2} \\ x = \frac{-\frac{144}{81}-\sqrt{\left(\frac{144}{81}\right)^2 + 100}}{2} \\ x = \frac{-\frac{144}{81}-\sqrt{\frac{20736}{6561} + 100}}{2} \\ x = -5.9672866142339736$
doesn't seem to work
$-5.9672866142339736^2 + \left(\frac{12 \times -5.9672866142339736}{9}\right)^2 = \\ -5.9672866142339736^2 + \frac{144 \times -5.9672866142339736^2}{81} = 98.91252649004433 \\ 98.91252649004433 \ne 25$
>>14161337
>25/9*x^2 = 25
where'd you get this?

Anonymous

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Anonymous Sat 29 Jan 2022 10:38:13 No.14162212 Report

Quoted By:

>>14160714
WHAT

Anonymous

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Anonymous Sat 29 Jan 2022 12:26:22 No.14162472 Report

Quoted By: >>14162791 >>14162815

Given a totally ordered set X of finite size n, for a given m <= n, how many ordered tuples, call the number Q(n,m), are there?

(E.g. if n=7, i.e. X={1,2,...,7} and m=3, the tuple (2, 4, 7) would be one of many)

Anonymous

Anonymous Sat 29 Jan 2022 14:02:47 No.14162791 Report

Quoted By:

>>14162472
Have you ever heard about binomial coefficients?

Anonymous

Anonymous Sat 29 Jan 2022 14:10:47 No.14162815 Report

Quoted By:

>>14162472
>knows about totally ordered sets
>never heard of binomial coefficients
The absolute state of /sci/

Anonymous

Anonymous Sat 29 Jan 2022 14:59:44 No.14162979 Report

Quoted By: >>14162998 >>14163189

>>14160243
>Profs often reply even to emails from schizi let alone nonschizi.
No they don't

Anonymous

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Anonymous Sat 29 Jan 2022 15:05:52 No.14162997 Report

Quoted By:

>>14152168
Yes, Kähler

>Politically, Kähler said that he was inclined toward German nationalism (like many of his colleagues), and Hitler awakened in him the feeling of a greater Germany (which he apparently responded to by desiring military service, rather than by joining the party). The Führerprinzip was, he felt, not bad in itself: for to be Führer meant to be responsible. His oath to Hitler (as a civil servant) was very important to him: he thought of Hitler as his Kaiser. There was a "cult of genius" around Hitler; hence, in Kähler’s view, there are no neo-Nazis because one can’t be a Nazi without Hitler, whose real aim was the nullification of the Versailles Treaty. He thought Hitler’s high politics could not be widely understood, as they were supranational, like Roman politics. No one had dug so deeply into history as Hitler. No doubt there were criminals in high places in Hitler’s Germany, but the leadership of the country was not criminal. Similarly, Kähler thought the blaming of the whole German people, a Kulturvolk (cultural nation), for the criminal acts of some was not only inappropriate, but resulted from an intentional desire to make Germany politically impotent.

Anonymous

Anonymous Sat 29 Jan 2022 15:05:53 No.14162998 Report

Quoted By:

>>14162979
Thanks, your opinion means a lot to me.

Anonymous

Anonymous Sat 29 Jan 2022 15:12:33 No.14163032 Report

Quoted By:

>>14152168
Honestly, he just sounds like a cunt. I don't imagine those black studends had an easy time getting into a university under that kind of climate; they must have been fairly competent and determined to make it. I generally hate niggers, but being indiscriminate to THAT degree just seems like irrational malice,.

Anonymous

Anonymous Sat 29 Jan 2022 15:33:58 No.14163098 Report

Quoted By: >>14163101

what's up with finitism on this board?
is it mostly just contrarianism?

Anonymous

Anonymous Sat 29 Jan 2022 15:35:07 No.14163101 Report

Quoted By: >>14163103 >>14163122

>>14163098
Something with people getting fed up with mental frameworks that are fundamentally divorced from reality and violate human intuition.

Anonymous

Anonymous Sat 29 Jan 2022 15:35:54 No.14163103 Report

Quoted By: >>14163106

>>14163101
how do you know what reality is?

Anonymous

Anonymous Sat 29 Jan 2022 15:36:49 No.14163106 Report

Quoted By: >>14163111

>>14163103
Yeah, exactly... that whole line of thought. Many people have grown nauseated with it, and reject it.

Anonymous

Anonymous Sat 29 Jan 2022 15:38:27 No.14163111 Report

Quoted By: >>14163116

>>14163106
how do you know your particular framework corresponds to reality better than the standard one?

Anonymous

Anonymous Sat 29 Jan 2022 15:40:17 No.14163116 Report

Quoted By: >>14163119

>>14163111
You simply refuse to understand what you're readinhg, which is part of why people have grown to hate everything associated with your belief system.

Anonymous

Anonymous Sat 29 Jan 2022 15:41:32 No.14163119 Report

Quoted By: >>14163122

>>14163116
you're dodging the question
I've also never stated my position anywhere

Anonymous

Anonymous Sat 29 Jan 2022 15:43:22 No.14163122 Report

Quoted By: >>14163125

>>14163119
I answered your question here: >>14163101
Your followup is completely irrelevant except in demonstrating the point.

Anonymous

Anonymous Sat 29 Jan 2022 15:44:46 No.14163125 Report

Quoted By: >>14163129

>>14163122
ok I see
you just won't answer then
you usually get these "just because" replies from contrarians

Anonymous

Anonymous Sat 29 Jan 2022 15:45:52 No.14163129 Report

Quoted By:

>>14163125
I answered your question. You have not been able to address that response beyond primitive "tu quoque" retorts.

Anonymous

Anonymous Sat 29 Jan 2022 16:02:47 No.14163189 Report

Quoted By:

>>14162979
often =/= always, tooker

Anonymous

Anonymous Sat 29 Jan 2022 16:04:57 No.14163195 Report

Quoted By: >>14163200

finitism and communism have many paralells

Anonymous

Anonymous Sat 29 Jan 2022 16:07:18 No.14163200 Report

Quoted By: >>14163391

>>14163195
>everything I don't like is communism

Anonymous

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Anonymous Sat 29 Jan 2022 16:09:29 No.14163209 Report

Quoted By: >>14163220

>finitism and communism have many paralells
The absolute state... If anything, leftism and modern mathematics have much in common in their obsession with meaningless mental constructs.

Anonymous

Anonymous Sat 29 Jan 2022 16:11:46 No.14163220 Report

Quoted By: >>14163239

>>14163209
>everything I don't like is leftism

Anonymous

Anonymous Sat 29 Jan 2022 16:16:22 No.14163239 Report

Quoted By: >>14163270

>>14163220
Who are you quoting, schizophrenic brainwash vicitim?

Anonymous

Anonymous Sat 29 Jan 2022 16:26:36 No.14163270 Report

Quoted By:

>>14163239
>Who are you quoting, schizophrenic brainwash vicitim?

Anonymous

Anonymous Sat 29 Jan 2022 17:09:01 No.14163391 Report

Quoted By:

>>14163200
are you projecting your dislike of communism?

Anonymous

Anonymous Sat 29 Jan 2022 17:36:33 No.14163486 Report

Quoted By:

>>14160676
Autism

Anonymous

Anonymous Sat 29 Jan 2022 18:38:21 No.14163658 Report

Quoted By: >>14163685 >>14163728 >>14163935 >>14163939 >>14163940 >>14168648

Do you write Tchebychev or Chebychev?

Anonymous

Anonymous Sat 29 Jan 2022 18:43:02 No.14163685 Report

Quoted By:

>>14163658
I write Tscheboratev

Anonymous

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Anonymous Sat 29 Jan 2022 18:45:57 No.14163698 Report

Quoted By: >>14163727 >>14164089

how to solve this

Anonymous

Anonymous Sat 29 Jan 2022 18:53:45 No.14163727 Report

Quoted By:

>>14163698
It must use that the continuum hypothesis is undecidable in ZFC if the answer is undecidable.

Anonymous

Anonymous Sat 29 Jan 2022 18:53:46 No.14163728 Report

Quoted By:

>>14163658
I write Chebychev but Tchaikovsky, for no reason I can think of other than habit.

Anonymous

Anonymous Sat 29 Jan 2022 19:10:30 No.14163785 Report

Quoted By:

>>14160676
it is useless effeminate abstraction, homosexual schizophrenics become obsessed with decomposing reality into a world of static forms. See: Hegelian philosophy

Anonymous

Anonymous Sat 29 Jan 2022 19:52:42 No.14163935 Report

Quoted By:

>>14163658
just write ?e???e?

Anonymous

Anonymous Sat 29 Jan 2022 19:53:43 No.14163939 Report

Quoted By:

>>14163658
?ebyšev

Anonymous

Anonymous Sat 29 Jan 2022 19:53:55 No.14163940 Report

Quoted By:

>>14163658
Czebyszew.

Anonymous

Anonymous Sat 29 Jan 2022 20:38:01 No.14164089 Report

Quoted By: >>14164412

>>14163698
True with CH, false with Easton's theorem. With Eastons theorem you can make all cardinals k with k<l we have 2^k=2^l.

Anonymous

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Anonymous Sat 29 Jan 2022 20:40:49 No.14164095 Report

Quoted By:

>12/15 on calc quiz because I couldn't define a function for an arbitrary size of epsilon
>gonna get below a 90% on discrete math quiz on proof methods, I can feel it.

Anonymous

Anonymous Sat 29 Jan 2022 22:19:40 No.14164412 Report

Quoted By: >>14165101

>>14164089
thank you
https://en.wikipedia.org/wiki/Easton%27s_theorem
so just to make sure i got this correct:
i can just take G that maps 0->2, 1->3, 2->3
the cofinality conditions work out because successor cardinals are regular
so we get a model where
2^?0 = ?2 (=continuum)
2^?1 = ?3
2^?2 = ?3
and equality in the problem statement follows.

Anonymous

Anonymous Sun 30 Jan 2022 00:53:17 No.14164979 Report

Quoted By:

>>14161749
n is the number of times the algo is performed
T is "a number of times it could be performed", Tn denotes which number that actually is

Anonymous

Anonymous Sun 30 Jan 2022 01:20:11 No.14165101 Report

Quoted By:

>>14164412
Yeah. You don't need the full power of easton for this of course, you can do this directly with a forcing construction.

Anonymous

Anonymous Sun 30 Jan 2022 01:45:09 No.14165196 Report

Quoted By: >>14165214 >>14166674

Fellas, am I setting myself up for disappointment by trying really hard to get straight A's in a math major? I am three weeks into two math courses, and I'm teetering at 91% and 94% respectively for both courses. Last semester I was able to get two A's in math, but classes get harder and more abstract the more I go into it. Thinking of it logically, I am by no means a math wiz or high end graduate material, but if I did get straight A's, it would imply I were. Therefore, I should be satisfied with B's and C's which more closely align with my self image in math.

Anonymous

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Anonymous Sun 30 Jan 2022 01:53:46 No.14165214 Report

Quoted By: >>14167131

>>14165196
>Therefore, I should be satisfied with B's and C's which more closely align with my self image in math.
The reason you're in university is to learn the course material.

Anonymous

Anonymous Sun 30 Jan 2022 09:13:53 No.14166100 Report

Quoted By: >>14166122

So I know if I have a sheet of paper and glue both its opposing edges together in the same orientation I'll end up with a torus, but what if I started with a cube? What (I assume it's 4d) shape do I end up with?

Anonymous

Anonymous Sun 30 Jan 2022 09:26:34 No.14166122 Report

Quoted By:

>>14166100
A "3d torus" (seriously)

Anonymous

Anonymous Sun 30 Jan 2022 14:44:17 No.14166666 Report

Quoted By: >>14166830

I need someone to talk to. Im self teaching logic and set theory to myself with enderton. But theres no one i can talk to. Where and how can i find someone to talk to about math. I dont need help, i just want someone to talk to.

Anonymous

Anonymous Sun 30 Jan 2022 14:50:16 No.14166674 Report

Quoted By: >>14167131

>>14165196
the only reason to care about letter grades is GPA. your GPA only matters with respect to your education because your future employer isn't going to give much of a shit about it, and a few years out of college it won't matter at all

unless you intend to stay in education and become a teacher or something in which case I don't know how GPA factors into that, but I'd be surprised if it mattered beyond making sure it's not something sub 2.

ALL OF THAT ASIDE your letter grade in a class also reflects who is teaching it, how they are teaching it, and what material is being covered in what order and how your mastery of each topic is verified (homework, tests, etc). None of which are objective, so a B in a course with one instructor might easily be an A or C with another. So there's no point in worrying about how a grade reflects your knowledge in a subject. YOU know how much you learned, and that's what is going to matter the most.

Anonymous

Anonymous Sun 30 Jan 2022 16:05:15 No.14166830 Report

Quoted By: >>14170380

>>14166666
What would you like to talk about gigasatan?

Anonymous

Anonymous Sun 30 Jan 2022 16:22:35 No.14166884 Report

Quoted By:

can there be a prime factoring algorithm that takes primes found and recycles them back into the algorithm elliptically making the process increase in speed as the algorithm increases in difficulty?

Anonymous

Anonymous Sun 30 Jan 2022 17:50:35 No.14167131 Report

Quoted By:

>>14165214
>>14166674
Thank you for the encouragement. In the end, I am not interested in a PhD, just a masters, so I should worry more about understanding than stress over points on tests.

Anonymous

Anonymous Sun 30 Jan 2022 18:12:32 No.14167198 Report

Quoted By: >>14167453

I'm going over intro to proofs in class.
The book we are using is Rosen's "Discrete math and its applications", and I am using book of proof and a transition to advanced mathematics as supplementary reading.

So far the way I understand it, it seems that to prove anything, I need a small toolkit of basic identities and basic proofs(to use as lemmas) in order to answer proof questions. That is, if I have a problem such as;
"prove that if n is a positive integer, then n is odd iff 5n+6 is odd.
So this is a biconditional statement and I have to prove p->q and q->p, but the way I've answered this problem and similar ones, is by proving the product of odds are always odd, sum of odd and even, product of two evens, etc. Once I have all the sub processes proved for any arbitrary number, it the proof to the larger question follows.
Now this leads to a tricky spot, where I do not know how far down to prove things. At what point do we take something for granted as an axiom? If we took the product of odds as an axiom, why not say "we take that if n is a positive integer, then n is odd iff 5n+6 is odd" is an axiom? Do I need to list all identities for every problem?
I did email my professor but he won't get back to me today since its sunday, and I'm a bit stuck here. Not stuck as in I cant continue, as I already turned in all the work for the week with what seemed reasonable, but stuck in my own head in determining what are the customary axioms in basic proofs.

Anonymous

Anonymous Sun 30 Jan 2022 19:20:37 No.14167453 Report

Quoted By:

>>14167198
restating the problem as an axiom doesnt really show you understand it
think of the general form for an even number, and the general form of an odd number
it should be 1-2 lines of algebra to show each 'direction'

Anonymous

Anonymous Sun 30 Jan 2022 20:22:33 No.14167696 Report

Quoted By: >>14167704

>>14146782
can an irrational number be commensurable to another irrational number?

Anonymous

Anonymous Sun 30 Jan 2022 20:24:07 No.14167704 Report

Quoted By: >>14167740 >>14167796

>>14167696
wait am i retarded? wouldn't the answer to this just be yes because if you divide an irrational number by 2 then that new number is commensurable to the old number by a factor of two. so then the question is it even meaningful to describe irrational numbers as incommensurable, seeing as if you have a unit 1 it can be commensurable to any irrational number just by multiplying it by that irrational number.

Anonymous

Anonymous Sun 30 Jan 2022 20:32:18 No.14167740 Report

Quoted By:

>>14167704
One length being commensurate to another basically means one is a rational multiple of the other.

Anonymous

Anonymous Sun 30 Jan 2022 20:45:12 No.14167796 Report

Quoted By:

>>14167704
a in R \ Q
Q[a] \ Q

Anonymous

Anonymous Sun 30 Jan 2022 20:57:12 No.14167841 Report

Quoted By:

>>14147111
If you don't understand computational methods you have no hope in the academic world. I'm sorry, but you will end up filtered.

Imagine getting a math degree and not learning the most effective methods for solving most problems. Even just digging into the methods themselves is pretty beautiful. It's literally amazing how accurate you can get with just elegant computations.

Anonymous

Anonymous Sun 30 Jan 2022 21:06:28 No.14167868 Report

Quoted By: >>14177973

>>14153752
Yes there is. It's a pretty well defined problem in time series analysis (just less often used). If it's a simple dataset, you can probably just do a polynomial regression and be fine. If it's more complex, pop open a time series analysis text and search for backwards forecast.

Anonymous

Anonymous Sun 30 Jan 2022 23:31:22 No.14168413 Report

Quoted By:

Where do I go after introductory logic and set theory?
I enjoyed working with symbolic logic and translating language to logic.

Anonymous

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Anonymous Sun 30 Jan 2022 23:39:34 No.14168449 Report

Quoted By: >>14168452 >>14168522 >>14168611

Hey everyone, I'm trying to learn math all over again but I'm really confused regarding the solution of a rather simple equation.
The equation itself is just:
\frac{ \sqrt{2} }{\sqrt{10}+\sqrt{2}}
Wolfram says that it's the bottom one, but I don't understand why, I understand how to get there but I cannot see the reasoning. One of them must be wrong since they give out different answers.

Thanks.

Anonymous

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Anonymous Sun 30 Jan 2022 23:40:35 No.14168452 Report

Quoted By:

>>14168449
I don't know how to make TeX work, sorry.

Anonymous

Anonymous Sun 30 Jan 2022 23:57:01 No.14168522 Report

Quoted By: >>14168590

>>14168449
How can you possibly think that
(2 sqrt(5) -2)/8 = (sqrt(5)-2)/4 ?

Do you think (4-2)/2 = (2-2)/1 ?

Anonymous

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Anonymous Mon 31 Jan 2022 00:05:08 No.14168544 Report

Quoted By: >>14168564 >>14168683 >>14168743

Can someone help me out here. What is the cardinality of the set of all real functions that integrate to 1?

Anonymous

Anonymous Mon 31 Jan 2022 00:10:27 No.14168564 Report

Quoted By: >>14168579

>>14168544
50%, either it integrates to 1 or it doesn't.

Anonymous

Anonymous Mon 31 Jan 2022 00:14:46 No.14168579 Report

Quoted By:

>>14168564
arent there more probability distributions than real numbers?

Anonymous

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Anonymous Mon 31 Jan 2022 00:18:46 No.14168590 Report

Quoted By: >>14168661

>>14168522
>Do you think (4-2)/2 = (2-2)/1 ?
No, because in this case I'm not multiplying.
I was thinking about it and i believe my error was not using the parenthesis.I tried to explain with picrel.

Anonymous

Anonymous Mon 31 Jan 2022 00:23:41 No.14168611 Report

Quoted By: >>14168630

>>14168449
If you don't understand what is going on with a fraction, or anything, break it down into simpler terms that you do understand.
$ \frac{2\sqrt{5} - 2}{8} = \frac{2\sqrt{5}}{8} - \frac{2}{8} = \frac{\sqrt{5}}{4} - \frac{1}{4} = \frac{\sqrt{5}-1}{4} $

Anonymous

Anonymous Mon 31 Jan 2022 00:28:57 No.14168630 Report

Quoted By:

>>14168611
That makes a lot of sense, I understand it completely now.
Thank you very much anon, I'll try to break things down when I'm in doubt.

Anonymous

Anonymous Mon 31 Jan 2022 00:29:27 No.14168632 Report

Quoted By:

>>14152700
Dembo’s notes are good. Also Montanari has some good stuff on his course page.

Anonymous

Anonymous Mon 31 Jan 2022 00:35:31 No.14168648 Report

Quoted By:

>>14163658
Chebyshev.

Anonymous

Anonymous Mon 31 Jan 2022 00:39:43 No.14168661 Report

Quoted By:

>>14168590
You need to understand that your second row there is absolutely wrong. Why would you think you can do this? Is this an order of operations issue?
$\frac{2*\sqrt{5} -2}{8} = \frac{(2*\sqrt{5}) -2}{8}$
If you want to cancel out a factor of 2 from the denominator, you need to cancel out a factor of 2 from each term being added (or subtracted) in the numerator, not just the first one. After all, you could break this up into multiple fractions as $\frac{2*\sqrt{5}}{8] -\frac{2}{8}$

Anonymous

Anonymous Mon 31 Jan 2022 00:44:32 No.14168683 Report

Quoted By:

>>14168544
Pretty sure it's the same cardinality as the reals.

Anonymous

Anonymous Mon 31 Jan 2022 01:03:46 No.14168743 Report

Quoted By: >>14171263

>>14168544
Riemann or Lebesgue integration?
I think I have seen a claim that the cardinality of the set of Lebesgue measurable sets is greater than the cardinality of the reals, and it shouldn't be that hard to map each such measurable set to a real function that integrates to 1.
(Something like, Map those sets with a positive measure by pointwise applying e^x, and then scaling the indicator function of the resulting set by the reciprocal of its measure. Also pointwise apply e^x to sets of measure zero, but then add the interval [-1,0], and give the indicator function of the result.)

Anonymous

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Anonymous Mon 31 Jan 2022 04:08:41 No.14169271 Report

Quoted By: >>14169870 >>14173605

I HATE CANTOR
I HATE CANTOR

Anonymous

Anonymous Mon 31 Jan 2022 08:38:41 No.14169734 Report

Quoted By:

>>14153314
>They're literally inventing a million genders and saying math is racist.
You're conflating the different sciences and journalists with scientific researchers

Anonymous

Anonymous Mon 31 Jan 2022 09:55:52 No.14169870 Report

Quoted By: >>14170097

>>14169271
A major field of set theory is finding ways to avoid AC.

Anonymous

Anonymous Mon 31 Jan 2022 12:00:56 No.14170097 Report

Quoted By: >>14170164

>>14169870
what about DC?

Anonymous

Anonymous Mon 31 Jan 2022 12:32:44 No.14170164 Report

Quoted By: >>14170365

>>14170097
I heard that the Potomac river was pretty nice.

Anonymous

Anonymous Mon 31 Jan 2022 13:47:41 No.14170337 Report

Quoted By: >>14170417

So two lines meet at a point and one dimension up from that two plane figures meet along a curve.
Is arc length of that curve the higher dimensional equivalent of the angle of that point or is there more structure to it? Since two different curves can have the same arc length I think some other measure has to apply.

Anonymous

Anonymous Mon 31 Jan 2022 14:03:07 No.14170365 Report

Quoted By:

>>14170164
They obviously mean Dependant Choice anon.

Anonymous

Anonymous Mon 31 Jan 2022 14:07:58 No.14170380 Report

Quoted By:

>>14166830
Nvm, i was just lonely. I felt alone. Maybe im okay now.

Anonymous

Anonymous Mon 31 Jan 2022 14:28:19 No.14170417 Report

Quoted By:

>>14170337
Extending the intersection of two non-colinear lines to the intersection of two non-coplanar plane regions is pretty easy, not sure what you're finding an issue with.

Anonymous

Anonymous Mon 31 Jan 2022 14:41:22 No.14170446 Report

Quoted By: >>14171247

Finished studying Aluffi's Algebra and need a treatment of representation theory, commutative algebra and a bit more Galois theory. Ideally enough to get me through a course on schemes and another on algebraic number fields.

Any recommends? Considering reading relevant chapters in Jacobson or maybe some course notes.

As an aside, hurts my gonads to have to do this after working through Aluffi's tome, but it was great nevertheless.

Anonymous

Anonymous Mon 31 Jan 2022 15:01:16 No.14170499 Report

Quoted By:

Looking to begin a PhD in applied mathematics this year. Would getting balls deep into machine learning be a good idea for my career going forwards at this point? I no particular interest, but many of the projects and positions I see emphasise the desire of the given department to start looking for ML applications in whatever their research is. (I'm skeptical of this but whatever)

Anonymous

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Anonymous Mon 31 Jan 2022 18:39:46 No.14171247 Report

Quoted By: >>14173454

>>14170446
Since you chose Aluffi you may find this article useful: https://scholar.rose-hulman.edu/cgi/viewcontent.cgi?article=1078&context=rhumj

Anonymous

Anonymous Mon 31 Jan 2022 18:44:32 No.14171263 Report

Quoted By:

>>14168743
You could also integrate the indicator functions of complements of subsets of the Cantor set relative to [0,1]. This would have size equal to the size of the power set of R.

Anonymous

Anonymous Tue 01 Feb 2022 02:47:46 No.14173204 Report

Quoted By:

I'm struggling with some homework on the Jordan separation theorem. I'm supposed to prove that R^N is divided into two disconnected parts by a single infinite R^(N-1) space in the same way but can't do it. Somebody suggest some reading please.

Anonymous

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Anonymous Tue 01 Feb 2022 03:21:47 No.14173331 Report

Quoted By: >>14175198

So what do you do with mathematics exactly? Where can you apply the knowledge? I'd like to know, as a guy who can't even do basic counting without instantly enabling mental fatigue and intrusive thoughts, if it's worth pursuing along with something like linguistics or so. Genuinely interested in getting into it, but I've always had a hard time with numbers.

Anonymous

Anonymous Tue 01 Feb 2022 04:14:06 No.14173454 Report

Quoted By:

>>14171247
Had no idea this was a thing but not sure how I feel about the categorical reformulation invoking the non-categorical result in its proof. Maybe missed something when scaning. In any case, pretty cool desu

Anonymous

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Anonymous Tue 01 Feb 2022 05:38:56 No.14173605 Report

Quoted By: >>14174211

>>14169271
Set theory? That's another hoax just like the reals.

Anonymous

Anonymous Tue 01 Feb 2022 12:46:33 No.14174211 Report

Quoted By:

>>14173605
> this is what an /x/ poster looks like

Anonymous

Anonymous Tue 01 Feb 2022 12:50:18 No.14174216 Report

Quoted By: >>14175173 >>14177932

Where do I begin with analysis? Suppose my goal is to eventually do functional analysis, what should I learn to get to that level (textbook recommendations appreciated)?

Anonymous

Anonymous Tue 01 Feb 2022 13:40:09 No.14174321 Report

Quoted By:

how do i git gud at proving something?

Anonymous

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Anonymous Tue 01 Feb 2022 18:26:53 No.14175173 Report

Quoted By:

>>14174216
Be really good at Linear Algebra and Analysis in general. Functional Analysis is the study of non-finite vector spaces.

Some books
>Axler or Shilov Linear Algebra
Why? Good solid non-retard introductions to Linear Algebra. A good place to start. I think the former is more proof heavy than the latter but Shilov doesn't fuck around either

>Roman Advanced Linear Algebra
Your bible. Take turns with your waifu at night.

>Analysis
Blue Rudin, Green Rudin, Lang. If you're feel weaker grab Abbott and do every exercise you can

>Functional Analysis
Kryezig or Lax I believe are good choices to start. Not sure what the bible of this subject is but Rudin sounds like a contender

As always spam the mother fucking triangle inequality and practice from the Cauchy Schearz Master Class book.

That should be more than enough. If you get this far I'll buy you a pizza.

Anonymous

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Anonymous Tue 01 Feb 2022 18:31:38 No.14175198 Report

Quoted By:

>>14173331
Most mathematicians aren't concerned with doing anything with mathematics. They simply do mathematics for its own sake.

If course, math obviously has applications. Literally pick anything and math has applications. Linguistics is a big one, look into mathematical linguistics

>Bad at numbers
Math has very little to do with numbers unless your a number theoriest and even then not in the way you're thinking. Mathematics is entirely about structure, symmetry, pattern recognition, and theorem proving (amongst other things).

Anonymous

Anonymous Tue 01 Feb 2022 20:53:20 No.14175772 Report

Quoted By:

>>14146782
How hard is Calc 3 webassign?

Anonymous

Anonymous Tue 01 Feb 2022 21:35:33 No.14175960 Report

Quoted By:

Are there any applications to the classification of manifolds or is doing so just the goal in of itself?

Anonymous

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Anonymous Tue 01 Feb 2022 23:53:08 No.14176450 Report

Quoted By: >>14177895

So I just finished Khan Academy's multivariable calculus course, it was amazing and very enjoyable.
But what is the deal with directional derivatives, those are introduced very early and I think those are never mentioned again, at least not directly, in the ~150 videos after their introduction.
Gradient, curl, divergence all of those are mentioned and used throughout the whole course but directional derivatives are not, which is strange because they seemed like a big deal. Or maybe I'm missing something.

Anonymous

Anonymous Wed 02 Feb 2022 01:49:01 No.14176669 Report

Quoted By: >>14179818

So I graduate my mba program in May. I graduated from my undergrad in 2016 and have the itch to expand my knowledge in number theory since my favorite classes were number theory and algebra 1&2.

Are there any online materials (besides textbooks) that offer the opportunity to learn more about it? If not, any recommendations for textbooks? Thinking about going up to my old college and talking with an advisor about the opportunity to take and learn some of their material from the graduate number theory course

Anonymous

Anonymous Wed 02 Feb 2022 04:41:58 No.14177062 Report

Quoted By: >>14178727

Despite having topology notes to work through I've been thinking about how a line of slope 2 has a crazy irrational angle measure.
Is there any work in showing the algebraic independence of arctan a and arctan b, or arctan a and log b, for rational a,b?

Anonymous

Anonymous Wed 02 Feb 2022 12:11:21 No.14177895 Report

Quoted By: >>14179354

>>14176450
If you want something more challenging that uses these concepts get a textbook on differential geometry. You may want to do general topology first though since they both use manifolds.

Anonymous

Anonymous Wed 02 Feb 2022 12:30:45 No.14177932 Report

Quoted By:

>>14174216
Amann and Escher's Analysis series.

Anonymous

Anonymous Wed 02 Feb 2022 12:47:12 No.14177973 Report

Quoted By:

>>14167868
Why even bother posting this? It isn't right and won't help the other anon actually solve his problem with any degree of surety or accuracy.

Anonymous

Anonymous Wed 02 Feb 2022 17:57:35 No.14178727 Report

Quoted By:

>>14177062
arctan a and arctan b are not algebraically independent in general. for example 2arctan(1/2) = arctan(4/3)

Anonymous

Anonymous Wed 02 Feb 2022 19:08:54 No.14178964 Report

Quoted By:

>Algebra: Chapter 0
is that book fun?

Anonymous

Anonymous Wed 02 Feb 2022 19:29:02 No.14179027 Report

Quoted By: >>14179708

>>14149048
Why are LGBT types attracted to CS and category theory tier math?

Anonymous

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Anonymous Wed 02 Feb 2022 20:52:36 No.14179354 Report

Quoted By:

>>14177895
Is that useful for engineers? I heard topology is really though, differential geometry sounds interesting. My level is college math applied for engineering.

Anonymous

Anonymous Wed 02 Feb 2022 22:44:26 No.14179708 Report

Quoted By:

>>14179027
They like making arrows go in the opposite direction.

Anonymous

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Anonymous Wed 02 Feb 2022 22:49:01 No.14179717 Report

Quoted By:

whats the best programming language to deal with mathematical statistics? like probability distributions etc

Anonymous

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Anonymous Wed 02 Feb 2022 22:52:18 No.14179724 Report

Quoted By: >>14179729 >>14179754

The Continuum Hypothesis: false!

Anonymous

Anonymous Wed 02 Feb 2022 22:53:51 No.14179729 Report

Quoted By:

>>14179724
(judge my paper)

Anonymous

Anonymous Wed 02 Feb 2022 22:58:20 No.14179739 Report

Quoted By: >>14179743

CH is false.
my proof: it is more beautiful if it was false

Anonymous

Anonymous Wed 02 Feb 2022 23:00:18 No.14179743 Report

Quoted By:

>>14179739
Set theory looks needlessly complicated.

Anonymous

Anonymous Wed 02 Feb 2022 23:07:01 No.14179754 Report

Quoted By:

>>14179724
https://www.youtube.com/watch?v=5hfYJsQAhl0

Anonymous

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Anonymous Wed 02 Feb 2022 23:25:57 No.14179816 Report

Quoted By: >>14180484

Final draft of my paper. Post!

Anonymous

Anonymous Wed 02 Feb 2022 23:27:04 No.14179818 Report

Quoted By: >>14179831

>>14176669
Pls respond with recommendations for Number Theory textbooks

Anonymous

Anonymous Wed 02 Feb 2022 23:30:46 No.14179831 Report

Quoted By: >>14179851

>>14179818
Elementary Number Theory (Jones, Springer)
A Classical Introduction to Modern Number Theory (Rosen, Springer)

Anonymous

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Anonymous Wed 02 Feb 2022 23:35:58 No.14179851 Report

Quoted By:

>>14179831
Lol so I knew it sounded familiar and I used I the first book by the same name but with the author of the second one. I will be sure to check out the latter though. Thanks friend.

Anonymous

Anonymous Thu 03 Feb 2022 01:05:58 No.14180100 Report

Quoted By: >>14180176 >>14180235 >>14180480

>>14146945
What is the non-faggy, beyond reddit reading list?

Anonymous

Anonymous Thu 03 Feb 2022 01:26:31 No.14180176 Report

Quoted By:

>>14180100
start with the greeks

Anonymous

Anonymous Thu 03 Feb 2022 01:39:12 No.14180235 Report

Quoted By:

>>14180100
start with homer

Anonymous

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Anonymous Thu 03 Feb 2022 03:20:51 No.14180474 Report

Quoted By: >>14181022

>>14159436
>>14159494
>start with $a_0 = 1$
>let $a_{n+1}=a_n (a_n +1)+1$
>then each $a_{n+1}$ has a prime factor that is not a factor of any $a_0,\ldots,a_n$
Not groundbreaking, but a little different from Euclid’s proof in that it’s constructive (at least mostly: you do have to perform some kind of search to find the prime $p_n$ ) and does not use contradiction.

FWIW I highly doubt that this proof is actually new.

Anonymous

Anonymous Thu 03 Feb 2022 03:24:06 No.14180480 Report

Quoted By:

>>14180100
There isn't one.

Anonymous

Anonymous Thu 03 Feb 2022 03:24:49 No.14180484 Report

Quoted By:

>>14179816
That is not what #X < #Y means in the context of this problem.

Anonymous

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Anonymous Thu 03 Feb 2022 07:14:18 No.14181020 Report

Quoted By: >>14181045

>>14159436
>old proof: make one new prime
>new proof: iterate the argument to make more new primes
This dude was 5 years out of his PhD when he wrote this, like HOOOOOLY shit lmao was he having a nervous breakdown or something?

Anonymous

Anonymous Thu 03 Feb 2022 07:16:10 No.14181022 Report

Quoted By: >>14181029 >>14181245

>>14180474
Euclids proof is constructive you idiot.

Anonymous

Anonymous Thu 03 Feb 2022 07:19:36 No.14181029 Report

Quoted By:

>>14181022
Not him but the last guy who thought so >>14159525 got btfo by his own link within minutes. Do you feel lucky?

Anonymous

Anonymous Thu 03 Feb 2022 07:27:13 No.14181045 Report

Quoted By: >>14181532

>>14181020
no it's more like
>old proof: these two things can't both be true
>new proof: this thing is true

Anonymous

Anonymous Thu 03 Feb 2022 07:30:24 No.14181052 Report

Quoted By: >>14181057 >>14181215

>>14159532
Hand-waving

Anonymous

Anonymous Thu 03 Feb 2022 07:32:25 No.14181057 Report

Quoted By: >>14181215

>>14181052
it's a valid proof, it's just literally a reduction to absurdity which is what the op specifically wanted to avoid

Anonymous

Anonymous Thu 03 Feb 2022 08:44:33 No.14181215 Report

Quoted By: >>14181684

>>14181057
>>14181052
>>14159532
It's a direct and constructive proof. Reduction to a contradiction is how you directly and constructively prove the negation of a statement (in this case that none of the primes in the list divide the number). The the other proof you posted uses a claim whose proof is omitted but if he were to try to prove it it would look almost the same (assume p divides both n and n+1, then p divides 1, contradiction. Ergo n, n+1 are coprime)
You are so fucking stupid its unbelievable. Go back to elenentary school

Anonymous

Anonymous Thu 03 Feb 2022 08:55:13 No.14181245 Report

Quoted By:

>>14181022
proove that given any collection of n primes that iteration of the process outlined will give all primes

Anonymous

Anonymous Thu 03 Feb 2022 11:39:59 No.14181532 Report

Quoted By: >>14181684

>>14181045
I really hope you’re trolling, or undergrad/retarded

Anonymous

Anonymous Thu 03 Feb 2022 11:50:54 No.14181552 Report

Quoted By: >>14181611

>>14146730

new thread

Anonymous

Anonymous Thu 03 Feb 2022 12:25:03 No.14181611 Report

Quoted By:

>>14181552
>new thread
>279 replies
Is this what passes as a new thread these days?

Anonymous

Anonymous Thu 03 Feb 2022 13:01:00 No.14181684 Report

Quoted By:

>>14181215
>>14181532
retard meet retard

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