/sci/ - Science & Math

>>14951840
>animu posters have got to be very lonely inside to consistently animu post edition

Regardless of board of thread, there is nothing more interesting to post than a big titty anime maid.

>>14951840
How would you quantify an infinite amount of Spooky scary skeletons?

>>14951840
Missing two, faggot, the middle row rightmost, and the bottom row, second from right both have a mirror orientation. There is literally no reason to mod out by mirror orientation

>>14951840
I guess I have an actual math question. Every time I look at a problem and think it is interesting, it ends up being in something called "Combinatorics" which someone told me is just fancy counting.

I was buying cheese sticks in a restaurant and I was given a $250 book ticket. I am debating picking every cheap old book with the word "Combinatorics" in the title, opening them in a random order until I find one I can comprehend and reading it. The rest would be reference or read as needed. Unneeded ones will be turned into gifts for other people. If I do this I should get somewhere between 25-50 books. Maybe more if I am lucky.

Is this a good use for a book ticket?

It doesn't have to be old books, it just has to be $250 in books, but old ones always seem like a better use of money.

>>14951850
then there's me just flailing about crying as I learn to solve everything in the wild because for some reason a random thread on 4chan does higher level maths than me

>>14951941
It's okay fren. I am not any good at math. I just like looking at old books because seeing drawings and symbols is nice.

There are people here who are genuinely good at math like vampire maid from touhou. I looked at the set theory book she told me. It is expensive but I could get it with my ticket if I am willing to accept less Combinatorics books.

I think I am because vampire maid from touhou was very nice to find me a book about Set Theory from someone called Thomas Jech so I can read about Cantor's ideas without having to read anybody German.

I suppose the other 10 or so books can just be random combinatorics ones.

>tl;dr: Remembered vampire maid said get a book. Going to get that one and fill in the rest with random combinatorics books.

>>14951905
It's certainly better than not using the ticket at all.

>>14951941
>:D

>>14951840
HOW DO I LEARN MATHATATICS????

What software does 3b1b use for graphs and animations?

>>14951995
go refresh on geometry and algebra 1 and see where you are.

>>14951999
He created his own Python library, called "Manim".

>rightoid is a crank who schizobabbles
shocker

>>14951999
He links his software package in the description of his videos last I knew. It's open source.

Also that JBP post is fucking retarded. Can you evaluate axioms? If yes, he's wrong. If no, there's no reason to accept his axiom over literally infinitely others. If he further claims the pragmatic, and you cannot evaluate axioms, then ALL OTHER ALTERNATIVES ARE EQUALLY PRAGMATIC. Principle of explosion, the second fork cannot be accepted.

So there's a simple proof against presuppositional apologetics like he retardedly expounded there. Any attempt to avoid accepting "axioms can be evaluated" leads to a contradiction, because it produces infinitely many contradictions. Fucking hell why are people so stupid

>>14952013
>Also that JBP post is fucking retarded. Can you evaluate axioms? If yes, he's wrong. If no, there's no reason to accept his axiom over literally infinitely others. If he further claims the pragmatic, and you cannot evaluate axioms, then ALL OTHER ALTERNATIVES ARE EQUALLY PRAGMATIC. Principle of explosion, the second fork cannot be accepted.
What caused this post?

>>14952022
>What caused this post?
My genetic predisposition for hatred of stupidity.

>>14952028
Your sort is always filled with self-hated. Either way, the reasons for accepting something as an axiom are that it's necessery and self-evident.

>>14952022
potentially solving or effecting existential truths, connects very deeply with people.
But that immensity translates into strong negative feelings if the claim is not sound or perceived as sound. So if someone were to be in opposition to such claims, their feelings would be more fierce than usual as we observed.

>>14951970
Please don't be mean to them. I suspect they manipulate things for me and probably other people too.

I post can someone please help me find a niche book and vampire maid from touhou comes and helps and finds it even though I am not on her board at the time. I make a post about vampire maid's book being expensive, but decide to buy it anyways because I have a ticket and a strong preference for paper books and vampire maid from touhou is always right when we talk and suggests nice things.

5 minutes later I find that same book at a vastly reduced price. A seller who quoted it yesterday at $112 is now allowing it for $14 and also giving me a free book about logic by somebody called Haskell Curry for free and also a snocone if I go to the store so she doesn't have to mail books? Now instead of spending half a ticket on that book I only had to spend $14 and it gets another book I didn't know about too.

I come here and I talk and reality changes in nice ways. Things get manipulated somehow and become nicer or more accessible. If you're the one doing this vampire maid, thank you. I'm sorry you got assigned to me instead of a better one, but I will try to take things as far as I can.

Hopefully I can get one of them to tell me a computer design to use Stable Diffusion with so I can draw the library maid. The closet must be changed into some kind of advanced Stable Diffusion Drawing Computer. I have never owned a desktop or workstation and don't know about them. I am very excited that Python has a practical application now though!

I am currently banned from /g/ but it expires in a couple hours so I will ask dra/g/ons!

>>14952031
>if someone makes existential claims i disgree with, it upsets me deeply
Okay, but why lash out against the concept of self-evident truths? It's pretty obvious that you can't get anywhere, logically speaking, without axioms.

>>14952022
He got baited
JBP is a funny guy, i like his tweets because they make me laugh.

Anyway whatever happened to JBP? Last time i checked him he couldn't speak a sentence without crying and talking about weird dreams, i think he lost his sanity at some point from taking too much xanax.
At least he was comprehensible in 2013.

>>14952029
>Either way, the reasons for accepting something as an axiom are that it's necessery and self-evident.
If you simply declare "it is necessary", I can simply declare infinitely many alternatives as necessary. If you instead try to demonstrate necessity, you've eliminated the very point of claiming "some axiom is the prerequisite for all proof" as you are now relying on demonstration instead.

Repeating a contradiction doesn't help your case.

>>14952037
>I can simply declare infinitely many falsehoods I don't believe in to make my schoolboy point
Who cares?

>>14952039
>Who cares?
Desperate morons trying to feel better about their mortality by inventing adult santa.

>>14952040
How does your ability to falsely claim that something is self-evident to you, prove anything? You will deflect again.

>>14952042
>How does your ability to falsely claim that something is self-evident to you, prove anything?
That is exactly the question you need to answer. That's hilarious

>>14952042
>How does your ability to falsely claim that something is self-evident to you, prove anything?
I'm jumping into this conversation, but isn't this the point that the guy you're replying to is trying to make against crab man?

>>14952043
Why do you keep deflecting?

>>14952046
You're both apparently too stupid to keep track of a conversation. The mongoloid tried to argue that he can lie that some falsehood is self-evident to him for the sake of contrarianism. How does that prove anything?

>>14952046
YEP
>>14952047
>Why do you keep deflecting?
I am directly saying you need to answer that very question. A deflection would be an evasion. I am directly, pointedly, agreeing with your question and pointing out YOU are the one who needs to answer it. If you can't, REGARDLESS OF WHETHER ANYONE ELSE CAN'T, you've conceded my point.

pls can you share your wisdom books anon

>>14952052
>you need to answer that very question
Why do I need to answer that question? You seriously seem to be losing your mind.

>>14952051
Because he's using crab man's logic against him.
Crab man: "this is true, just because"
Anon: "using your same reasoning, all of THESE are true as well"

>>14952056
>Why do I need to answer that question? You seriously seem to be losing your mind.
Because you're the one claiming something is self-evident, and I've explained why that necessarily leads to a contradiction already >>14952013
>>14952037
What's the matter? Can't follow a conversation, anon?

>>14951840
we have R-modules M and N. when are all maps between prime localizations of M and N at P, the result of the prime localization of a "bigger" map between M and N?
[math]
\psi: M_P \to N_P \implies
\exists \phi: M \to N \text{s.t.} \phi_P = \psi
[/math]

>>14952058
>Because he's using crab man's logic against him.
No, he isn't. Your retarded strawman has nothing to do with what Peterstein says.

Happy Halloween guise, the retards are arguing about another self-help guru

>>14952059
>you're the one claiming something is self-evident
I wasn't claiming that anything is self-evident. Take your meds already.

>that necessarily leads to a contradiction already
What's the contradiction, again? What do you think follows from the fact that you can be highschool contrarian and lie about what seems self-evident to you?

>>14952063
>>14952061
Man it's just way too easy when you're reduced to hurling insults and feigning illiteracy. Up your game.
>>14952058
This is basically how 100% of these conversations go. Explain the paradox that leads to principle of explosion, get narcissistic schizophasia in response. I find it funny that such followers of "wisdom" are so hysterically inept.

>>14952065
What's the contradiction, again? What do you think follows from the fact that you can be highschool contrarian and lie about what seems self-evident to you? Why do you keep deflecting?

>>14952067
>What's the contradiction, again?
What's the matter? Can't follow a conversation, anon?

>>14952013
The funny thing is that what he describing has nothing to do with mr gurdel. this is basic logic as old as play-toe.
you have axioms/premises from which you derive theorems/conclusions. in the realm of mathematics soundness aka "truth of axioms" doesn't matter but when you are talking about real life things you can't just say "it's an axiom" and call it a day.
even then, god isn't the necessary prerequisite for proof, the only necessary prerequisite for proof is that it exists in any meaning of the word "exist" (in a mind as an idea or physically exists, etc).

>>14952070
It's obvious that simply claiming that something is self-evident doesn't prove anything one way or another. In your psychotic head, however, it seems like that disproves Peterson's point. I just want to see the actual logic behind that.

>>14952061
You seem too far gone.
You're being defensive over a decade old tweet of your favorite celeb.
If you want to have a discussion, you ought to be cooperative and understand what the other side is saying.

>>14952060
You want this for a specific prime or for all primes?

>>14952072
>It's obvious that simply claiming that something is self-evident doesn't prove anything one way or another
Again: That's the point. You two are agreeing.

Peterburger says "God existing is self-evident to me", and that does not make it true. What he's implicitly saying is that one party can claim whatever they want as self-evident and the other party should agree.
Then we just use it against him to arrive at contradictions.

>>14952071
Oh, I agree. But it really is just repeating presupposition apologetics, and they like to co-opt fancy language to sound smarter.
>even then, god isn't the necessary prerequisite for proof, the only necessary prerequisite for proof is that it exists in any meaning of the word "exist" (in a mind as an idea or physically exists, etc).
Well if you want absolute bedrock the sole and only prerequisite is "cogito". That I exist is self-evident, therefore the basis of all subsequent inference is grounded in the mere fact of one's existence in some reality (that which you exist in). At no point does one need insert a deity or anything else, and what follows is just applying Hume.

It beggars belief we're so long after Hume and still have a planet chocked full of such stupid people unable to grasp basic concepts.
>>14952072
>It's obvious that simply claiming that something is self-evident doesn't prove anything one way or another.
Great - so why are you defending JBP doing so, now that you're saying you agree with me?

>>14952073
>If you want to have a discussion, you ought to be cooperative and understand what the other side is saying.
I'm glad you people go around and post shit like this. I don't believe in any gods and I never liked Peterstein, but after running into subhuman trash like you repeatedly, I understand what the real problem in society is, and what the rational method of dealing with your likes are (protip: they don't involve any talking).

>>14952077
>You two are agreeing.
>. What he's implicitly saying is that one party can claim whatever they want as self-evident and the other party should agree.
Why do you keep blatantly lying?

>>14952079
>>14952081
Yup. Too far gone.

>>14952073
just a specific prime initially. I'm tempted to say yes because of the tensor product isomorphism [math]R_P \otimes M[/math] to [math]M_P[/math]. perhaps you can compose and then project to get a mapping between M and N that localizes at P to the desired inital map.

>>14952082
Why do you keep lying and deflecting? I'm still waiting for you and your butt buddies to explain why someone's ability to claim that any arbitrary statement is self-evident invalidates Peterstein's point.

>>14952087
>I'm still waiting for you and your butt buddies to explain why someone's ability to claim that any arbitrary statement is self-evident invalidates Peterstein's point.
People have. What's the matter? Can't follow a conversation?

What level of school or University are you guys? This stuff is basic though I could give you advice.

>>14952089
>People have.
They haven't. You're profoundly mentally ill and you don't seem to have any concept of what a valid argument even looks like.

>>14952060
You can't make a stable reality from a Mandelbrot set. All of that is <1.

>>14951905
>order cheese sticks
>rewarded with $250 in math textbooks
God is real, and He loves /sci/ posters

How to motivate myself to complete a plug and chug problem set? I know I need it as I'm just at a baby level, so I'm not arrogant enough to just skip stuff like that, but every time I finish reading a chapter and see that the exercises are 15x use algorithm discussed I immediately start doing something else

>>14952130
You could try interspacing it with something more immediately rewarding. Some people can do that with exercise. The importance is sticking on task, though, so set a timer or something to require you go back to finish once you've spent a minute or five away. Even getting up and walking or going outside for a minute could help. Depends on how bad your ADHD is.

>>14951840
>not even a halloween themed image

>>14952141
Yeah, that's what I've been doing in a sense. Problem is I lose the will to even get started with "brainless" tasks. I'd have no problem doing them while I'm waiting in a queue or something, but it feels gay to sit down and grind them in my freest of free time

>>14952171
>I'd have no problem doing them while I'm waiting in a queue or something, but it feels gay to sit down and grind them in my freest of free time
Well if you genuinely cannot manage any trick, interspacing exercise, or anything. If you've already tried it, and nothing works, that's what ADHD meds are for. I'm assuming this is a general problem of procrastination and not a one-off "I just find this SPECIFIC thing boring", but it isn't normal to be genuinely ruinously stuck just because of "boredom".

Another trick people I know try is interspacing some game in between. Play some mobile or brainless skinnerbox thing while doing it. But the main thing is you gotta be able to switch back not "lose 5 hours".

>>14952194
Thankfully I don't think it's ADHD or anything like that, just a motivation thing. I got started and realized I'll be done with them faster than I would've guessed because it's all just in the head.

I think I made my problem sound a lot worse than it is, in reality I can do these things if I "just do them" instead of complaining. But sometimes it feels like the complaining helps in getting started, even if that may be a harmful habit, I don't know.

>>14952165
>cool Halloween maid
Why does touhou have so many maids if it isn't a maid show?

>>14952245
maids control the universe

>>14952034
/sci/ is my main board, not /g/
>>14951960
Make sure It's "Introduction to Set Theory" not just "Set Theory", the former is a introductory text and the latter is a reference book.

Also i'm not as good in math as you think i am.

>>14952130
Read better books.

>>14952267
Lang's basic math feels pretty good with the amount and quality of the exercises, I mean you can't really mix it up for this elementary level I'd guess.

The more advanced books might make me feel nostalgic for these extremely simple exercises one day.

>>14952003
ok

https://strawpoll.com/polls/XOgOJM19Xn3

Undergraduate physics is the most nigger tier easy mode shit imaginable. Its literally plug and chug after you dejumble word problems. Honestly embarrassed to be in these courses, what the fuck, its like being in highschool.

Assume we have 2 pairs of arbitrary line segments in 3d space. Each segment is described by a point and a vector, point + vector * 1 = end of segment, point + vector * 0 = start of segment. I'm looking for a way to find points where:
p = seg1(a) + (seg2(a) - seg1(a)) * c
and
p = seg3(b) + (seg4(b) - seg3(b)) * d
Where a,b,c and d are [0 1].
In other words the points must be both on a line between a point a certain percentage along segment 1's length and the same same percentage along segment 2's length, and the same must apply for a seperate percentage between segment 3 and 4. Anyone know how I could go about solving this, or whether it's even solveable?

>>14952254
>mfw

>>14952265
Thank you vampire maid from touhou. I made sure to get the intro one. I have been asking dra/g/ons about the Drawing Computer and they are being nice. I will see about how to buy parts and assemble it.

Numbers program is waiting on me to make a thing called a serializer. Serializer's job is to write stuff in a file. The default ObjectOutputStream one explodes because Java's internal stack is too small and I get StackOverflowError. I have to make an iterative one. I have never had to make a serializer before.

I am going to try seriously to resolve this now, unless I fall asleep again. I kept falling asleep and waking up a lot of times earlier. I don't know if the maid was involved because when I would fall asleep I could hear talking but now I don't remember what talking said. If she is trying to send me a dream somehow it probably won't work. I don't think I can dream in sleep anymore.

My first strategy to make the serializer will be to put a lot of breakpoints in the one Java gives me, find the part which explodes. Make an ObjectOutputStream implementation of my own which overrides that one part so it is iterative instead of recursive.

Right now recursive serializer has a StackOverflowError when I try to save my radix 2^(16) number and I refuse to try a smaller number. I am already working with less than radix 2^(64).

>>14952037
>I can simply declare infinitely many alternatives as necessary
They can all be shot down by basic reasoning (such as saying the universe is eternal and doesn't need a creator, thus contradicting your first definition of universe)

>>14952040
>by inventing adult santa.
Did your parents lie to you and told you Santa Claus was a real thing? Sorry you were a victim of a psyop to create atheists.

truth is a meme

>>14952647
>They can all be shot down by basic reasoning
Congratulations, you too have chosen "try to demonstrate necessity". Dear lord you people are so fucking dumb it's getting hard to enjoy mocking you. You idiots just keep falling all over yourselves desperate to agree with me, all while thinking it's some clever point.

>>14952673
>being this mentally ill

>>14952288
That book is a meme. If you want to actually learn basic mathematics but at a higher level, read old school olympiad books.

>>14952730
I've seen the book called "a meme" a lot, but I haven't seen any real arguments. I find it appropriate for refreshing some stuff I already learnt and filling in some gaps before I move on to calculus. Anything I might miss I'll encounter in other books or research when needed.

imposter syndrome kicking in again

Is there a proof that there are countably infinitely many order types in the set of all totally ordered countably infinite sets? It obviously can't be rational.

>>14952791
At least countably many:
Consider Z with one, two, three, ... points at the end.
At most countably many:
False. Take any sequence a_i of zeros and ones, and take the following order type:
whenever you have a 0, put one isolated points to the right, whenever you have a 1, put a copy of Z to the right and an isolated point to the right of it. Every two such order types are distinct, since you may read off the digits by:
- first digit is 0 if no first element. Remove the initial segment until the first element without predecessor
- first digit is 1 if order has first element. Remove it.
Continue the process with the order that is left.

if anyone tells you a cuboid is a rectangle, they are just projecting

>>14952845
>if anyone tells you a cuboid is a rectangle, they are just projecting
ban him

You can multiply two matrices in 16 ways, all rotations. But you can represent an N-dimensional space with a cubic matrix of vertices or a flat matrix of vectors. In sinusoidal coordinates, frequency metrics require less notation.

>>14952927
I don't know what any of these words mean. Can you make a computer draw it?

i dropped out of high school and want to self study math. where do i start?

>>14953100
khan academy

I'm interested in harmonic analysis, signal processing, PDEs, and similar analysis topics.
What's the Probability book for me?
I can't narrow it down from Chung, Williams and Shiryaev

What is the greatest math mistake?

>>14953137
grundlage

>>14953137
Declaring expressions to be the only valid form of mathematical notation.

I just spent around 20 hours studying, solving over 100 problems over the course of 2 days for my calc 2 exam... I'm pretty sure I failed it.

why do I do it?

Is this question wrong? I posted it to /sqt/ 5 hours ago and the only answer I got implies that the question is wrong.

>>14953259
Forgot pic.

>>14953270
This is what I did so far.

>>14953270
Yes it's wrong, I have no idea how it can even be so wrong.

Hello! Here's another problem. Seems fun so far. I haven't managed to solve it yet myself but hopefully by the end of the day I'll get it.
Perhaps it's actually quite easy to some of you folk here. Either way, if you do solve it please reply. I'll let you know if the answer is correct or not. That's all. Good luck and happy Halloween.
>>14951905
HEY! Combinatorics is a very fun subject. Very vast and diverse, counting being just one part of it. This problem I posted is actually from a combinatorics book. Anyway, I don't think you should order every book you find with combinatorics in the title. First of all, for elementary books you'd probably get so much overlap it'd be kind of a waste. Secondly some of those books might be at a very advanced level and might be useless to you. If I were you I'd do a bit of research, very little, to find one or two introductory books on combinatorics. And then do something else with the rest of the money. That's only what I think though.

>>14952775
>but I haven't seen any real arguments
You showed why

>>14953430
I get a probability of 3/34.
Consider our coinflip sequence as a sequence of runs of heads and tails, alternating, which we terminate after the first heads run with length at least 5. We seek the probability that, after we terminate, all tails runs have length 1.
The probability of a heads run having length at least 5 is 1/16, so the probability of terminating after n heads runs is [math]15^{n-1}/16^n[/math].
If n is known, then our sequence contains either n or n-1 tails runs, depending on the side of the first coinflip (which is 50/50 independent of n).
The odds of only having length-one tails runs before termination is therefore [math]\frac12\cdot(2^{-n}+2^{-(n-1)}) = \frac32\cdot 2^{-n}[/math].
In total, the unconditional probability of only having length-one tails runs before termination is
[math]\displaystyle \sum_{n\ge1} \frac32 \cdot \frac{1}{2^n}\cdot \frac{15^{n-1}}{16^n} = \frac{1}{10}\sum_{n\ge 1} \left(\frac{15}{32}\right)^n = \frac{1}{10}\cdot\frac{15/32}{17/32} = \frac{3}{34}[/math]

>>14953516
Your answer is correct! Good job!
I'm not reading the rest of your post to not spoil myself of the solution but your answer is definitely correct. What did you think of the problem?

>>14953430
I set up a state graph, kept the important parts of it, and that had 4 states (1H, 2H, 3H, 4H). Then I set up equations for each one to reach 5H, then made a matrix and inverted it to get the answer: From 1H to 5H, that's 2/17.
So from no flips to 5H is (3/4)(2/17) = 3/34.

>>14953625
>I set up a state graph, kept the important parts of it, and that had 4 states (1H, 2H, 3H, 4H).
Interesting, I also set up a state graph and kept the important parts, but those 4 states were exactly the ones that I ended up collapsing.

the excitement of math

>>14952060
I'm interested in this problem. I only found very trivial cases.
It is false for [math]M = N = \mathbb{Z}[/math] and [math]\mathfrak{p} = (0)[/math].
It is true for [math]M = N = \mathbb{Z}/n\mathbb{Z}[/math] and [math]\mathfrak{p} = (m)[/math] with [math]m\land n = 1[/math].
I'll try to find more.

>>14953653
Oh wow, your way is MUCH easier.

[math]\DeclareMathOperator{\Hom}{Hom}[/math]
[math]\DeclareMathOperator{\loc}{\mathfrak{p}}[/math]
>>14953672
Some more thoughts: if [math]M[/math] is finitely presented then
[math]\Hom_{R_{\loc}}(M_{\loc}, N_{\loc}) = \Hom_R(M, N)\otimes R_{\loc}[/math].
So you are winner if [math]R_{\loc}[/math] is free of rank [math]1[/math].

>>14953430
I found a combinatorics workbook for middleschoolers and I am going to start there. It seems like there are a couple different kind of combinatorics and I don't know which one to care about yet.

Also something about an Olympiad for highschoolers or something. I am glad the intro work is so weak. I don't think humanity knows a gentler intro than middleschool math.

Thank you for reading my post.

>>14953708
Hello, i can recommend some easier and shorter intros to probability, probably only useful if you know nothing about probability.
https://www.sydney.edu.au/content/dam/students/documents/mathematics-learning-centre/counting-techniques.pdf
https://www.sydney.edu.au/content/dam/students/documents/mathematics-learning-centre/basic-probability.pdf
https://www.sydney.edu.au/content/dam/students/documents/mathematics-learning-centre/further-probability-theory.pdf

do you do sports. If so, what sports do you do? If not, why don't you?

Is my prof insane?

>This course will serve as an introduction to algebraic number theory, also known as arithmetic.

>>14953879
Thank you vampire maid from touhou. Always good to see you. I will study those and maybe find a middleschool probability workbook too.

I forgot math books come at easier strengths than college level and can be used as a ladder to s stronger book.

>>14953625
First things first, your answer is correct! Very nice job.

Secondly, regarding your solution. I have seen something similar before I believe. Or at least the same words... Either way, it looks very amazing and interesting. Could you direct me somewhere where I can learn more about what you have done? A book name would be best but anything to set me in the right direction would be appreciated.
>>14953653
A state graph, so that seems like what popped into some of you qualified people's heads... again if you have any resources recommended to learn what those are, they'd be appreciated. Thanks, I'm bad at this stuff despite liking it a lot.
>>14953708
Good luck anon. I think you can handle something harder than a middle school one but of course it's up to you. If you wish to do so, check out Path to Undergraduate Combinatorics by Titu digitally and order it if you desire to do so. I think it's a pretty good book. Either way, I wish you the best on your journey! Combinatorics is fun. If you don't mind and have the time to do so, please also attempt the problems I post time to time. They're all combinatorics problems and not too difficult.

How do you make you remember what you've learned? I have no problem grasping a concept sooner or later, but remembering it in any meaningful detail, especially formal notation seems impossible. I feel like a dumbarse when someone asks me to explain something and all I can conjure up is a vague response.
>just solve questions!
Thats fine for high school and undergrad math, but once you get past that there's barely any problems to do and it more an issue of remember the concept itself.

>>14954140
make a graphical visualizer tool to test and apply knowledge, if you have no other regular application medium.

another one for the Lang errata if I'm not mistaken

>>14954110
>A state graph, so that seems like what popped into some of you qualified people's heads...
Anons are actually thinking of Markov chains, they just forgot the term.

>>14954110
>Path to Undergraduate Combinatorics by Titu
Are there any prerequisites to this book? You've piqued my interest.

>>14954193
RIGHT, RIGHT.Markov chains...
They kept showing up in places and I actually asked someone before about how to learn them but it didn't really go anywhere because you know how it is, school and excuses got in the way blah blah. But alright, I'll look at Markov chains for sure this time when I'm free from school.
>>14954243
I'm not sure fren. I think it starts okay and then gets progressively difficult so not a lot of prerequisites besides sticking to it and studying lots. Here's the preface. Definitely get the pdf of the book from libgen if you do consider buying it.

I have a fluid dynamics test in about a week but the profs notes are all over the place. Anyone have a preferred text from which they study fluid dynamics. I believe the prof is working from a book but for some reason forces us to study from the notes she gave us.

Calculus II was my highest grade in undergraduate. Well, is my highest grade so far. I even got 100's on exams that most of the class failed, like sequences/series and the final.

Why is the rest of my degree so difficult? I feel lied to. I was told Calculus II was the hardest course, yet every other course I've only had high B's and they're a much bigger struggle. Nothing has been harder, more counterintuitive, and rage inducing than probability though. I still don't know how I got a B, but asking me what is the probability that one event with .35 chance happens, and one with .45 doesn't happen, might as well be magic until its explained to me as a simple addition problem.

Has anybody tried enumerating all of the series of the form [math] \sum_{n=0}^{\infty} \frac{1}{137 f(x)} [/math] over some polynomials [math]f(x)[/math] to see if you get the fine structure constant? At least for polynomials with integer coefficients.

>>14954296
Don't forget -1^(n) or -1^(n+1) in the numerator anon.

>>14954296
https://www.scirp.org/journal/paperinformation.aspx?paperid=85840

>>14954110
This anon >>14954193 is right, what I called a "state graph" (aka. "transition matrix") is only a visual aid to help model the problem, and the underlying theory is that of a Markov chain.

For learning to solve probability problems by (worked) example, my go-to recommendations are Sheldon Ross's "A First Course in Probability" and "Introduction to Probability Models" (Chapter 4 of the latter is devoted to a thorough study of Markov chains), but I've also heard that they can be overwhelming for people who aren't already mathematically inclined.

If you just want a high-level overview of Markov chains, I found this short primer:
http://www.aquatutoring.org/ExpectedValueMarkovChains.pdf
which also demonstrates, with examples, how to use Markov chains to solve probability problems.
The only "trick" that I used in my solution >>14953653, which that primer didn't cover (but I personally think is very good to know), is to write the probability of a desired event [math]A[/math] (in this case, [math]A[/math] = the event of encountering 5 heads before 2 tails) as the expectation of a payoff, where this "payoff" is a {0,1}-valued random variable that indicates whether event A happened or not. For this reason, the payoff is often called an "indicator variable", and written as something like [math]1_A[/math]. Mathematically speaking:
[eqn]\mathrm{E} [1_A]=\mathrm{Pr}(A) \cdot 1+(1− \mathrm{Pr}(A)) \cdot 0= \mathrm{Pr}(A)[/eqn]

>>14952013
> Any attempt to avoid accepting "axioms can be evaluated" leads to a contradiction
What are you talking about? Axioms aren't evaluated, nor are formulas. Evaluation is a part of computer science and parsing, not mathematics.
You seem to not understand that formal proofs arrive unexpectedly and largely expand the language of mathematics. Formal axiomatic theories integrate these new language structures.
A formal proof uses inference rules, signature-agnostic axiom schemas of classical logic like law of excluded middle in conjunction with axioms to derive theorems of (first-order) classical logical theories.

>>14952029
This is not a metaphysics board. The metaphysics boards are /lit/ and /his/.
> the reasons for accepting something as an axiom are that it's necessery and self-evident.
That isn't how things work here. Those are philosophical words that have to do with non-mathematical uses of logic.
Go to /lit/ or /his/ if you want to discuss logic this way. This is a board for MATHEMATICAL discussion, not general logical philosophy.

>>14952791
Can you rephrase? What do you mean by in the set?
Even first order arithmetics like that of Peano encode countable ordinals such as [math] \omega, \omega^{\omega}, \omega^{\omega^{\omega}}, \omega^{\omega^{\omega^\omega}}, \dots [/math]

>>14954340
>What are you talking about?
Not what you're talking about. I am talking about soundness, epistemology, not the internal world of axioms you think you can lecture me about. Evaluated with respect to reality, i.e. its truth content, soundness.

>>14952065
>This is basically how 100% of these conversations go. Explain the paradox that leads to principle of explosion, get narcissistic schizophasia in response.
It's HIGHLY UNLIKELY that the problem is the topic of the conversation. It is far more likely that both parties are abusing the conversation.
This idea that there is a problem with some part of the curriculum such as the principle of explosion as elaborated on Wikipedia is indicative of your own inability to understand and teach the material, not the inherent weakness of the material itself.
Insulting the material won't get you anywhere, and you don't see teachers complaining about the distributive law, now do you?

>>14954393
>This idea that there is a problem with some part of the curriculum
Someone can't read. Are you drunk? It was about JBP's presup bullshit not math curriculum.

>>14954397
Okay, so you're admitting that you're misusing the board.
This board isn't for discussing philosophy or metaphysics. The people here don't have anything that would help them in that respect.
Do you understand why there is a lot of pressure to get people to use /lit/ and /his/ as metaphysics and philosophy boards?

>>14954397
You clearly have a language problem, you're bringing unwanted material to the board, you're pretending you can just barge in here and discuss whatever topic you want...yikes...I doubt anyone wants you here, but you certainly can't piss and shit here with you off-topic garbage.
If you can, then you're a nuisance and a tolerated rule-breaker.
Who knows? I vote for taking this trash out of here.

>>14954404
>Okay, so you're admitting that you're misusing the board.
Science concerns epistemology as it is an epistemology. Swing and a miss.
So let's recap: The conversation came and went and you're now dredging it up to virtue signal your opinions. Cool story bro.
>>14954410
>I vote for taking this trash out of here.
Don't let the door hit your ass on your way out.

>>14954414
this is /mg/ and you can start a thread about epistemology called /eg/ epistemology general
WHY DO YOU THINK WE GIVE A SHIT ABOUT EPISTEMOLOGY?!?!!?

>>14951999
>[random statement]
>Godel proved it
Quite frankly, Gödel has a reputation as a meme peddler, not a mathematician.
This idea that he proved anything and that BECAUSE HE PROVED IT THEREFORE YOU SHOULD ACCEPT IT is a weird internetism.
I mean...why not just give the argument instead of going
>GÖDEL PROVED IT
>YOU'RE AN IDIOT
>GÖDEL PROVED IT
>YOU'RE AN IDIOT
You should start a Gödel thread over at /lit/ and have fun with the fine folks over there

>>14954429
Tbqh I find philosophers borrowing isolated conclusions from mathematics and physics and shoving them into philosophical subjects absurdly funny.

>um sweety QM disproves determinism okay? Your metaphysics is wrong, just wrong
>honey, Einstein proved the universe isn't euclidean
>baby, that's a very interesting theory of the mind, but it clearly falls apart because of bicameralism

>>14954429
I posted the pic as a (You) bait, the way this website works is that if you want a guaranteed reply you must post bait pics and that picture was so remarkably retarded i used it. i was actually asking about what software 3b1b uses and i got the answer i was looking for

>>14954429
>>14954442
Refreshing to read this. Also bothers me. Less that they believe such things, but more that I am spoken to or addressed as if I give a fuck about their ramblings or that I should consider myself their associate. Math faculty should start becoming outright hostile to these people.

>>14954442
https://www.youtube.com/watch?v=Qi9ys2j1ncg
this interview especially between JBP and some physicist.

>>14953959
I think i already told you Kurumi is just a vampire not a maid vampire, there's like only one or two pictures on the internet with Kurumi in a maid dress as far as i know. Just refer to her as Kurumi.

>>14952060
It holds when your collection of maps 'continuously depends' on [math]p \in Spec \ R [/math].
See https://mathoverflow.net/questions/51802/under-what-circumstances-do-morphisms-on-the-stalks-of-a-sheaf-induce-a-sheaf-mo

>>14954508
Thank you kurumi. I will try to remember your name right. I remember you saying there weren't many pictures of her, so I am going to use Stable Diffusion to draw her in a maid dress a big number of times so I can practice the tool and you can maidpost with her easier. I can probably make a hypernetwork out of tohou images sources on booru sites or maybe just from warosu whenever it comes back.

My plan is to just tell it to draw thousands of images of her overnight and then go through them and manually delete bad ones.

Dra/g/ons helped me design a Drawing Computer and now I am buying parts.

Do you work with someone called rpyth? He keeps asking me go on a website called litechan and read about Eremias which is an experimental Python with nice syntax based on goto and BASIC and make Eremias nicer?

I am trying to see can I get an A6000 for drawings. My ticket can cover it but not much money is left if I go that road.

>>14952085
Consider [math]R= \mathbb{Z}[/math].
Every homomorphism [math]\mathbb{Q} \to \mathbb{Z} [/math] is 0,
however there are lots of non-zero homomorphisms [math] \mathbb{Q}_0 \to \mathbb{Z}_0 [/math]

>>14954448
That's cute, but I would've given you the answer anyway. So your idea of how things work amounts to pigeon superstition.

>>14954508
>>14954535

>>14954535
>I will try to remember your name right.
Her name, you mean.
Do not engage in schizophrenic RPing on my board.

>>14954535
I appreciate your efforts but i'm not in need of any pictures of Kurumi as i found i can get enough of them from Pixiv, besides, i find Stable Diffusion images somewhat soulless. I'm not interested that much in SD.
>Do you work with someone called rpyth?
No, i have no idea who this is.

Good luck trying to figure out how SD works.

>>14951840
Recomend books to get into multivariable calculus by myself. Ive just finished an Abstract Algebra book

>>14951995

> go into your local uni math program
> pick some topic that has a fancy name
> check requisites
> read book
> repeat

>>14953307
Thanks, anon

>>14954603
>i find Stable Diffusion images somewhat soulless
Yes.

>>14954590
Please be nice to maid anon, he had traumatic brain injury some years ago. He may not realize that i'm not the literal physical embodiment of a fictional character now but i believe he will probably eventually figure it out on his own.

>>14954442
It gets a lot less funny the more you have to deal with the tardlings running about uncritically parroting these "thinkers". The more you know the worse it gets.

I really want to do game theory and probability.
Why did that stupid youtube channel ruin the entire field of study? Nobody ever talks about fucking game theory because of that stupid youtuber. Ruined an entire field of study. Fuck.

>>14954324
Anon that is so pog. Thank you so much what you've wrote. I can't promise I'll take a look at all you've mentioned simply because of how much time school and cram school takes this year but despite that I'll try to get the best use out of what you've written. Ross' probability book is actually one I heard of before but I don't think I ever checked it out. If it has markov chains then that is also simply poggers. The PDF you've shared also seems very useful. I'll get it printed out tomorrow, and hopefully I can understand and use it.

Also additional thanks for solving the problem I shared. That is also appreciated.

Please have a good day/evening/night and keep being awesome. I hope we talk again sometime by chance.

>>14954725
Question: Do you pronounce it anOHn like a cringe redditor or do you see anEN like original 4chan classic oldfag? I need to know

I just had some fun with [math]\int_0^1 x^{-x} = \sum_{n\geq 1} n^{-n}[/math]. Impressive, very nice.

>>14954782
Proof that anEN is the classic pronunciation?

>>14954845
nigga trust me

>>14954850
Post a really cute image and I'll determine whether you're trustworthy or not.

>>14954857
NTA
Also that anon's dumb
but have a cute anyway

>>14954857
this is just the beginning..

>>14954864
That's cute.
>>14954869
That's not cute. The low resolution really detracts from it.

>>14954838
max at [math](\frac{1}{e},\ e^{\frac{1}{e}})[/math]

>DON'T TALK ABOUT METALOGIC AND METAMATHEMATICS IT'S NOT MATH
>posts homosexual anime and furry trash
kys

>>14954894
>every post is the same anon

>>14954838
What is the integral in the interval [math][0,\ \infty[[/math]? I numerically calculated 1.99540.. it is correct? What is the meaning of this number? Is there any relation to pi maybe?

How many differential equations per day to keep the Fs away?

>>14954603
>I'm not interested that much in SD.
I just realized something. If you don't care about Stable Diffusion why did I get a big equipment ticket? Am I supposed to build something else instead?

>>14955049
I don't know, i did not give you the ticket, do whatever you want with it i suppose.

>>14955068
Weird. Well, I am probably going to be banned soon because maids are getting deleted. If that happens, it was good talking to you and I will be back whenever the ban timer ends.

>>14954782
I pronounce it like anOHn. I'm a bit of a newfag anyway so it's quite natural.

I need to know why you need to know though.

>>14954894
nil I ripped this to shreds at a mental institution
feelsgood.jpg

>>14955267
>I need to know why you need to know though.
I was forced to ask at gunpoint.

>>14955328
Ah okay, that's understandable you asked then. I hope they didn't shoot you anon(pronounced anOHn), that'd be terrible. I heard that can kill people sometimes.

>>14953660
I refuse to believe that this person would write a
review like that. It's badass...What book was it?

>>14954959
Five of each type...and a glass of water.

>>14951840
Given a [math] (M,d) [/math] metric space, I know that [math]\forall x \in M[/math], {[math]x[/math]} is a connected set in [math] (M,d) [/math]. It's trivial to proof that also [math] \emptyset [/math] is connected in [math] (M,d) [/math]. I was wondering if it allways happens that [math]M[/math] is connected in [math] (M,d) [/math].

At leats it happens on trivial metric spaces like [math] \mathbb{R}^{n} [/math]. Help me please.

>>14955539
Miklos Bona
Walk Through Combinatorics, A: An Introduction To Enumeration And Graph Theory (3Rd Edition)

Is this a Q&A thread too?
Help me with this notation, please.
I know what attaching spaces via the gluing map means. But what does gluing via the Cartesian product of map and {1} mean?

>>14951840
Use AI to asess your personality like HR would.

https://personal-ambiguator-frontend.vercel.app/

so basically everyone here sucks at math and cant even into plotting functions am i getting this correct?

rude

>>14955140
I didn't know what this is so I looked it up. It looks like it could be a fun game and I like the maids. I have to decline though because my free time is limited and I have to make computers do things and write a lot of pages.

I had some of a dream last night which is very strange because I do not dream. I lay down for a span of time that feels short and then it is hours later instead and I am less tired. This time I kept falling asleep and waking up a lot of times. I was a TV camera in the dream. There was a math class at a school I went to a very long time ago when I was a teenager. It was full of students sitting at tables taking notes. I never saw the lecturer because the camera kept pointing at notebooks.

The notebooks had Maid Space drawings made by students in black pen. I couldn't understand anything the lecturer was saying or tell what her voice was because I was getting sent incoherent thoughts. It only lasted 3 or 4 seconds, then I woke up.

I didn't know I had this ability. Last time I had a dream of any kind it was a 200X year. I don't know if it was a physical process I triggered or if the maid did it. I was talking to dra/g/ons about a Stable Diffusion Drawing Computer and I kept falling asleep and waking up a lot of times. I tried to stay awake to talk to dra/g/ons more about graphics cards, but ended up falling asleep.

If I remember about it tonight I will try to see can I do the same thing? Try to stay awake when tired comes and see do I end up with a dream?

>>14955601
The two-point metric space is not connected.

>>14955140
I went to a junk store to get a coat and buy soda. When I was leaving the guy at the counter told me not to forget my book and gave me a copy of this.

>Don't forget your book (mine is from 1988)
https://b-ok.cc/book/965708/18a7c1

I have never heard about this book before, but when I open it it looks nice. It has a big amount of information about making assembly code and optimizing it.

I never made an optimized compiler because my thought is they enable writing bad code and just teach the programmer not to write bad code instead of designing the compiler to handle bad code nicely. Then the compiler has less lines and is easier to maintain. This book has a lot of symbols and drawings. I only recognize like half of them so maybe it is different from green dra/g/on (see attachment) in techniques.

The book has something about Ada, so probably I was given this on purpose and have to do something with Ada later. For now the book will live on a shelf until current projects get further.

I half solved my serializer problem. I can save big Maid Chain and nothing crashes but when I try to load it it gets mad.

Java seems to decide if boolean[][] is a primitive (it should be, because small b?) or an object in whatever the least convenient way for whatever my use-case is. Java might be a bad tool for this but I don't feel like breaking out C yet because I would have to make a lot of things by hand that Java gives for free.

If I can solve the serializer loading then radix 2^(16) number has a working demo. It took me about 10 hours to fix the save because internet resources were not helpful.

can anyone help me with this?
i havent done linear algebra in 2 years and now i dont remember how to solve this easy equation. i know omega has two solutions. dont solve it just tell me the steps i have to take, thanks.

>>14955859
Start with calculating the eigenvalues of the matrix on the right. The values of omega are then just the squareroots of the negatives of the eigenvalues.

>>14955981
thanks friend

>>14952053
I bet it doesn't exist, just to make you mad

>>14952130
Program the algorithm. Or work on application based problems.

>>14956069
bucket of pastas...

N is open and closed in M, if and only if N is empty or N is M. Is this correct?

In real polynomial functions,
I have three roots and are asked to find all possible grade 4 polynomials that go through those.
I can't find anything on how to solve it.
The guide has the answers, but I don't know how to go about it. Using the factored form I get a grade 3 solution.
The textbook simply squares each factor, giving three possible solutions. But can't really see why.

Any hope would be gladly appreciated.

Solution says [pic related]. But shouldn't it be

[math]|z|^3 \leq 3 \iff |z| \leq \sqrt[3]{3}[/math]?

What am I missing?

>>14956290
Sorry, I forgot.

>>14956216
No.
Consider
[math]M = [0,1] \cup [2,3][/math]
and
[math]N = [0,1][/math].

But it is true if M is a connected space.

>>14956278
I've asked in sqt. Maybe its more suiting there.

>>14956278
There is something called the Factor theorem.
If [math]r [/math] is a root of [math]p(x) \in \mathbb{R}[x][/math] then you can find a polynomial [math]q(x) \in \mathbb{R}[x][/math] of one degree lower with
[eqn]p(x) = (x-r) q(x)[/eqn]


So if you have three roots [math]r_1, r_2,r_3[/math] then

[eqn]p(x) = (x - r_1)(x - r_2)(x - r_3) q(x)[/eqn]
where [math]q(x)[/math] is a polynomial of degree 1. Now if you don't want the polynomial to have any other roots than the roots of q(x) must be included in the set [math]\{r_1, r_2, r_3\}[/math] so the only possiblities are
[eqn]q_1(x) = a (x - r_1) \\
q_2(x) = a (x - r_2) \\
q_3 (x) = a (x - r_3) [/eqn]
where [math]a \in \mathbb{R}^*[/math] is any constant.

>>14956374
thank you

Rotman-sama, i kneel...

>>14956389
This makes sense, taking what I've been said in class.
Thank you for replying anon.
Were I to ask for some free material to actually understand all this, is there anything available? Or at least how to search for the topics that would concern it, given a general idea of what would and/or should be known. (Not really into libgen and so)
While accepting what I've been told before, it is reasonable, I honestly can't for sure tell what the q(x) factor really is, or how the theorem properly works. And though possibly approving an exam like this might be not hard, that wouldn't really be the point.
I'd like to understand it in the mathematicalish way that people seem to do here, where everything can be derived from self evident premises. And it doesn't really look as though it is one or two questions away.

Once again, in any case, thanks for replying, anon.

>>14956424
>circular definition
he should know better

>>14956501
Or the avoidance of an omission in establishing a self-evident truth. That's how careful.

>>14956202
huh shizo ?, did you forget to take your meds

For two polynomials with algebraic coefficients f,g are the roots of f^g algebraic?

>>14956950
>f^g
Is that... exponentiation...?
You're exponentiating two polynomials?

>>14952036
He got addicted to benzos and fried his brain

What's the best way to self-learn math stuff? And what's the best path?
I am currently starting with calculus using online courses.

>>14956980
What courses are those? I'd also be interested.

>>14956986
I'm doing the ones on Udemy (by krista king)

>>14956990
I'm looking at them. Kinda out of budget. They do look cool, though. I'm also seeing there is at least some content available in her channel.
Thanks for sharing.

>>14956959
example: [math](6x^{4} -0.3x^{2} +4) ^{51x^{8} -6x^{5} -x^{3} + \sqrt[6]17}[/math]

>>14957053
No, the roots of (x^x)+f are generally not algebraic for algebraic polynomials f, let alone that. I have no idea if the roots of f^g for algebraic polynomials f,g form an interesting field but probably not.

Are there any interesting spaces where Weierstrass approximation doesn't work?

>>14955601
Are you asking if all metric spaces are connected? Certainly not.

>>14955705
I'd assume just the constant map to 1.
[math] (\phi \times \{1\})(x) = (\phi(x),1) [/math]

>>14955836
That's the answer I was looking for.

>>14956950
No, see Gelfond–Schneider theorem

[math]\text{Spec}(\mathcal{O}_K)[/math] have to be the best spaces.

>>14958006
[math] \text{Spec} (\mathcal{O}_K) [/math]

>>14957851
>>14956950
>>14957248
Wouldn't the roots of f^g just be the roots of f that aren't roots of g?
Is this a collective brain fart?

>>14958037
What did I mess up? I used alt+m.

>>14958037
do you recommend atiyah commutative algebra or what's best?

>>14958071
>>14958037
While you were talking about the best spaces, I
placed some spaces in the code which fixed it.

>>14958059
It's this guys. If f^g=0 then you can exponentiate both sides by 1/g. This is calc 1 stuff, come on.

Is it Gelfand or Gelfond?

Let's say I have a field K and its extension L/K. The field K and the extended field L are both of characteristic 0. Simple, nice infinite fields that we love.

I have proved that any extension of K of degree two is automatically normal.

Now, the question is "is this in general true for any extension of degree greater than 2?".

Answer is obviously no. But how do I prove it?

My thoughts. For example let's say we extended K by an element and now we have basis 1, a, a^2. Degree is three.

Basically, normality of an extension is the fact that we can create automorphisms from one roots\ to other roots. Only in such case we can swap them if the polynomial is irreducible. So if we have a root in our extension field L over K of degree 3, a nice automorphism (conjugation) that we used in degree 2 case is no longer available. we kinda missing something, that must extend our L into new field so we can unlock these automorphisms.

Now the question, how to mathematically show this "missingness" ?

>>14958349
>But how do I prove it?
So what's the question exactly?
"There is no field K of characteristic 0 such that every extension of degree n > 2 is normal"?

>>14958349
If you want to show something is not true then you just need a single counterexample for example [math]\mathbb{Q}(\sqrt[3]{2})/\mathbb{Q}[/math].

>>14958355
My question is how do i prove that, in general, for any extension field with degree greater than 2, it is not true that they are normal.

>>14958358
Yes, we have tackled degree 3 extensions. Now we have to find counterexamples for all other extensions with degree greater than 3.

Do we have to inductively find counterexamples for each degree or is there some elegant way to show that every extension field with degree greater than 2 is not automatically normal?

>>14958366
>Now we have to find counterexamples for all other extensions with degree greater than 3.
You have to find for each n in [3..inf[ that there is an extension of degree n that is not normal?

>>14958372
Well kinda yes. So i think about finding an elegant prove.

>>14958375
What is the degree of Q[X]/(X^n-2) over Q? Is it normal?

>>14958376
Well, this quotient ring can be mapped by a homomorphism to the splitting field of X^n -2 and in theory each root is correspondent to a homomorphism from the ring to the extension field or i should say splitting field. The degree of your quotient ring is n-1.

It cannot be classified as normal or not, since it's an extension of Q by indeterminate x.

Self studying baby Rudin, got a question.
All three of these have the same cardinality, but their complements in [math]\mathbb{R}[/math] have different cardinalities:
[math]\mathbb{R} -[0,1][/math]
[math]\mathbb{R} - \mathbb{Q}[/math]
[math]\mathbb{R} - {1,2,3}[/math]
Is there a notion resembling size that distinguishes these without reference to their complement in [math]\mathbb{R}[/math]?

>>14958401
So you have your answer.

>>14958410
:D That's the moment you start to play with infinities. No one made a "complete" theory for that question. The best you have today is the theory of measure. So keep reading, it will bring answers, but you'll understand that there will always be an infinite number of non answered questions.

>>14958418
how come?

>>14958433
You have a non normal extension of degree n-1, so you have a non normal extension of degree n for every n>=3.

>>14958442
you're a schizo

>>14958449
Why? I don't understand your reaction right now.

>>14958453
woah i have been illuminated. Thanks for the answer and sorry for my impatience and rudeness. Thank you very much :D

>>14956493
bump

>>14958401
>It cannot be classified as normal or not, since it's an extension of Q by indeterminate x.
what? You can still classify it as normal or not, Q[x]/(x^n - 2) is a field extension whose arithmetic you know totally

>>14958410
That's the moment you realise the scam that is Analysis.

>>14958410
>reference to their complement
But you defined them using their complements...

When I do trigonometry I'm reminded of SOHCAHTOA and I read it in my head like "suck a toe, ahh~", and it's a very lewd image of some sexy toe(s) being sucked, very erotic, and I'd post an image for maximum comedic value but I don't wanna get banned because I love you guys too much.

>Finished all math courses, just need the natural science electives to graduate
>take physics
>professors, textbooks, notes, problems, are all using notation incorrectly, derivatives done wrong based on patterns they memorized
>professor takes integral of a vector variable, turns it into something else that doesn't even follow mathematically
>conversions for constants, units of measurements, all rounded up to the nearest whole number because its "good enough"
>even with all this slop, get upset when error value for experiments has too many significant digits, even its just more accurate, because "its not the way things are done"

Fuck physicists, literally a bunch of dumb cargo cult niggers, just plastering equations and symbols without even doing actual math. Should have taken chemistry instead. Less math, but at least they don't pretend they're math experts.

>>14951941

>>14958927
Why isn't it "suck a toa"?

>professor keeps proving contrapositive and calling it proof by contradiction
This is a commutative algebra course wtf

>>14958986
Nice, that's gonna keep the toes out of my mind.

>>14958992
Contrapositive is a type of proof by contradiction

>>14959069
No

i get why R is semisimple, but not why there's only 1 matrix ring factor in its decomposition. the number of these factors is the number of isomorphism classes of simple R-modules, so equivalently, why is there only 1 simple R-module up to isomorphism in this context?

>>14959079
nvm, a product ring can never be simple, that's why

If [math]A[/math] implies an undecidable and [math]\lnot A[/math] implies an undecidable then [math]A[/math] is undecidable, innit?
Has this ever been used to prove something is undecidable?

>>14959069
No, it's called proof by contraposition

>>14959110
No. If A is "x = x" and B is "x =/= x" and C is any undecidable statement which is true, then A and B both imply C

>>14959132
ESL moment.

>>14959110
It depends on if LEM holds. In the example you gave, let’s say A implied C and not A implies C. Well then (A or not A) implies C. In the presence of LEM, (A or not A) is true, so C is true.
I think the tricky part is that even if A is undecidable, it will still be the case that (A or not A) is true

>>14959167
I think he means if they imply different undecidable statements. In which case, A would be undecidable: if you could decide that A is true, then you can decide that C is true, a contradiction, and if you can decide that A is false then you can decide the other undecidable is true, another contradiction

Lots of algebraic numbers questions earlier, wow, I've got a never read copy of Baker's transcendental number theory.
Are there any interesting sets between the algebraics and the computables besides the Liouvillian (not Liouville) numbers?
If yes, I'm gonna read the book when I finish with Bollobas, if not I'll put it up for sale.

I was doing a programming thing over in /g/ and someone mentioned something that reminded me. I feel like there was a thing I learned long ago in being able to convert summations into formulas (might have been discrete?)
I want to make summation below into a formula.
I don't want you to solve it. What subject/method should I look up to learn how to do it?

[math]
\sum_{i}^{n-1} \frac{i+1}{n-i}
[/math]

>>14959272
I don't think there is any particular subject specifically for summations.
Combinatorics may be the closest thing.

For your sum, you may want to look up generating functions. They're really useful, especially for sums.
Look up the "generatingfunctionology" (yes, that's real).
Though if you have the indexing variable in the denominator, it's usually difficult, e.g. the harmonic numbers.

>>14959294
ok, so I guess I probably did do something like this in discrete.
but yea, probably not that complicated.
but i guess that stuff will be added to my list of stuff to learn

>>14959300
Just to give a hint, your sum looks like a convolution product, so maybe your sum is the coefficients of some power series that is the product of 1/(1-x) and ln(1-x)

>>14959272
The sum looks simple assuming it starts at 0.

[eqn] \sum_{i=0}^{n-1} \frac{i+1}{n-i} \\
= \sum_{i=0}^{n-1} \frac{i-n+n+1}{n-i} \\
= \sum_{i=0}^{n-1} (-1 + \frac{n+1}{n-i}) \\
= \sum_{i=0}^{n-1} (-1) + \sum_{i=0}^{n-1} \frac{n+1}{n-i} \\
= -n + \sum_{i=1}^{n} \frac{n+1}{i} \\
= -n + (n+1) H_n
[/eqn]

>>14959110
It is naturally used where A not only implies and undecidable U, but also U implies A, i.e. U<=>A.
E.g. in ZF you prove A="All vector spaces have a Basis" to be equivalent to A="Full choice", and thus proved A undecidable too. I grant you that this example for your technique has collapsed too many aspects of its generality.

I think the reason why it might be hard to come up with other examples of your proposed proof strategy is that if you found out U to be undecidable and also found out that A=>U, then A is strong enough so that you've already found out that it's undecidable by other means.
E.g. of course A="Full choice" implies X="Dependent choice". And since X is undecidable in ZF we know that A is undecidable. But of course A is stronger and so we probably already knew A to be undeicdable.

>>14959132
>No. If A is "x = x" and B is "x =/= x" and C is any undecidable statement which is true, then A and B both imply C
If C is undecidable and so can't be judged true in the theory, then your theory does not prove "True implies C".
If you want to interpret also this "implies" metatheoretically, then you'd not have a proof technique.

>>14959167
>It depends on if LEM holds. In the example you gave, let’s say A implied C and not A implies C. Well then (A or not A) implies C. In the presence of LEM, (A or not A) is true, so C is true.
I don't think this has much use given anon asked about concluding "A is undecidable", not anything about C?

>>14959314
>>14959272
I really wouldn't call that a "closed form", since the only way to calculate the harmonic numbers is by summing them.
This seems as equally difficult as OP's original problem.

>>14959172
I'm confused by your post.
>if you could decide that A is true, then you can decide that C is true, a contradiction, and if you can decide that A is false then you can decide the other undecidable is true, another contradiction
Why does it matter if the undecidables are different in this part?
>>14959324
>I grant you that this example for your technique has collapsed too many aspects of its generality.
Yeah, it's basically just [math]A \to U[/math] and [math]\lnot A \to \lnot U[/math] (which is [math]U \to A[/math]).

>>14959340
>Why does it matter if the undecidables are different in this part?
The argument anon gave relied on the undecidables being the same. If the undecidables are the same -- if both A and neg A implied the same C -- then this would be a proof of C (using classical logic as we are not retarded)

>>14959272
Read chapter 2 of "Concrete Mathematics" by Knuth.

>>14959314
>>14959294
oh, is harmonics essentially a sigma simplified? I guess that's kinda nice to know
I was imagining that I could make a formula that can solve it easily in one go. maybe saving compute time.
but I guess that isn't really possible for more complex things

>>14959356
will do

>>14951840
>watching a math video about some random topic
>"let's talk about the axiom of choice"

>>14959358
I just pulled conc math because i feel i saw this sum before, and this sum looks similar to a sum done by Knuth on page 41, i think it's in fact the same sum but i can't be bothered to check.

>>14959349
>The argument anon gave relied on the undecidables being the same.
Which anon?

>If the undecidables are the same -- if both A and neg A implied the same C -- then this would be a proof of C (using classical logic as we are not retarded)
If we know C to be undecidable, and we find A=>C (or even notC), then we know we can't prove A. If we find notA=>C (or even notC), then we know we can't prove notA.
We don't need LEM to get to this conclusion.

>>14959368
I don't know why some schizo so obsess about this axiom instead of any of the others. AOC is certainly more intuitive then the axiom of infinity or the axiom of regularity.

I had a strange, perhaps non-standard idea:

If we assume the following:
* p,q ∈ a (can be any)
* √2 is irrational

Then we can construct this

|p| > |p - q∙√2| = ε > 0

and we want to have an ε arbitrarily close to ε.
Now my strange idea is: this can be done, because |p| and |q| can be picked to each have any arbitrary large value. Because of this, the irrationality of √2 can be exploited: it being irrational is is equivalent to the statement that there are no repeating or terminating sequences of digits within it. This in turn means there should be infinitely many unique subsequences can be "addressed". In any way, it's a source of limitless? entropy.

Now, I know that irrationals are not necessarily "normal" or patternless like Pi. E.g. something of a form like
0.10100100010000 etc. can still be irrational. But we also have p, q at hand, and we should still be able to generate with only these three ingredients of p,q, and √2 either:
- any(?) real
or
- or at least, any real that is smaller than some bound

By method: for p and q, choose each one big enough so one can "home in" onto any arbitrary index of the decimal expansion of √2. e.g.

1415 - 1000*(1.41421356237) =
1415 - 1414.21356237 = 0.786...

Now, p and q can be given an additional fractional part where the ratio between these two can be used to further specify the desired number.

1415.2 - 1000.6*(1.41421356237) = 0.137...

Of course, the original goal wasn't to generate specific reals (which may or may not be possible with this method), but only an arbitrarily small one, which means it should be still doable even if there are such addressing "gaps".

I didn't specify my idea this elaborately and assumed, it was an already existing idea. But the corrector just wrote (paraphrases) "I don't geddit xD".

So, does this actually work?

>>14959388
>intuitive
What do you mean by that?

>>14959390
Ah I meant to say that I can use one rational coefficient for either p or q.

>>14959390
>we want to have an ε arbitrarily close to ε
I don't geddit

>>14959388
Idk OP, but for me, it just bothers me how it's the complete opposite of constructive. I come from CS.
I accept it, but just don't like it.

>>14959388
I'd say because N and its subsets are simply necessary to code infinite sequences or rationals (e.g. via 2^index · 3^sign · 5^numerator · 7^denominator) and regularity can be replaced by transfinite induction (which doesn't involve set existence)

>>14959402
If you got a harder equality than the extensional one (like in set theory), then your (co-)domains are more robust and, in turn, in something like dependent type theory choice becomes a theorem.
Beyond type theory, I don't think you ever need to adopt (and accept) choice if you're not doing topology/algebraic topology in a non-CS sort of way.

topology/algebraic geometry

>>14959383
>Which anon?
14959110
>If we know C to be undecidable, and we find A=>C (or even notC), then we know we can't prove A. If we find notA =>C (or even notC), then we know we can't prove notA.
True, but the point is that if we know A=>C and notA=>C for the same C, then we have a proof of C, and so this situation will never arise for undecidable C

>>14959407
>I don't think you ever need to adopt (and accept) choice if you're not doing topology/algebraic topology in a non-CS sort of way.
I'm going into algebraic geometry and algebraic number theory.

>>14959407
You need the axiom of choice the prove the Hahn-Banach theorem in Functional Analysis. Without it you can't do shit in areas like PDE theory.

>>14956290
>>14956293
I guess? But it seems so obvious that I am worried we are missing something.

>>14959417
Okay. I'd still say "why is this the point, given we want to prove A undecidable with the technique and for this we don't need an unconditional proof of C"

>>14959434
Zorn's dilemma

>>14959457
Work with nicer spaces

I quit my studies to become a full-time function plotter

>>14959555
Can someone make the coomer meme but with "plooter" instead?

How do you read the sum on the right? Anyone knows?

>>14959727
Map all numbers n to the tuple of their prime factors and any sum in n becomes the same sum over the prime factors

e.g.
3 + 6 + 10 = 3 + 2*3 + 2*5

>>14959744
I did comprehend the general concept. But I don't understand how the specific summation is supposed to be done. If we had

[math]\sum_{n = 1}^{10} \frac{1}{n}[/math],

then how would the sum on the right look like?

Why do I keep getting [math]y^2-x^2=4[/math] for (c)? Shouldn't the answer be [math]x^2-y^2=4[/math]? Intuitively, looking at the graphs, the latter is the correct answer, but where am I going wrong?

why would you ever want to use newton's method (iterative root finding) when you could just use gradient descent instead?

>>14959755
The order is not specified but it's natural to keep the order

1/1+1/2+1/3+1/(2*2)+1/5+1/(2*3)+1/7+1/(2*2*2)+1/(3*2)+1/(2*5)

Can you construct the naturals with an alphabet of 0, 1 and all elementary functions when you can only use 1 once?

>>14959783
In a footnote, they said it stood for this...

>>14959757
>where am I going wrong?
How are we supposed to know if you don't post your work?

>>14959057
>>14958986
I miss those days.
>>14959079
What book if I may ask?

I just woke up from a dream where I had a roommate and he brought a prostitute, then took her to the bathroom to help him with his proof that the reciprocal of primes series diverges

>>14960311
That's...a rather interesting dream.

>>14960357
I once was cuddling with a prostitute and our discussion *almost* resulted in me explaining the halting problem to her. (not a dream)
The beginning of the conversation was about how she liked Courage the Cowardly Dog as a kid.

>>14960311
That's...a rather interesting dream. Now that I think
about it, it must have been a tutor...which means
that tutors are prostitutes of knowledge.
Always on call, gives great instruction, rarely cheap.

Looks like I cracked the code here...

>>14960370
>>14960380
Well then...if you can segue into a halting problem
conversation, she would have came twice!
You, my dear anon, have fucked her mind.

>>14959808
n+1 = n+0^0

>>14960311
I have this dream my daughter-in-law kills me for the money. She thinks I left them in the will. The family gathers round and reads it and then someone screams out:
>She's laughing up at us from hell!

>>14960106
Knapp's Advanced Algebra, it's the sequel to his Basic Algebra. both are fantastic textbooks and are available on his website for free

New thread
>>14960838
>>14960838
>>14960838
>>14960838
>>14960838