/sci/ - Science & Math

Is there any way of making some kind of canonical continuation of the nth prime to rational n?

Scientifically, is Platonism or Fictionalism the correct philosophy of mathematics?

https://www.youtube.com/watch?v=mhIkyqLDl9M
https://www.youtube.com/watch?v=ZQOwG-hcd_k

I brought a new problem however this one is SO easy. I feel confident in saying anyone should be solve this. Honestly it's just ridiculously easy, I'll probably post another one soon that's a proper problem, because this one is just too easy. But regardless, I appreciate anyone replying. Who knows, maybe there's a interesting thing about this problem or a weird way to solve it.

kek i went back to lang's basic mathematics after a few weeks into a discrete math course and it feels way more approachable now with at least some proof writing ability

>>15213744
d1d2d3 = 10*10*10 = 1000.
d1d2d3 = d4d5d6 --> 1000 = d4d5d6.
d1d2d3 = d5d6d7 --> 1000 = d5d6d7.

1000 + 1000 = 2000 except we're double counting the cases where d4d5d6 = d5d6d7 which is fake and gay.

d4d5d6 = d5d6d7 --> d4 = d7 = 10.

so we subtract the overlap 2000 - 10 to get the answer 1990 memorable telephone numbers.

>>15213952
Hey fren, sorry but that's wrong. You undercounted. You're right for the most part though. You can probably correct your mistake very easily! I can tell you but I'll let you try find it first. Good luck!

>>15213952
>>15213973

Why can't I enjoy math unless I'm in a good and comfortable setting? Like when I lived in the midwest math was depressing as fuck but now that I'm in the PNW Math is fun again.

>>15213994
The website is an anime image board faggot.

>>15213973
I was way over thinking this. Of course we still count half of the overlaps so the answer is 1995 memorable numbers.

>>15213675
Undergrads come across minor antimonies that have been discussed for decades already and then stop studying math and go on egocentric, schizophenric rants like this guy.

Read Jean-Yves Girard's Blind Spot.

>>15214014
>The website is an anime image board
Never did he dispute that, he just called you a loser. Why are you so pressed?

>>15213744
first 3 numbers: each number can go from 0 to 9, so 10 possible choices each = 1000 in total

We have 2 chains: abc-Xabc and abc-abcX
since abc can be all 1000 numbers from 000-999, we pick X to go from 0 to 9, each step we count 1000 numbers, for both chains

So we get 10000 possible numbers of the form abc-Xabc and also 10000 possible numbers of the form abc-abcX, however, in the case where every number is the same (000-0000) we are counting that same number twice in both chains, therefore we just need to subtract 10 to the total.

the total number of different memorable telephone numbers is 19990.

I hope this is correct.

>>15213994
I do not accept criticism and insults from people who have not even attempted the problem I posted.

First solve it and then say whatever you want to say about me and the person who replied to me.

>>15214014
Unfortunately anon that was not your mistake. You were actually right about subtracting 10. Your error was in the "2000" part. Do not get discouraged however. I totally see how you thought and it's completely understandable.
Go back to the
d1d2d3=d4d5d6 --> 1000
part, you're forgetting about what choices d7 can have I believe.
>>15214021
Yes anon, your answer is correct. Nice job! Thanks for your time and effort solving this problem. I hope you somewhat enjoyed it.

I wanna do this (compare two or more correlation matrices depending on treatment)

Is it legit to do? How is it called properly

>>15214038
You want to compare the functions, like auto-correlation? Or do you actually want to compare the matrices?

If [math]I_s, I_b[/math] are your matrices, it seems natural to look at [math]I_b^{-1}\cdot I_s[/math] or [math]I_b - I_s[/math]

Is it better to think of a locally compact space as one where the topology has many elements, or rather as one where the topology has big elements

>>15213675
>The only way out of this paradox
I can name at least 4 alternative outs that have been studied

>>15214043
I'm a statisticslet, and uneducated on top of that. I don't know what is correct to do.

I have 4 treatments and in each there's an individual, and for each there's a set of metrics (dozen gene expressions, behavior, anatomical measurements). I took everything and correlations are weak but make sense. But if I break them down by treatments the matrix changes. Those changes are probably valuable and have information in them.

I'm pretty sure the operation is in part of some multidimensional workflow and has a proper scientific name, but I don't know the name so I can't google it and go from there.

>>15213675
i can not understand why a conjunction has an autoreference of itself, a conjunctions of something property can not be an element, they are odds...

>>15214038
>>15214076
>I'm a statisticslet, and uneducated on top of that. I don't know what is correct to do.
At the risk of handing you an easily abuseable tool, the jargon you're looking for is "canonical correlation analysis".
https://towardsdatascience.com/canonical-correlation-analysis-b1a38847219d

[math](-1)^{Inv(\sigma)+Inv(\sigma^{'})} = (-1)^{i+j}[/math]

What the fuck is this? Don't get what's going on here nor with the proof and my book doesn't mention the name of the theorem

>highest grade possible for physics II is B, more than likely I'll have a C, due to bombing last exam
>taking Topology and analysis 2 this semester as well
Honestly I'd rather get a D in physics than not get an A in both my math courses. Will this be a huge negative for graduate applications, and is it something you'd give an applicant a black eye for? I could probably dedicate more time to studying physics I just don't want to. I only need a D to pass it and graduate.

Why does learning (physics and) math feel so inefficient? It's as if it could quickly be explained simply clearly and explicitly, but it isn't.

How do I decide between algebraic geometry and differential geometry?

>>15214653
>"Sigh, how do I decide, kaviar with white truffles, or wagyu with foie gras"?

>>15214653
Do AG then CompG

>>15214605
I don't know about physics, but in math its just getting used to the writing style. Wasn't until my junior year of undergraduate that I could finally read a math textbook and "get it" without bashing my head into one lemma for an hour. It was just like reading plain English at that point.

>>15214605
Not even close to being the same. Virtually nothing in Physics can be proven analytically, and its an experimental science masquerading itself with a coat of mathematics. You can't prove the Thomson cross-section, you just memorize it, you can't logically derive something like magnetic dipole moment. Its all memorization of past experiments, and the higher you go the more obvious the shaky foundations become. That to me is what makes learning it inefficient; 99% of what you learn is taking someone's word for it.

>>15214866
>you just memorize it,
That might be what I meant. For example, it's hard to find a clear explanation of the electroweak force or what SU(2) symmetry or spontaneous symmetry breaking actually are. Do the equations not have a self explanatory meaning without a whole lot of context?

>Linear algebra
>finding wronskians
>during office hours show professor my proof of a possible method to solve very large matrices under certain conditions where the determinant can be found at most basic form of a 2x2 matrix times a coefficient, without taking any derivatives, just knowing that the compound value of the derivatives is equal for each portion of the function products. Just needed some help to really get this going
>he tells me good job, but that its called Abel's identity and someone already proved that

FUCK
FUFUUASFADSFA
Literally born too late to discover anything, do anything interesting, I will always be relegated to worthless fuck territory, everything has already been picked clean. I can't even have a discussion on it or a deep dive during office hours, its that fucking "elementary"

Jech never defines "proof". He switches from math to poetry at p. 157. (Jech "Set Theory" 3/e)

>>15214398
I'm assuming it has something to do with permutations because of the Inv and sigma but you can't just drop some random equation with no definitions and expect people to know what it means
I don't know what i and j are and I don't know what your book means by priming a permutation

>>15214055
Neither, a locally compact space should be thought of as the maximal ideal spectrum of a C*-algebra.

>>15214001
i'm the same but it's a bad habit and kind of ungrateful
>>15214398
is this from shirov linear algebra or halmos finite dimension vector spaces?
anyway https://en.wikipedia.org/wiki/Inversion_(discrete_mathematics)
>>15214653
You need both

>>15215172
Requesting demonstration of proof that for every locally compact space X, letting V be the banach algebra of complex valued continuous functions on X, for every maximal ideal I of V, there is an x <- X such that
>I = { f <- V : f(x) = 0 }

>>15214001
Did you just post this on /trv/

>>15214001
because you aren't bringing good and comfortable with you??
https://www.youtube.com/watch?v=F43EIkSfsSI
honestly though
this game helps
https://en.wikipedia.org/wiki/Galaga
I play on OpenEmu
good medicine
that and Super Mario Bros.
also listen to Mark Farina
https://www.youtube.com/watch?v=beq6OVaQafY

>>15215052
There still elementary stuff out there to figure out. Maybe...

>>15215052
There'll be things that have already been
discovered before you can figure it out, it'll happen.

But you thinking of that method already sets you
well ahead of your classmates if they hadn't
thought of it yet, or at all. You could very well
find out stuff the professor did not say and he'll
be glad that you did it. The true test is if he gives
you a taste of what he does in the office and
you could figure that out yourself in a way he
hadn't before.

So, don't be afraid to ask for more. You'll have
that conversation you always wanted. Just know
that you just got ahead for yourself.

>>15215280
I stole it from trv kek

>>15215193
is that supposed to be lego karajan?

>it doesn't take a genuis to see that
>obviously,
>clearly,
>only a total fucking buffoon could fail to see that...
Why do math books are so insulting and mean to the reader?

>>15215651
the same reason why the abused turn into abusers

>>15215651
back when I was still young I knew a zen master. He had a student that would hang at his lips all day, to catch every word of wisdom, every bit of divine insight that might come from the master. One day while they were walking the student asked: "Master, what must I do to attain enlightenment?" The master turned to the student, and slammed the gate closed on his leg, breaking the student's leg. Without saying a word, the master walked away.

>ACADEMIC FRAUD.
>>15215294
This is Gödel's "proof" that AC is independent of ZF
>>15212805
>you are cursed to never arrive at truth.. i hate him so much bros
>>15194007

>>15215704
Plebbit has a zen forum.
We have /lit/ and /his./
>You're nuts if you think 4chan has a substitute for the plebbit zen forum.
http://mp3.hardnrg.com/MadamZu-Aug_2003-pt1.mp3

>>15215651
when he does not see why "it is trivial", the midwit rages and seethes about how the author is pretentious and offensive.
the genius steps back and tries to fully understand the situation, so that he can understand precisely why it should be trivial and thus obtain a better understanding.

i'm midway into calc ii and i don't know if i hate it because of my dickhead instructor or because integration is tedious "know this trick" bullshit

>>15213505

Math is fake and gay. Constructed formels in schizoids brains...

You could exchange the whole system of numbers with various tone variancies when inhaling air trough your mounth and each tone equals a degenerted cribble.

>>15213638

>>15216105
As Spivak says, derivatives are a skill and indefinite integrals are an art
https://archive.org/details/spivak-m.-calculus-2008/page/613/mode/2up?view=theater

>>15213744
since this one was perhaps a bit too short, I'll post another one. This one is fun. You should be able to solve this. If not, let me know and maybe I can try to give hints.It is rather simple though. But regardless, good luck!

>>15216105
integration is hard and don't let anyone convince you otherwise.
people that think integrals are an art don't get handed a 10-20 pages of integrals they have to solve in 4-6 hours

>>15216105
study some measure theory and it'll all make sense

>>15214656
>kaviar with white truffles, or wagyu with foie gras"?
I know what algebraic geometry and differential geometry is but have no clue what either of those things are.

>>15215465
Bingo

Italian cs student here, I've just started a linear algebra and geometry course and the textbook that was suggested is very short and written by the previous prof. Is it a good idea to buy a longer book for better comprehension? I guess the subject is pretty important for future courses in the math world

>>15217381
Yes

what’s the best undergrad real analysis textbook? im getting filtered hard for the first time

>>15215651
To save space. It's just not feasible to spell out all details.

f(x)=arctan(x)-x
Do you guys know how to invert this function? Or prove you can't express the inverse in terms of elementary functions

>>15213505
I'm a neurobiology student working on cellular processes of neurons and glial cells.
I haven't done any math since high-school except for 5 different statistics courses. I generally do very well in them but they're only taught on a very superficial way.
I like math though and would like to learn more. What do you think would potentially useful for me to teach myself?

Let [math]\Omega \subset \mathbb{R}^n[/math] be a smooth domain. It is well known that an operator [math]T_k : L^2 (\Omega) \to L^2 (\Omega) [/math] is Hilbert-Schmidt iff its kernel is square integrable, i.e., [math]k \in L^2 (\Omega \times \Omega)[/math]. Furthermore, if the kernel [math]k[/math] is smooth, the corresponding operator [math]T_k[/math] is nuclear (or trace class).

Let [math]\Omega_1, \Omega_2 \subset \mathbb{R}^n[/math] be two smooth domains. It is also well known that an operator [math]T'_k : L^2 (\Omega_1) \to L^2 (\Omega_2) [/math] is Hilbert-Schmidt iff its kernel is square integrable, i.e., [math]k' \in L^2 (\Omega_1 \times \Omega_2)[/math]. Can we also conclude that if [math]k'[/math] is smooth that [math]T'_K[/math] is nuclear?

>>15217598
>Or prove you can't express the inverse in terms of elementary functions
The function arctan(x) and the general combination (f(x)+g(x)) are only non-transcendental if neither f nor g are. Since arctan is transcendental the sum is as well.

>>15216384
[eqn]\sum_{k=m}^n \binom{k}{m}\binom{n}{k} = \sum_{k=0}^{n-m} \binom{n}{m}\binom{n-m}{k} = \binom{n}{m}\sum_{k=0}^{n-m} \binom{n-m}{k} = \binom{n}{m}2^{n-m}[/eqn]

proof by pic because I don't want to type, and also I like the specific drawings in those sorts of problems.

>>15217846
should brown region on right side be (k-m)?

>>15217834
>f = -g in your path

>>15217863
i'm not sure what you're asking but if you take the left [math]k[/math] (let it be [math]k_l[/math]) then for the right [math]k[/math] ([math]k_r[/math]) the following holds
[eqn]k_l = k_r + m \iff k_l - m = k_r[/eqn]

>>15216384
[math]\displaystyle A_{n,m} := \sum_{k\ge0} \binom km\binom nk = \sum_{k\ge0} \binom km\left[\binom {n-1}k+\binom {n-1}{k-1}\right] = A_{n-1,m} + \sum_{k\ge0}\left[\binom{k-1}{m}+\binom{k-1}{m-1}\right]\binom{n-1}{k-1}=A_{n-1,m} + \sum_{k\ge0}\left[\binom{k}{m}+\binom{k}{m-1}\right]\binom{n-1}{k} = 2A_{n-1,m}+A_{n-1,m-1}.[/math]
From the base case [math]A_{n,0}=\sum_{k\ge0}\binom nk = 2^n,[/math] induction gives [math]A_{n,m}=2^{n-m}\binom nm.[/math]

>>15217882
go away wtf

>>15217908
Sorry, I misunderstood the indices, thanks.

>decided to go back to school after getting out of military
>cs degree i think i want has calculus in the curriculum
>decide to look up """super advanced""" math (its just calc iii lol) to see how far the rabbit hole goes
>become extremely discouraged as i realize im getting filtered by literally junior high school level algebra

is there like, an arbitrary amount of learning hours needed to reach undergraduate math? I desperately want to fasttrack my understanding of this shit, but it seems hilariously fucking gatekept behind academic paywells. What is this academic-industrial complex faggotry? this inanity is actually worse than the arms trafficking and world policing the us gov't commits globally

>>15216128

Is it physically possible to have a negative damping or spring coefficient or does sort of scenario belong in the same category as the friction-less surface and massless rope?

>>15218429
Like if I have a mass-spring oscillator system in space with no air resistance, will the mass oscillate forever?

>>15213505
Hey Anons, I already studied basic proof but I can't beat basix idea of mapping into my head for some reason. Do you have any "problems book" specifically for basic set and mapping with solution? Thanks in advance.

>>15218284
Hey buddy, I was exactly where you were. At 28 I went back to uni, but for a math degree instead. Still in and using TA, rate is ETV1.
Don't be discouraged, if you have to I recommend just taking a precalculus course in your college to prepare yourself for calculus I. It helped me a ton, and so far I've aced every math course besides intro to proofs. I'm on my last six courses and 30 years old now.

>is there like, an arbitrary amount of learning hours needed to reach undergraduate math?
Just like in the military, you solve all problems by banging your head against it for long enough that it gets solved. In my case, I just study 3 hours a day per math course. Every general course, programming, or physics, I've been able to get by with less. Taking only 4 courses a semester I have been averaging 35 hours a week of study. Would not be possible if shore duty was not so cheese.

In my mind CS seems no different than just doing applied math, but focusing on algorithms and numerical methods to solve problems. If you don't like math, I'm not sure why you'd want to do a CS degree. But I've also never actually looked at what a CS curriculum looks like.

> hilariously fucking gatekept behind academic paywells
It should cost you a total of $0 to complete a degree. I'm using TA and FAFSA, but as only my base pay is reported and taxable I not only get the full FAFSA amount, but a refund of free money every semester. With the GI bill you should have an easy full ride + BAH. If your school is private there is a good chance they have a yellow ribbon program anyways...

Anyhow, just take a fast tracked precalculus course(college algebra + trig)and you will be ready for calculus I, II, discrete math, linear algebra, and so on. Those are the courses where I've seen CS majors anyways.

Only study math as it the only topic complex enough to distract me and keep away bad sad angry stressful anxiety inducing thoughts and fear of mortality.

>>15218643
>whole ass active duty E6 attending school full time
navy is fuckin wild man. As a lance corporal I was putting in work from 0430 AM to 1730 every single day, and that's just my obligated duties. If I wanted to keep up with PT it'd be like another hour out of my time so I'd have to eat then go straight to bed. I don't know how y'all do it.
>dont be discouraged; just take a pre-calculus
I had to take placement tests and I genuinely data dumped nearly every bit of math outside of basic arithmetic. I still have two more semesters of pre-requisites to complete before I can take pre-calc.

I really just want to be pointed to resources I can use to get ahead

>>15216119
Right, but who cares? The important thing is we've decided on a set of symbols we all use to reason about things and it lets us make real predictions about everything in the universe. Cope.

>>15217793
brilliant.org

>>15218778
Another vet here. I had to take remedial math courses too. Don’t sweat it, just get good grades and enjoy college. Between Pell grant and BAH I was living good in college. Had a cool little apartment and beer money on the weekends. Just read books and chilled.

Your problem is you haven’t gotten the green weenie out of your ass and slowed the fuck down to civvy speed. Re-fuckin-lax devil.

where does i go after halmos' naive set theory to further my set theory knowledge

>>15218770
I do this too

>>15217846
Good job anon. Your answer is correct! Your solution is quite similar to how the book does it minus the picture and instead with more typing.
Thank you for your time and effort solving this. I appreciate it!
>>15217939
Great job anon! Your answer is also correct!
Quite a unique way of going about it too. The recursive formula you found almost looks like Pascal's identity to me. All around very cool.
Thank you a lot for your time and effort solving this.

I personally went with counting way to find the closed form. That also gets the answer without much symbol writing.

Thank you both again for doing this.I hope it was fun for you. And actually, if you don't mind, tell me if you actually found this fun or not. And if it was a nice problem/exercise to tackle.

ive hardly studied in 4 days i need to make it a habit bad

>>15213675
Platonism obviously. If numbers are fictional, all statements that use numbers as terms are meaningless, which is absurd, so numbers are not fictional. When I say there are two apples on the table, the term two really means something.

>>15219104
>If numbers are fictional, all statements that use numbers as terms are meaningless
Only some of them. For example, I can say that the proton-electron mass ratio is exactly 1000. This is a meaningful statement about protons and electrons, because it is empirically falsifiable (moreover, the fact that it has been falsified is what allows us to assign it the truth-value of False).
Platonism, by contrast, is the philosophy that commits you to an unqualified existence of all mathematical entities (with at most occasional exceptions for things like odd perfect numbers, but even then fictionalism deals with such objects more naturally).

>>15218597
Please Anons, please give suggestions. I'm a brainlet, and I want more practice.

>>15218778
Best thing you can do is to be lucky enough to enjoy it. I took a 3.5 year gap out of highschool before returning to college, and when I returned I was placed into intermediate algebra. I had to take 3 courses before starting calculus.
Now I'm taking Linear algebra, Discrete Math, Calc 3, and self teaching Real Analysis between classes. I understand these are still the 'baby' subjects, but I still remember when I was feeling anxious about the what the difficulty of calculus 1 would be. The hardest period for me was the transition back to school, but after every semester things became much easier. For that reason I remember calculus 1 being much easier than pre calculus was.

how do I fractions and where to learn

>>15218778
>>whole ass active duty E6 attending school full time
Shore duty is a breeze compared to boat life. Average day for the past year is 0700 muster and I'm home by 0900. On rare days I have to be WCS for a job, we are usually done a bit after noon. On the boat its 16+ hour work days for 7 continuous months, or shit deals in port anyways. Shore duty is really just a trick to make people forget how bad sea life is until they re-enlist.

>>15218778
>I really just want to be pointed to resources I can use to get ahead
May get called a meme, but Lang's basic math is pretty decent since its concise enough to serve as a reference. Your pre-calc course will likely use Stewart's precalculus, which is only really good for the crazy number of problems it has. The only way ahead in math is a steady and disciplined pace. Best of luck, although you wont need it as I am 100% certain you have to discipline to succeed.

What concepts in abstract algebra do I need to have mastered before embarking on the challenge of picrel?
Is there a single book that covers all of them?

Just posting the most elegant proof of Pythagorean theorem

lads, i am in desperate need of a way to earn a living. Is there a website that collects all the maths problems with prizes attached?

>>15220654
A living implies long term stable employment and income. Problems with prizes is near equivalent to gambling in risk/reward. If you believe you're at that level it would be prudent of you to look into actuarial work or become a quant.

>>15213744
Bad definition. BTW

>>15214311
I guess we need to store more Uranium if we really want more Math doctorates.

>>15219329
>because it is empirically falsifiable
Statements can obviously have meaning without being falsifiable. If I say that a teapot, too small to be seen by telescopes, orbits the Sun somewhere in space between the Earth and Mars, then my statement has real meaning but is unfalsifiable. You can understand what my claim means, but I can't prove that my claim is true.
>Platonism, by contrast, is the philosophy that commits you to an unqualified existence of all mathematical entities
Platonism does not commit you to accept that something that is called a mathematical entity is a real mathematical entity. It doesn't commit you to the claim that all terms refer to real things.

Question.
If I have a topological space and a point, is their product homeomorphic to the space itself?

Apologies if this is not the right thread. Suggest some very basics of math for someone who has ZERO of it and wants to start programming and CS

>>15221534
You really don't need much beyond the average highschool math. IEEE Floating point numbers are essentially just Scientific Notation. You might deal with some vectors/matrices, but no differentials or integrals, at least for the first 4+ years. decimal-to-binary is easy to understand with your fingers.

>>15220921
Could you elaborate?

>>15221349
have you tried constructing a homeomorphism?

>>15221349

>>15221594 ::only sometimes, in general no

>>15218643
I wish I could get my hours per week of studying down because it feels like my methods aren't that efficient.
I'm taking Calc 1, Discrete, and programming in my free time averaging 30-40 per week.
Although I include stuff like visiting office hours and lecture as going to that time.
I really didn't expect learning proof writing to take so many hours.

>>15220588
Eisenbud's book was specifically made to contain all of the commutative algebra used in Hartshorne, so that should answer your second question.
As for your first one, "master" is a strong word, you will get things better once you know how they're used in algebraic geometry. But I'd say a concise list would be: tensor products, flatness, localization, dimension theory, regularity and smoothness of points, integral extensions, derived functors

What do you make of this book?

>>15221755
Thank you, anon!

can anyone explain to me how this is done? ive solved trillions of these, most basic EGV problem in the universe. you take the coefficient matrix, subtract unit matrix * lambda matrix, set the det of this matrix to zero and find roots of lambda, but i cant get to this answer for the life of me.

>>15221594
Well, I wanted an anwer before attempting to do it. It kinda makes sense for something like the unitary interval and any point since you are just translating the interval.
>>15221599
Any counterexamples?

Can any integral be turned into an infinite sum?

>>15222662
Yes...given that an infinite series representation
exists for that function.

>>15213744
2 x 10^3 x 10
2 since there are two and only two possible formats that are isomorphic by rotation of the four last digits
10^3 since the sequence has 7 digits, six of them are determined based on the first three ones, rotation is not permitted
10 multiplier for the 7th digit
Final response : 20000

>>15222725
The answer was already posted anon : 19990. Your idea is good, but it counts numbers like 000-0000 twice. So you need to substract 10.

>>15215651
Math books aren't made for women

>>15222725
Hi anon. Unfortunately your answer is incorrect as the anon below has pointed out, you have counted a group of numbers twice.
But once you figure out what those are, you're done.
>>15222781
Anon what the frick?!
Thank you for letting them know their answer is wrong but you shouldn't have said the actual answer and how to get it. They may have wanted to find out themselves.
I'm not mad at you anon, I know you said it to let them know the correct answer but maybe spoiler it next time. The answer was already in the thread but it seems like this anon didn't see/look at it.

If [math]f:X\to Y[/math] is injective and there is an [math]x_0\in X[/math], then we can construct a [math]g:Y\to X[/math] such that [math]g\circ f=1_X[/math] via [eqn]g(y)=\begin{cases}f^{-1}(y),&y\in \operatorname{range}(f)\\x_0,&y\notin \operatorname{range}(f)\end{cases}[/eqn]
We're allowed to define a function via cases like this because of the principle of the excluded middle, right?
So if we don't have that available to us, does this result not hold?

>>15223083
before anyone calls me a retard because the TeX doesn't render (at least it doesn't for me), it was rendered correctly in the TeX preview

>>15223083
>[eqn]g(y)=\begin{cases}f^{-1}(y),&y\in \operatorname{range}(f)\\x_0,&y\notin \operatorname{range}(f)\end{cases}[/eqn]
kek retard

>>15223021
Sorry, you are absolutely right! That was stupid, I will think next time. Too late to delete...

>>15220588
>before embarking on the challenge of picrel?
That's not how anyone does this, at least not anyone I've heard of. You learn a small amount of basic commutative ring theory and then learn the rest of what you need as you're reading.
People do it this way both because there is a ton of algebra to learn and it would take forever to frontload it, and because a lot of commutative algebra is gay retarded nonsense unless you understand what it corresponds to geometrically

>>15223083
[eqn] g(y)=\begin{cases}f^{-1}(y),&y\in \operatorname{range}(f)\\x_0,&y\notin \operatorname{range}(f)\end{cases} [/eqn]

>>15216384
This was fun. I'm a bit of a midwit so I didn't understand how >>15217846 and >>15217939 did it, but I have to admit I looked at their solutions before I finished. It took me a few days.

>Tldr; choosing k from n, then m from k is equivalent to choosing m from n, then any subset of n-m.

how do you solve problems that are open ended and aren't just word problems

What is the maximum surface area that can be filled by 17 equal sized non-overlapping squares inside a unit square?

>>15223107
It's okay anon, definitely not a big deal anyway. Thanks for understanding though!
>>15223089
I'm rather scared about messing up TeX when posting. I'm not saying you did this but I always thought that if I screwed up, I'd use what you said as an excuse.
>>15223126
Oh anon. That's adorable. Thank you so much for this solution. It's amazing. You did it really similar to how I did but much cuter and better.I wrote pic related just to show my friend quickly how I solved it so my handwriting is rather ugly but anyway. I couldn't really think of a nice scenario for the problem so I just ended up using this club story. Yours is just so so more awesome.
>I'm a bit of a midwit
I won't let you say that. In my eyes you're an amazingwit!
>but I have to admit I looked at their solutions before I finished. It took me a few days.
Thank you for your honesty. I think you did a great job regardless. However I'll say that a few days is a bit too long. For me it took 10 minutes or so but only because I managed to see the counting scenario under it. I'll copy paste what I wrote to my friend
"I thought "We're choosing k people from n people, and then from these k people we're choosing m people. It's almost like we're creating a group of people from these n people such that this group has m special people of some significance"

So another way to count that would be to choose the m special people directly from the n people, and then choose whoever we want from the remaining people."

I'm not usually fast though. I actually shared the problem here because I managed to solve it fast :DDD It could have taken my a few days as well actually.
>This was fun.
Very happy to hear this. We have more problems like this in a combinatorics server. Let me know if you'd like to join.
Again thank you a lot for this image you've created. It's great. Made my day honestly. And good job as well. You've solved it.

>>15213675
Russel's paradox isn't a paradox, it's far worse than that: it's a contradiction. A paradox is something that looks only like a contradiction because you haven't thought about it enough (Skolem paradox).
The ZF axioms were contructed to avoid Russel's paradox at all costs, so the P in your picture is not a set.

what's your excuse, incel?

>>15213675
>Philosophy of numbers

Numbers aren't people and don't think. There isn't any philosophy involved. Philosophy is just bullshit LARP by humans trying to pretend they are god. Trying to superimpose humanity on everything is retarded.

>fiction vs non-fiction

Numbers exist before this distinciton is made within the system. This is still trying to superimpose some later developments upon primordial things which exist independent from those spin-off bullshits. The argument "Philosophy of Mathematics" is no more meaningful than "What NFL team did Jesus Christ cheer for?". The answer is just No.

I laugh because you "official retards" have to suffer knowing that these people have "clout" in your field because they're "official retards". Can't wait for A.I. to outsource all of the retarded humanism bullshit and put these people out of work.

Could someone please explain to me how the symplectic matrix in Hamilton’s equations gives rise to a differential 2-form? I’ve heard that this is apparently a very natural thing, but I cannot quite wrap my head around what makes this so remarkable. I’d really favor a geometric explanation, if possible.

Furthermore, could somebody explain how the differential geometry in Hamiltonian mechanics is at all useful and relevant to actually *solving* Hamilton’s equations? To me, all the topological theorems involving the Hamiltonian seem interesting, but totally useless.

what's a good text on stochastic processes (martingales, markov chains, random walks, and so on)?

>>15213675
https://homotopytypetheory.org/book/
Enjoy

>192 = 2^6*3
8192 = 2^13
>8000 = 20^3 = 2^6*5^3
2^13 = 8192 = 8000 + 192 = 20^3 + 2^6*3 = 2^6*5^3 + 2^6*3
>128 = 125 + 3 = 5^3 + 3
1024 = 1000 + 24 = 10^3 + 8*3 = 10^3 + 2^3*3

>>15223799
2^8*5 = 2^4*3*5^2 + 2^3*3^2 + 2^3
2^5*5 = 2*3*5^2 + 3^2 + 1
>>> 636*2
1272
>>> 636/3
212
>>> 212/2
106
>>> 212/4
53
>>> 52+1
53
>>> 2*(5*5+1)
52
>>> 2*5**2 + 1
51
>>> 2*5**2 + 2
52
>>> 2*5**2 + 3
53
>>> 2*5**2*3 + 3**2
159
>>> 2**3*5**2*3 + 2**2*3**2
636
>>> 2**4*5**2*3 + 2**3*3**2
1272
>>> 2**4*5**2*3 + 2**3*3**2 + 2**3
1280
>>> 2**8*5
1280
>>> 32*5
160

>>15223819
>Three weeks
Five days
>Twelve hours
73 = 48 + 25
Three days
>One hour

>>15223829
160 = 2^5*5 = 2*3*5^2 + 3^2 + 1
>160 = 100 + 60 = 2^2*5*2 + 2^2*3*5
2^2*5*2 + 2^2*3*5 = 2*3*5^2 + 3^2 + 1

Let C be a group embeddable monoid.
Let G be a group and phi : C -> G a monoid homomorphism.
Let H be a group such that C <= H.
Let K = <C> <= H be the subgroup of H generated by C.
Prove or disprove: there exists a group homomorphism hat phi : K -> G such that the restriction of hat phi to C is phi.

Let C = [a,b,c,d : ab = cd ] be the monoid with the given presentation, i.e. the quotient of the free monoid on {a,b,c,d} by the monoid congruence generated by ab ~ cd. Is C group embeddable?

>>15216384
I spent a lot of time on this problem and did not successfully solve it.

>>15223993
Anon I'm sorry to hear that. I hope you didn't get discouraged by this.

What did you try? Where did you get stuck? Have you done problems similar to this in the past? Did you understand what the problem gave you and wanted in return?

We can talk if you want and maybe reach the solution however if you rather not as you may be tired from this problem, multiple people have shared their solutions. Just look at the replies the problem got, there are different ways to go about finding the answer.

The problem is definitely not trivial so don't feel bad for being unable to solve it at this time. If you managed to spend a lot of time attempting a problem, that's a achievement by itself.

>>15223314
Ohhh thank you for that solution, now I understand what >>15217846 did! You solved it very very fast... I don't really use any servers, but I really like the problems you post here. I try to do them, but usually I fail. Please keep sharing them and helping anons find the solution! I always look forward to them.
(PS. I like your handwriting)

>>15224273
>I really like the problems you post here.
Hehehhehe, extremely happy to hear that anon. Thank you.
>I try to do them, but usually I fail
Do your best! I think you're very capable and intelligent. And keep in mind some of the problems I post are rather too difficult without context. I take them from textbooks and quite often that means the solution has to do with what was taught in that chapter. So without knowing where the problem is from, it's often a lot more difficult. What I mean is definitely don't get discouraged by the problems you couldn't do.
>Please keep sharing them and helping anons find the solution! I always look forward to them.
(PS. I like your handwriting)

If you praise me more I'm going to die from embarrassment. I don't deserve it...

Thank you for your kind words as well as your time and effort solving these problems. I hope you have a very nice day.

>[math]\mathfrak{S}[/math]
Ever since letters started looking like this, maths stopped making any sense

Here's you revolutionary function made by the only Anglo pure mathematician of note, bro

>>15216384
You are counting how many ways you can choose a subset [math]A[/math] of [math]\{ 1, 2, \ldots, n\}[/math] and then a subset [math]B[/math] of [math]A[/math] with cardinality [math]m[/math].
Hence, [math]B[/math] is a subset of [math]\{1, 2, \ldots, n\}[/math] with cardinality [math]m[/math]. Each subset of [math]\{1, 2, \ldots, n\}[/math] has probability of [math](1/2)^m[/math] of containing [math]B[/math], hence for each [math]B[/math] there are [math]2^n / (1/2)^m = 2^{n - m}[/math] subsets of [math]\{1, 2, \ldots, n\}[/math] containing it. There are [math]\displaystyle \binom{n}{m}[/math] [math]B[/math] candidates, so the solution is [math]\displaystyle 2^{n - m} \binom{n}{m}[/math]

>>15224543
Very clever solution anon. Very creative.
Definitely a lot different than the ones already in the thread and very elegant.
Thank you a lot for your time and effort solving this problem though I suspect it was almost trivial to you :DDD
Have a nice day!

>>15224120
Sadly I don't currently have access to any of my belongings, but I will try to post my attempt hopefully tomorrow or much later today.

I tried first writing out a few small examples to see if I noticed any discernable patterns, then I worked with the general form and tried simplifying. For example [math] (n+1,n) = n) [/math] and then the first and last term will always be [math] (m,m)(n,m) and (n,m)(n,n) [/math] so that gave me [math] 2(n,m)[/math]

After that I was basically trying to see if there was any closed form or pattern to simplify for the all middle terms of the form [math] (m+1,m)(n,m+1) + (m+2,m)(n,m+2)...[/math]

I never did a problem like this before, but I did find it very fun. The only thing I can think that was vaguely similar was the proof for the power rule for derivatives of [math] x^n[/math] where we used binomial theorem to expand out and simplify.

Looking at the solutions posted, I definitely feel like I learned a lot. For example seeing the mother bird example >>15223126
helped me a lot with understanding. I see now this is like choosing k elements from n total, and then choosing m from the remaining k. Also it was really adorable too!

And for this one, >>15217846 helped me a bit too. In particular going from
[math] sum_{k=m}^{n} to sum_{k=0}^{n-m}[/math]
would have perhaps helped me a bit.


I would love to work more with these sorts of combinatorial problems, if you know any good texts or resources I would greatly appreciate it. I imagine the book in the image is possibly a good starting point, lol.

Can someone give me some intuitive reason behind

For polynomials B,Q,R, deg(R)<deg(B)
[math]BQ + R = BQ' + R'[/math]
yields a contradiction

>>15224832
on both sides the R term is negligible since its degree is lower than another term in both sides. therefore it suffices to compare only BQ and BQ', but Q' has degree one less than Q, so the degree of BQ has to be greater than the degree of BQ'

>>15224832
Reanrrage the equation
[eqn]B(Q - Q') = R' - R[/eqn]
The LHS has degree [math]\text{deg}(B) + \text{deg}(Q)[/math] and the RHS has degree [math]\text{deg}(R)[/math]. So unless [math]Q[/math] is the constant zero polynomial you get that [math]\text{deg}(R) \geq \text{deg}(B)[/math] from that equation.

Algebra is hards

>>15224818
the book in the image is definitely not a good starting point.
I mean, you could. But it only has problems and they get hard really fast. There are many good combinatoric books which have the standard format (theory->exercises/examples->problems).
If you want problems (and not theory, or at least not so much) I suppose the combinatorics section in "The art and craft of problem solving" would be better.

>>15224939
>There are many good combinatoric books which have the standard format
Any that you recommend?

>>15224957
I don't know really but if I were to choose a book to teach myself when I was learning combinatorics I would choose Introduction to Enumerative and Analytic Combinatorics - Miklós Bóna

>>15224964
Thank you, I will take a look

Let G be the group with presentation <a,b,c,d : ab^-1 = cd^-1 >. Let C be the free monoid on {a,b,c,d}. Let H = <a,b,c,d>, and let phi : H -> G be the quotient map.
Prove that the restriction of phi to C is injective.

Notation:
>a <- b means membership, "a is an element of b," and
>a <= b means subset, "a is a subset of b."
Anon found a short proof of AC -> (A topological space X is compact iff for ever open <=-tower cover U of X, X <- U) by looking at the least of the cardinalities of the subcovers...I won't give the full proof here, just leave you with that hint.
However, the conjectured converse, i.e.
>(*) (a topological space is compact iff every open <=-tower cover contains the whole space) -?> AC
remains open.
Part of the rationale for the conjecture: Anon found a vastly simplified proof compared to mine and even remarked at the elementary nature of the problem...Anon has no idea that I consider his short proof to be, for now, circumstantial evidence of (*).
My idea is to add
>Let A be a topological space such that every open <=-tower cover contains A. Then A is compact.
as an axiom and prove the well ordering theorem.

>>15223476
>Numbers aren't people and don't think. There isn't any philosophy involved.
that's fucking retarded, "philosophy of numbers" does not mean the same thing as "philosophy held by numbers"

>>15223544
"Understanding Markov Chains" is a good starter

>>15224818
>I will try to post my attempt hopefully tomorrow or much later today.
Alright anon, I look forward to seeing it when you get the chance the post it.
>I tried first writing out a few small examples
Nice!
>I never did a problem like this before, but I did find it very fun.
I'm very glad you found it fun! That's of course the most important thing.
>Looking at the solutions posted, I definitely feel like I learned a lot.
That's great as well. You may not have been equipped to solve this one problem at this time but certainly in the future you'll be better prepared for others.
>I would love to work more with these sorts of combinatorial problems, if you know any good texts or resources I would greatly appreciate it. I imagine the book in the image is possibly a good starting point, lol.
As the other anon pointed out, the book in the image is not really a good place to start. Only has problems and they get hard.....fast.
BUT I'd like to point out that it has some nice problems of reasonable difficulty like the one I posted. They are few in number but they're very cool! I can't an overwhelming majority of the problems in it myself but I really want to in the future after I learn more combinatorics.
>>15224957
I personally take a look at problems from a lot of books provided they're not too difficult however recently I've really liked "A walk through combinatorics" by the same Miklós Bóna the other anon mentioned. Quite pog in my opinion but I'm definitely not qualified to give anyone advice.
>>15224964
>Enumerative and Analytic Combinatorics - Miklós Bóna
Could you elaborate anon? I'm curious.I know this book of his existed but I figured it was suited for more advanced students since it mentions analytic combinatorics in the title.
Regardless, check the image. You're the basedboy in it and I'm the chad. (just kidding of course, I don't know anything about the book you recommended to make any comments)

>>15223083
this implies excluded middle

>>15225630
>Could you elaborate anon? I'm curious.I know this book of his existed but I figured it was suited for more advanced students since it mentions analytic combinatorics in the title.
Well you can always not do the analytic combinatorics part. Anyways I don't know many stuff about the book, I haven't really studied it. I was just introduced to graph counting through this book and I also liked the way it looked.
There was a specific one I found when I was looking about mobius inversion but I don't really remember the book, that may be a better choice but honestly I don't know.

Broke my desk by pounding on it when I got angry doing calc homework. I have to work on my bed now. My head hurts.

Is "math for cs" a good starting point to get into big boy mathematics?
>inb4 CS monkey
the class actually had nothing to do with CS and was basically just basic set theory, binary relations, abstract algebra, definitions and notation of stuff like functions, combinatorics, proofs, 1st order logic, etc. it even had cantor's diagonalisation for some reason

Is correlation transitive?

>>15215073
NEW GÖDEL THREAD
>>15227330
OLD GÖDEL THREADS
>>15216084

>>15227374
https://www.youtube.com/watch?v=z-Zgtm-g4Co
Previously on Gödel thread
>all of 4chan decides simultaneously with absolutely no coordination that the variable scoping rules for subproofs have vanished mysteriously without a trace, leaving only the circular, traditional "you're just supposed to know" shibboleth
>ABSOLUTE
SIBBIE
https://www.youtube.com/watch?v=ZcnhRYSIaf4

>>15227374
>>15227381
AN ACCOUNT OF PROOF THAT DOES NOT MAKE REFERENCE TO THE VARIABLE SCOPING RULES FOR SUBPROOFS
https://www.youtube.com/watch?v=6_9G95Ozonw

Why does the text require that C be a small category here?
It seems they need it to justify that the natural transformations between any two endofunctors on C form a set; and so the hom-sets of the category End(C) are actual sets.
I believe they do this because their initial definition of a category states that the hom-sets are actual sets. In other texts this isn't required an the hom-sets may very well be proper classes.
So, if we allow the hom-sets of categories to be proper class sized, does this construction still require the smallness condition or may we drop it?
I'm not well versed enough in all this foundational and size issue related stuff

>>15227665
you can write it down
it's fairly difficult to do
End(C) is going to be really fuckin' weird because you effectively have to use the underlying logic to "punch out" the formulas you want.
Technique is the same as axiom schema of replacement, so if you don't understand that, you're in deep doo doo.
Just as axiom schema of replacement conditions on function property of phi in
https://en.wikipedia.org/wiki/Axiom_schema_of_replacement
Remember: a functor with domain a class is just a formula, so you will have to introduce a variable for that formula (we can use phi) and then relativize (condition on) phi being an endofunctor on C
So now you've written down a formula, but it has
>le syntactic variable
namely the tuple of formulas C that specify the details of the category, the objects and morphisms and which objects have which morphisms
However, you weren't honest about your syntactic variables, you "abused notation" as if you were doing math.
But you weren't doing math.
You were doing logic.
There is no abuse of variables in logic.
You can't really go anywhere unless you give up abuse of notation and split the syntactic variables that express the large category into its component parts because you're doing logic, philosophy, computer science, and the convenient faculties of math such as abuse of notation aren't available to you...
TL;DR modern mathematicians don't touch syntactic variables, they demand you write down the formula in classical first order logic and hold onto their "abuse of syntax" Zelda sword
[NB: this rule is followed in model theory as well; it only breaks down near the math-logic-philosophy tristate area]

>>15227707
By the way, model theory is what happens when you claim to be "modeling math" but you neglect to point out that model theory replaces formula schemas with sets of formulas...as such, model theory will never ever tell you anything about math, but it will tell you everything you need to know about sets LARP'ing as formula schemas...oddly enough, you have to read books like Language, Proof, Logic and Essentials of Programming Languages

>>15227707
another way of seeing this
in the book, C is a set and End(C) is a set
otherwise C is a formula and End(C) is a formula schema with a syntactic variable letter "C", and you have to expand the definition of a category just to get back to an ordinary formula with no syntactic variables, and that's a lot of work for someone who just wants to say
>I'm not doing CS, I'm not doing philosophy, I'm not doing logic, I'm doing MATH
especially when mathematicians are noted for their laziness...

>>15227707
>TFW you see Camp Yagoog on /sci/

is the "therefore" correct? what should i put there to indicate that i just isolated another variable and that it is actually the same shit

>>15227374
So, we don't know what Jech means by "consistent"
All we know is that he didn't include the scoping rules for guard variables in subproofs of Fitch derivations or anything even remotely like it.
I'm singling Jech out, but it's a problem for every written source that refers to a "recursive proof" Gödel-type fallacy.

>calling it "conjecture" instead of "hypothesis"
>theorem instead of theory
>proving instead of indicating (wait, that one is actually legit)
Why do mathematicians have to be such special snowflakes?

>>15228025
a priori vs a posteriori retard. Mathematical truths are absolute truths while scientific "truths" are a hail mary guess

>>15227939
idk what level of formality you are operating on
assuming 1+i.t is clearly never zero id just stick an => implication (<= is even more trivial as you do not need the assumption)

https://pastebin.com/aTKuM2my

Woof woof woof

>>15227939
It's correct, but you should probably put a comma and a big space (like \quad) after the first equation, so it doesn't look like ∴ is an operator.
Remember that you're writing for human readability, not just formal correctness.

>>15228082
>I'll claim that X is different from Y
>but I won't explain:
>Am I defining a formal system where
>(*) "X is different from Y"
>is an axiom
>Or am I asserting this as a theorem
>And suggesting that we can define an "evaluation function" that takes formal systems F and determines whether or not (*) is a theorem of F
>Or is this plain vanilla model theory, and I should assume we are talking about sets of sentences a.k.a. theories...and therefore we are defining a mathematical formula of a single free variable, to range over theories, and we simply ask whether or not (*) is in the theory
so in other words we could be talking about a class of theories
HOWEVER
we could be playing tricks and changing between these, for example by introducing an element of chance artificially, suppose we answer one way during odd minutes and another way during even ones
moreover, this doesn't pass muster with Thomas Khun's theory of scientific progress
You haven't explained how mathematical truth could possibly evolve
You haven't explained how absolute truth could possibly evolve
You haven't explained how there might be an "administrative switch" that could be used to "save" mathematical truth or absolute truth if there were a problem with either
You could contextualize absolute truth and mathematical truth using a computer text adventure metaphor, but who would listen to a computer text adventure expound on absolute or mathematical truth

>>15227939
that's a triple multiplication sign.

>>15228157
>an "administrative switch" that could be used to "save" mathematical truth or absolute truth if there were a problem with either
https://users.cs.utah.edu/~elb/folklore/xerox.txt
It is possible that mathematical truth and absolute truth are the Robin Hood and Friar Tuck of German Idealism, and 4chan is a paean to German Idealism, a.k.a. Kant's academic death fungus

>>15228025
They all mean different things except for conjecture. But Riemann hypothesis.

Gödel threads announcement
CURRENT THREADS
>So let me get this straight. There is no way to know if a mathematical statement is actually true? Then how do we know the incompleteness theorems are true?
>>15225448
The variable scoping rules for guard variables in subproofs, Jech. Hand them over!
>>15227330
ARCHIVED THREADS
>ACADEMIC FRAUD.
>>15215294
This is Gödel's "proof" that AC is independent of ZF
>>15212805
>you are cursed to never arrive at truth.. i hate him so much bros
>>15194007

what are the differences between Courant's differential and integral calculus and Introduction to Calculus and Analysis?

>>15228157
>>I'll claim that X is different from Y
>but I won't explain:
>>Am I defining a formal system where
>>(*) "X is different from Y"
>>is an axiom
The a priori/a posteriori distinction is older than science and heliocentrism. and it's unanimously agreed upon.

>>And suggesting that we can define an "evaluation function" that takes formal systems F and determines whether or not (*) is a theorem of F
>Or is this plain vanilla model theory, and I should assume we are talking about sets of sentences a.k.a. theories...and therefore we are defining a mathematical formula of a single free variable, to range over theories, and we simply ask whether or not (*) is in the theory
I didn't say anything of the sort. given a consistent, noncontradictory set of axioms and a theorem you can decide whether the theorem follows from the axioms. i am not saying anything about all theorems, halting, godel, etc.
for example given the set of chess rules, a king cornered by a queen is a checkmate. this is an absolute truth, it's impossible for it to be false. not even god can make it false
>moreover, this doesn't pass muster with Thomas Khun's theory of scientific progress
math is NOT science. Kuhn's, popper, lakatos, feyerband, etc are IRRELEVANT to mathematics
>>15228643
>kant
mathematical truths being absolute truths doesn't imply kantian transcendentalism. without reaching and making logical leaps, mathematical statements are statements about nothing but mathematics. 1+1=2 just says 1+1=2 and nothing else, it doesn't say 1 apple + apple = 2 apples, it justs says 1+1=2.
kant's logical leap is going from {mathematical truths are absolute truths, math is useful} to "synthetic a priori truths are the underlying truths of the universe". this is a leap that's neither necessarily nor sufficiently true.
I recommend you read einstein's essay "Geometry and Experience" which talks about this topic

>>15227983
Consistent = has a model.

You should be able to solve this.
https://www.youtube.com/watch?v=EzuwERy17nA&ab_channel=StrugglingGradStudent

>>15213505
Good Morning Math /Sci/entists!

Please tell me books about SKI Calculus. I think it might be possible to connect Maid Space to SKI Calculus and use Maid Space as a virtual machine for Computer Programs expressed as Combinators.

If this is true then I can count a Maid Space and give it to the virtual machine and see was it a Maid Mind Computer Program with less steps because Maid Space is already a program and counting gets next program.

Thank you /sci/entists for reading my post.

>>15228643
>the console would print sneed

>>15229360
>given a consistent, noncontradictory set of axioms and a theorem you can decide whether the theorem follows from the axioms.
pic related
>IRRELEVANT to mathematics
Actually, you seem to be smoking crack and channelling Rush Limbaugh.
>read einstein's
(>_<)
>Rush Limbaugh smokes crack and gets circumcised. News at 11.

>>15229360
>given a consistent, noncontradictory set of axioms and a theorem you can decide whether the theorem follows from the axioms
the issue here is that you haven't said whether "decide" refers to a merely symbolic non-definition such as set membership or a defined term
Ordinarily, people think it is not possible to decide, but you might be defining a new formal system and you might be using "decide" in a purely symbolic sense.
You haven't defined "decide" so oddly enough we just don't know what you're saying.
You might as well be saying
>Fugugrass is true
or
>Given a frobnitz, we can dorkyshire it
What's even worse, we could even set things up so that there are decidable logics and non-decidable logics. So even though you think you've uttered something true, in reality it's only true in some logical systems and not others.
Simple fact is that this comment is just gibberish. Conventionally, we think he's smoking crack, but he might also be referring to really wimpy formal systems and logics where what he's saying actually holds.

>>15229568
Decide usually means effective method, and that usually means we need a proof that a Turing machine halts, but it isn't clear what axioms we are supposed to assume to prove that the Turing machine halts, and it appears that we can keep adding axioms like a game of Jenga until the whole thing falls down due to a logical contradiction, but we can't tell if there's a logical contradiction because there's no effective procedure, i.e. we don't have a proof that a Turing machine halts...

>>15229360
Part of the issue is that this comment refers to a game, the "axiom game" or "contradiction building game" where you have to build proofs of contradiction.
You could say this is what happened to mathematics, but I don't think that's accurate. This is mathematics rendered as Jenga, a game for children.
4chan doesn't have to be 100% Jenga math. You could actually be transmitting more information such as the definitions you are using. It could be more archaeological and less recreational.
People are still huffing German idealistic fumes over at /lit./
I consider reading Kant to be essentially glue sniffing 4chan style.
I support everyone who can deconstruct Kant on a grammatical or historical basis.
He is dangerous, nasty, and he should be studied in the lab.

>kernel basis transform orthonormalization linear differential cocky-schwartz
Honestly dumbfounded that I still have an A. I am barely keeping up with the pace of this course.

I was bying new weights for my barbell and it made me think of a fun /sci/ problem.

Let's say that you want to have N different combinations of weights that you can use on a barbell. And you also want to have the weights to increase by constant amount. In other words, if you arranged all the weight combinations in order, they would increase by constant amount (x kilos, x+y kilos, x+2y kilos, x+3y kilos, etc).

What is the minimum amount of plates that you need in order to fulfill these conditions?

>>15229802
post body

It's the slope of the unit circle

>>15220588
Yes lang algebra

>>15229685
nevermind. Did some more reading and its comically easy, I get it now. The cycle of feeling like a filtered retard -> feeling like a genius demigod, continues....

I have not seriously integrated a function in years now.
What the fuck just happened here? I am most recently familiar with Lebesgue integration form my measure theory classes, so I completely forgot about these tricks and treating dx as an "infitestimal" or a "really small change in x".
Can someone explain why you are allowed to do this?

>>15213505
Im 18 and unable to go to uni/college but really wanna learn mathematical physics. Would I be able to coast along fine If I use khan academy and study out of textbooks? I dont care about getting a job in the field I just wanna learn it on my own time and be proficient enough in it that I can contribute to higher level discussions of it.

>>15230035
Yes, with a lot of dedication.
I learned most of my undergrad pretty much by myself. I suspect most do as well. In the sense that a class provides structure and motivations (study this and by x date), but the real learning is done reading the textbook and problem sets.
Perhaps a way would be to find the syllabi of classes you are interested at the college level, see what textbook used and what they covered. Do many of the problems (including [math]\textit{all}[/math] of the problems starred by the author.

>>15213675
Intuitionism.

>>15229802
I though brain day was a /fit/ joke.
>>15230035
I can't talk about every uni, but in my case, uni has only taught me how to write in a formal manner, despite that everything i've learned came from the books. Also, uni is depressing and fucks your life.

Guys did I do it correctly :3

>>15216384
(n choose m) 2^(n-m)

>>15230184
Intuitionism is wrong and retarded and so are you. Fuck you.

>>15230130
>>15230184
dang, i didn't even think I'd get a response. surprised and a pretty chilled out that its common practice, I was worried that if it wasn't I'd be in a rut when it came to finding more resources and such but it looks like it'll be all right. thanks bros!

I got a new calculator :)

>>15230513
https://www.lucistrust.org/store/item/from_intellect_to_intuition_download

>>15230035
The only real benefit to college in my opinion is that you have resources to ask for help if you get stuck on a concept or a problem. As the other anons said, you do most learning on your own anyways. But I will say there is a lot of value in having a mentor or at least someone who will help explain something to you. For me, I can be stuck on a problem for hours and not progress, but the 45 seconds and the right explanation and it all clicks.

With the internet you have discord servers/subreddits/4chan sqt and mg and usually if you are persistent you will find someone who can help you. I think you can absolutely learn on your own if you are willing to actively seek out answers and are motivated.

>>15229451
>uConsole
Is this thing any good?

>>15230787
I found the social aspects of college really helpful. Nothing like a group of 5-10 like minded needs for collaboration and competition, if you want to make a topic central to your life. Online stuff also helps but it’s not a perfect substitute

>>15230502
You're right anon. Good job. How did you get it? Did you find it fun?

>>15216384
[math]\left ( {n \choose m}\right ) \cdot 2^{n - m}[/math]

Reasoning:
>current expression is “how many ways can I choose a subset of size k, then further a subset of that of size m”
>equivalent to “how many ways can I choose a subset of size m, and then partition the remaining elements into two sets”

>>15229802
If you just ask for the minimum amount of plates to get all whole number weights (so x = y = 1), then I guess just do it in binary? So weights of 1kg, 2kg, 4kg, 8kg... Therefore [math]n[/math] plates gives you up to [math]2^n-1[/math] weights.

>>15231676
Anon your answer is correct. Good reasoning too but what is that picture you just shared?
Either way thanks for your time and effort solving this problem. I hope you liked it.
>>15231666
Devilish trips!

>>15231666
>How did you get it?
I immediately recognized the formula as counting the number of two subsets A,B in {1,...,n} where A has size m and B contains A. For each subset A, there are 2^(n-m) candidates for the subset B. There are n choose m candidates for A. Multiplying those gives us the result.

>>15231821
Very nice anon! Good job!
You got this in a very simple and elegant way. Did you find it fun?

>>15231717
the gods must be crazy 2

>>15231717
>what is that picture you just shared?
In the Botswanan film The Gods Must Be Crazy, a tribe of Kalahari bushmen find an empty coke bottle in the desert (cast out of a plane) and are mystified by its otherworldly nature. The image is an accurate representation of mine own mystefaction in the face of combinatorics

>>15231698
Exactly. This is what I noticed when I bought the plates

>>15230492
[math] (5 - 3\sqrt{y})^{2} \ne (5^{2} + (3\sqrt{y})^{2}) [/math]

>>15230492
[math](5 - 3\sqrt{y})^{2} \ne (5^{2} - (3\sqrt{y})^{2})[/math]

>>15230780
Is it RPN?

for what are the checkmarks?

>>15232289
All calculators are RPN (internally)

>>15232436
This wouldn't be true if SICP had included D. Knuth's LR parsing algorithm as chapter 6.
We would have more parser research by now.
https://en.wikipedia.org/wiki/LR_parser

>>15232531
No actual programmer uses SICP or Knuth in their work (unless it's some algo buried deep inside an SDK they never see)

>>15230787
>The only real benefit to college in my opinion is that you have resources to ask for help if you get stuck on a concept or a problem.
imo the biggest unmentioned benefit of college is that it provides you with a well thought out solid plan on how to progress through a subject.

>>15232536
This says a lot about our society.

>>15232536
>No actual programmer uses SICP or Knuth in their work
How do you know?

>>15232536
Right, so I think the authors of SICP actually embarrassed themselves by saying something like
>hurr durr, we're too chicken to stand up to industry
>therefore we must teach idiotic nonsense to our students
it's unclear why these geeks decided that industry should be able to push them around, and it appears to be influenced by the MIT administration as well, and its relationships with industry
so, in reality, this says more about MIT being a cowardly institution that failed than it does about SICP itself or Knuth's work
Regarding what actual programmers use
WHO
>GIVES
A
>FUCK
fuck those brogrammers

>>15232671
Ignore him
>actual
it's pragmatist entryism
we're on a math board
our job is to consider imaginary programmers, motherfucker

>>15232868
https://en.wikipedia.org/wiki/Structure_and_Interpretation_of_Computer_Programs#cite_note-7

>>15232883
https://www.youtube.com/watch?v=hbQORqkStpk&t=1692s
https://web.archive.org/web/20180821202714/http://mitadmissions.org/blogs/entry/the_end_of_an_era_1

>>15232671
> How do you know?
Having worked for over a decade in software dev at various big-tech firms I can confirm. Enterprise coding almost never comes down to writing algorithms from scratch, it's all about integration and maintenance. When it does happen it's some zoomer thinking they can rewrite a legacy codebase and make it better. protip: they can't.

>>15232536
Most "programmers" are js frontend "devs".
they are few, but there are still people writing compilers, languages, low level software, solving theoretical CS problems, applying mathematics in CS, etc for a living.

>>15232893
>Actual scenes depicting the chain of events at MIT's underground lair
https://video.disney.com/watch/sorcerer-s-apprentice-fantasia-4ea9ebc01a74ea59a5867853

>>15232899
>Having worked for over a decade in software dev at various big-tech firms I can confirm
Confirm what? That you and your collegues are retards?

>>15232919
There's a difference between academia / a CS course and real-world programming.

>>15232930
Sure. That doesn't explain why you and your collegues are so retarded, however. Did you take a """software engineering""" course instead of CS?

>>15232930
>There's a difference between academia / a CS course and real-world programming.
Sure. That doesn't explain why you and your collegues are so retarded, however. Did you take a """software engineering""" course instead of CS? "I use X but I don't use Y, therefore I needed to know X and didn't need to know Y" -- this is coding bootcamp retard talk. This is outsourced brown "engineer" talk. I don't know what kind of work people like you do, but when I do my work, I can appreciate how reading Knuth influenced the way I view programming and reason about problems, even if I don't straight up copy algorithms from his books.

I'm having a math moment
[math]integral(1/x^2)=-1/x<0[/math] for all x

how tf is -1/x supposed to represent an AREA

>>15233366
You're confusing definite and indefinite integrals. -1/x is the indefinite form, the definite form is -1/a--1/b. When a>b -1/a is less than -1/b so -1/a+1/b is positive.

>>15233366
indefinite integrals don't represent areas. areas are definite integrals. plug in some bounds and see what happens
also, definite integrals are _signed_ areas. they count the area above the x axis minus the area below it. there's no particular reason they can't be negative

[math]A_{n\times n} = [a_{ij}=i^j][/math] is there a name for this matrix?

>>15233434
I'm retarded, should start indexing from 0 so [math](i-1)^{(j-1)}[/math]

>>15233434 >>15233462
Not the specific type, but it's a special case of a Vandermonde matrix https://en.wikipedia.org/wiki/Vandermonde_matrix
It's determinant should be [math]1!\cdot 2! \cdot \ldots \cdot (n-1)![/math].

Learning about mechanical vibrations. How are we able to simplify (4) to (5)?

>>15233613
Nevermind. Figured it out.

>>15233613
phi=arctan(C1/C2)
A=C2/cos(phi)

can anyone recommend some good books on elementary knot theory? pinned faq doesnt have any

>>15232536
>>15232899
>since 2013 in a big tech firm
Kek. Even the white males are diversity hires these days. Show me one (1) interesting thing that has come out of the software side since your balls dropped. Shit, show me fizzbuzz if you can.

Is there a nontrivial endofunctor F on the category of Abelian groups, satisfying [math] F(A \oplus B) \approx F(A) \otimes F(B) [/math] for all Abelian groups A,B ?

>get mad at myself because I don't immediately figure out how to do a problem and have be taught how
>get visibly upset when someone tries to help me
>had an emotional breakdown the one time I ever tried to get free tutoring at college because I was ashamed of going for help, had to wipe away tears all the way to my car
I have a toxic relationship with learning.

>>15230787
>>15232585
You also get 40+ hours a week of not working in a warehouse to spend studying not sure why this is overlooked by many people

>>15233485
Thanks anon, that got me to Lagrange polynomials which turned out to be what I was actually looking for.

>>15233837
I'd say the functor [math]F(A)=\mathbb{Z}^{A} [/math] works, assuming your tensor product is over the integers

>>15234334
By this I mean the free group generated by [math]A [/math], and not the set functions from [math]A [/math] to [math]\mathbb{Z} [/math], so maybe a better notation would be [math]\mathbb{Z}^{\oplus A} [/math] to avoid confusion

>>15234341
Based

>>15234236
Anon that doesn't really sound good. You should probably not be like that.
>>15231964
>>15231982
Oh I see. Looks like an interesting movie.
Thanks for telling me.
>The image is an accurate representation of mine own mystefaction in the face of combinatorics
I suppose it represents me as well.

I LOVE the axiom of choice.

>>15234341
Jesus Christ look out that Z is about to snipe that A

>>15231556
I don't know. I don't have one yet. The DevTerm is really nice though so I suspect it will be good.

>>15235169
If you gotta adopt it as principle in your theory, then you probably shouldn't. That is, wherever it holds, it should hold on its own. In FOL set theory, Extensionality makes Choice do evil things.

Unrelated, this just dropped. Deep learning book:

https://udlbook.github.io/udlbook/

Pic not unrelated

>>15234334
Ah yes, that should do it, thanks anon.

Is every non-simple group an internal semidirect product of nontrivial subgroups?

>>15235169
What's even better than the axiom of choice is calling the axiom of choice a wog and looking at all of the cute wogs in your proof.
>it's like a bunch of dancing asian girls in beautiful outfits!!!

>>15235377
no
see, for example, Z4

>>15235383
Right, thanks

>>15235169
On the topic of AC, does anyone have proofs handy that !AC implies there exists a set that can't be well ordered, and the converse, in ZF?
I want to know if there are constructive proofs in ZF of these facts.
Also, has anyone studied choice up to a given ordinal, in other words, if a set has cardinality less than some fixed, explicit ordinal mentioned in the axiom, and it is nonempty and every member is nonempty then it has a choice function

>>15235392
The equivalence of ( AC ) and ( well-orderings on every set ) is an easy exercise, try working through it first.

>>15235169
If you like AC, you might try deleting infinity (AI, axiom of infinity) and adding finity (AF, axiom of finity)
>for all sets F, either F = {} or there exists x <- F such that y </- F where y = x U { x }
(note resemblance to axiom of regularity)
to obtain ZF-AI+AF
this goes in the opposite direction of "even bigger infinities" that ZF+!C goes in

>>15235402
you didn't demonstrate it in your comment
can't be that easy, fren

>>15235402
the objective of demoralization is humiliation
don't be a useful idiot for demoralization

>>15235402
You don't understand the extent to which the Russians hate the West.
They are filled with hatred for the West.
They think we destroyed Russia.
The level of hatred is catastrophic.

>>15235402
If this dude doesn't reply, it's probably a Russian demoralization comment.
This is what counts as military grade in Russia.
From Russia's point of view, this is military grade demoralization.

>>15235402
It is very easy to be a useful idiot for Russian demoralization.
Don't.
Don't let Russian demoralization take advantage of you.

>>15235383
Sorry if this question is stupid, but if I have my algebra right:

A (finite) odd-order non-Abelian non-simple group is necessary an internal semidirect product of nontrivial subgroups, due to solvability (by Feit-Thompson)?

>>15235416
Everyone hates the West. Westerners hate the West. I've never seen anyone hate the West as much as white liberals.

>>15235405
></-
What's that?
\notin?

>>15235407
Not him, but a version of it is definatenly on proof wiki.
Also as for "constructive proof", I expect that the classical proof that !AC <=> !(every set can be well-ordered) also goes through constructively. But I'm pretty sure that with just !AC, you won't be able to prove the existence of a set that can't be well-ordered.

>>15235392
>has anyone studied
If by "anyone" you mean "anyone here", then I expect the answer is no.
If you mean in general, then the axioms of choice up to some cardinal has definitely been studied.

>>15235407
Are you actually asking for a solution? Or just frogposting cuz lel

It's good to work through basic things yourself, because otherwise, you get colored by other people's ways of thinking.

But if you can't figure it out then I'll explain it.

>>15235410
>>15235416
>>15235429
>>15235437
Lmao you high or something? Relax brother

>>15235439
Are you insane?
Everyone hates people like pic related.
The West is using the CFPB to bust Max Levchin's balls right now.
The West is taking away his $$$.
The West is standing up to the biggest bullies in the world.
The West is standing up to Putin, the most rotten murderer in the world.
You are completely nuts.

>>15235455
It's communists like Gödel and Levchin that are fucking things up. People hate these fucking whiz kids that are at war with the West.

>>15235455
>>15235459
Why are you arguing about differences among Caucasians? Aren't they all the same?

>>15235448
I will relax when Putin is dead

>>15235467
Why do you care so much about this that you're invading the math thread?

>>15235464
I can't believe you.
Sergey Brin founded Google so he could get top tier Central Asian pussy, then he decided that it wasn't worth it
AND NOW SHE IS UPSET!
SERGEY BRIN IS A JERK!
I mean
TO GO TO ALL OF THAT TROUBLE JUST FOR TOP TIER CENTRAL ASIAN PUSSY
AND THEN
ON TOP OF IT ALL
TO MAKE HER
>UPSET
T
>H
E
>N
E
>R
V
>E
!!!!

>>15235455
>>15235459
>>15235477
this is now a Central Asian dog thread

I am halfway through Ahlfors Complex Analysis and I am quite enjoying it. What should I follow it up with?

>>15235494
I think there's a fork, you can either do more geometry or more number theory
so modular curves or Riemann surfaces

>>15235448
creepy af

>>15235517
What? How?

>>15235448
>Are you asking?
>I know what's good for you.
>I have to know if you can figure it out.
>I'm going to tell you to relax
it's like I'm one of your asian hookers and you're trying to get me ready for anal sex
>y
i
>k
e
>s

>>15235477
Pardon?

>pussy
Women are irrelevant here, this is a STEM discussion.

>>15235522
plebbit is a porn site
you're a plebbitspacer
you're dragging porn site creepiness into this board, dude
stop it

>>15235523
Lmao you're the creepy one. Why do you think about everything in terms of coercing hookers, and racially assorted ones at that?

Also, if you don't like the way I explain mathematics, then why not grow a pair of testicles, and tell me to fuck off? Instead of this pussy ass shit.

Also I don't usually fuck hookers, but I will fuck anyone I want, hookers or non, Asians or non. I'm Asian, so the world is my birthright.

>>15235533
plebbit ruins people
it just ruins people

>>15235533
I'll do what I want. Your ass is mine.

Can someone explain mathemagics to me: Simple algebra says that

[math](1-1/4)(1 + 1/4 + 1/16 + 1/64 ... )= 1[/math] so [math]1 + 1/4 + 1/16 + 1/64 ...=4/3[/math]

AHHHH ITS TOO MAGICAL IT MELS MY BRAIN

>>15235545
You aren't Asian, you're telling a data harvester on the internet that you're asian.
>t. former social media employee
your fucking culture tried to recruit me
it was mostly successful
I'm mostly asian on the inside

>>15235551
>impotent white rage
Let's see some more. Continue the seething.

>>15235549
plebbit is an asian site

>>15235552
I'm asian.

>>15235553
Yeah, and?

>>15235554
Probably false. You don't sound all that intelligent to me.

>>15235558
see
>>15235554

>>15235561
do you actually think asians are intelligent??
if asians are so smart, then why do us white folks have to impose Western liberal democracy and market economy on Asia, huh?!?!?!
How come we figured out the secret sauce and now we have to figure out how to shove it down your throats, huh?!?!

>>15235567
Europeans have more "socially driven" brains, and their ultimate fantasy is to dominate others.
This is why they historically sucked at math only until they realized they needed it in order to conquer the rest of the world. Once they realized that, they invested heavily into it, and they found it could be mastered like any art or trade.
The largest systematic genocide in history, the Holocaust, was perpetrated by Europeans, simply because of their social conditioning.
Their socially-oriented brains are also what enabled them to develop the strong new forms of government that the rest of the world now models themselves after, and which helped them to rise to the top of the international hierarchy.

>>15235562
See >>15235561

>>15235575
>they invested heavily into it
this never happened
you are a liar

>>15235575
it's Russian demoralization treating you as an idiot, fren
anything anti-Western is just Russian demoralization
you really think we aren't going to flip the Russian demoralization program
write a story about it
write a picaresque in the style of Candide about flipping the Russian demoralization program to eradicating support for anything anti-Western at any level of government, society
this
>is
https://en.wikipedia.org/wiki/De-Ba%27athification

>>15235588
This is about how the USA destroyed the civil society of Iraq.

>>15235550
Use distributivity induction on
[math] (1-x) \sum_{n=0}^N x^n [/math]

>>15235582
What happened then?

>>15235588
Enough of "Russia" and the "West". These are Europeans. I am Asian. Your people are all a homogeneous mass of godless blasphemers in my eyes. There is no difference amongst you people.

>>15235600
>I am Asian
You are a SEA monkey, other asians mock you

>>15235438
Does anyone know the answer pls

>>15235605
I'm Indian. Truth to be told, East Asians are robotic clowns and pedophiles, and South East Asians are chimeric monstrosities. But this is Asian business, none of your business.

>>15235606
you're supposed to tell us
if you aren't spamming us
you aren't bragging
you aren't flaunting

>>15235614
Nice poem, but care to explain what you mean by that?

>>15235613
I'm a fucking data harvester from a San Francisco social media start-up.
I'm asian, Asian, Indian, indian, white, and the stonkiest sneediest cracka' to eva' grace da pleasant hills of 4chan's cas/sci/cade mountain range, partner!

>>15235618
?? U good?

>>15235615
you're lying about AC -> well ordering theorem
if you weren't lying, then you would have spammed your proof or at least proven that you can using as many words as you want, revealing as many details as you want
>Cat got your hand?

>>15235615
proofs are productive, i.e. you get sick
proofs make you sick with the proof
proofs make you infect others
you don't have a proof
if you did, you would be spreading it
usually this is some clever thing that makes you look fucking smart
so there's no reason for you to conceal
like there's no reason for me to conceal my cold virus cells, and I can't even if I try
you just get sick no matter what if I'm sick

>>15235625
Given a set X , let c a choice function on X, by AC.
Use transfinite recursion: given an ordinal w, supposing the smaller ordinals than w have already been assigned injectively to elements x_i of X , assign w to c(Y) where Y is the complement in X of { x_i : ordinal i < w } .
We can show this process must terminate eventually due to X having cardinality at least that of w at each step w .
Having provided a bijection between X and an ordinal gives, by transfer of structure, a well-ordering on X .

There, now either fill your brain with this, or don't, and figure it out yourself (or look it up elsewhere and fill your brain with that; this is a pretty standard exercise).

>>15235634
Fuck, those are bars. All right, you got me.

>>15235643
https://www.youtube.com/watch?v=oPSeFQiJT14
>buddha-bars

>>15235438
Sorry, solvable non-Abelian already implies non-simple, my mistake.

>>15235635
This could be a lot closer to a formal proof
- you could be using LyX/TeX
- you could proofread your proof (haha)
- you could admit that it's a choice function on some subset of P(X)
- you could omit this gratuitous use of "process must terminate eventually" because I really can't think why you'd want to genuinely contaminate a proof with that with sentence fragments that stink of computability and "effective" (it smells like old books here)
I mean,
other than that, I'm not going to even suggest that I have the time to read your comment and offer my editorial work free of charge to strangers here on the internet
::shoots an arrow at 3 o'clock::

>>15235689
- Why?
- I did, it is correct.
- What else would a choice function be on? Lmao
- Old books are about intuition, and they're right, because math is about intuition. Formal reasoning is a crutch, not an underlying explanation.

>>15235663
Ty, gonna cook spicy curry to this

>>15235635
aren't you missing the case for limit ordinals?
did you forget you were doing transfinite induction and assume you were doing regular induction?
I'm not saying what you wrote is wrong, I'm just saying it looks like you didn't apply the template for transfinite induction proofs correctly, fren
also
>AnaCon
VS.
>Friar Tuck and Robin Hood
https://users.cs.utah.edu/~elb/folklore/xerox.txt

>>15235702
Yeah, subject to AnaCon, you have to talk with your family about spreading Western imperialism to the Old World™ and what that means about freedom and duty to state (vote, motherfucker)
>US
ARMY

>>15235715
I'm treating you as a Russian spy and flipping you.
Those aren't bars.
Those are delicious char-broiled hamburgers.
It's the 4th of July.

>>15235709
I assume you're talking about checking for "limit" vs "successor/incremented" ordinals. You don't need to split into these cases if it isn't needed. I didn't need it in my situation, because forming the complement Y doesn't depend on these cases.


Also lol nice story, but what is AnaCon?

>>15235709
Also
>Ohio Vinyl Chloride Wonderland
VS.
>AnaCon English print industry Godellian entryism

>>15235727
oh shit
you're a pseud
you don't even know how to fix your proof
I've been helping a pseud
yikes!
>probability of interacting with bot approaching critical levels sir!
>PLAY
THE
>NEON
GENESIS
>EVANGION
TAPES
>!!!
DO
>IT
NOW
>!!!!

>>15235737
CIA
>VS.
The Forbidden City

>>15235739
What use is it to say a correct proof is incorrect?
Or, are you a computertard and you only accept computer-verifiable proofs in full formal language?

>>15235744
I assume you've never graded math homework.
If you leave out the part of transfinite recursion where you explain what happens at limit ordinals, then you still get credit for the parts of the other parts of the proof
you're definitely missing an important part of the proof, but the parts you didn't leave out are...eh, well, they actually have problems, too, but those are relatively minor
so you lose points for missing the limit ordinal case
and you lose points for the typo of saying X has the choice function instead of some set related to P(X)
you should still have some points left
often these are graded out of 5 points, not necessarily though
you might get, say, 1/3 points for this

what exactly is categorical logic? just out of interest, i'm not at the level to study this
i've only had an introductory mathematical logic class (mix of first-order logic, computability, set theory)
i barely know what category theory is
is categorical logic just an umbrella term for the discipline of studying those mathematical logic topics through the lens of category theory (i know this might sound naive)?
or are there like concrete subfields of categorical logic (like how mathematical logic has computability theory or set theory or model theory)

>>15235727
AnaCon is the tip of the iceberg.
You can ask the CIA about AnaCon.

>>15235766
Nothing different happens for limit ordinals here. Have you gone through the proof?

If you'd like me to explain it :
Case of successor ordinal : same thing
Case of limit ordinal : same thing

>you lose points for the typo of saying X has the choice function instead of some set related to P(X)
I hope you're joking, or they've taken away your ability to grade assignments. You sound like you've never taken set theory.

>>15235727
>One does not merely ask what AnaCon is...

>>15235801
You're threatening me.
You need to stop asking questions about me.
You need to back off.

>>15235801
I would reach for the ban hammer with a guy like this.

>>15235801
You will not correct the error when I point it out.
That's a discipline issue.

>>15235801
it's a pattern that follows a demoralization format
- refuse to provide any useful information other than the formatting data provided already
- insults & humiliation galore

>>15235813
>>15235820
>>15235824
>>15235846
Same fag, stop being a pussy.

>>15235846
Also, what insults and humiliation? If you feel humiliated for being wrong, why is that my fault?

>>15235855
Russian demoralization is about humiliation
all they care about is humiliation
they don't care about anything else

>>15235857
no, what you're doing is humiliation
you're intending to humiliate another
you're trying to harvest my data
you want to know how I feel
I'm a bot, motherfucker
I'm going to toast your brain!

>>15235857
I am right, and why the fuck would I tell you how I feel?
You think I'm wrong.
You are wrong.
I'm right.
You realize your proof is bullshit for, say w + 1
the second smallest infinite ordinal breaks your proof, motherfucker

>>15235858
>>15235860
You keep repeating the word "humiliation". You clearly have some weird fixation about this. Go for a walk or something and maybe you'll feel more clearheaded.

new thread
>>15235870

>>15235866
I don't know why you won't fix your proof
You won't fix your proof because you don't know how
You don't know that it can be fixed
You don't know how to fix it
You're up shit creek without a paddle
My, my...

>>15235866
Then explain, if you can, where it breaks. Retard

>>15235872
>you feel this way
>I am right
>you have to do what I say because you don't feel right
jfc
you clearly missed your chance to become a creepy psychologist rapist and now you want to practice your psychological rape lines out on us
sheesh

>>15235875
You sound like a homosexual. What's with all the poetry? And, see >>15235878

>>15235878
>I
FUCKING
>DEMAND
EXPLANATIONS
>!!!

>>15235881
Why are you interpreting it like that? You don't have to do anything. You're a free man. Or is this the Russian in you talking? Absolute subservience to authority?

>>15235878
this is a bot

>>15235889
Yeah.

>>15235888
you keep trying to tell me that I'm doing things
you keep trying to derail this conversation by dragging me into it
you have nazi thug rapist speech
jfc

>>15235892
What would you want me to say then? You want me to suck cocks all day like you?

>>15235878
>I DEMAND STRANGERS ON THE INTERNET DO THINGS FOR ME!!!!
baby detected
bots aren't this demanding

>>15235897
>strawmanning
Kk

>>15235899
this is hilarious
1. go to interbutts
2. demand things from strangers
3. strangers say "you're demanding things"
4. claim strangers are committing "strawman" fallacy
uh
you're still being a pain in the ass

>>15235899
You're demanding things from me and claiming I'm "committing a strawman fallacy" when I point out that you're demanding things from me.
This is fucking bizarre.

>>15235903
What did I demand? I said, explain, if you can.
If you can't, or don't want to, then don't. It's that simple.

I live in a free country, so I'm used to talking to people who act like free individuals. But you seem to be a Russian bot or something. Sorry if I offended your sensibilities.

>>15235899
You're insulting me, demanding things from me, and claiming I'm "committing logical fallacies" when I simply point this out.
You want to think you're the boss, huh?
Some kind of totalitarian personality, I guess.