/sci/ - Science & Math

Reminder that LEM does not exist, mathematically speaking.

>>11059858
Here's hoping this thread is better than the last one.

What are you studying? I'm reviewing differential and Riemannian geometry, will go for harmonic maps in manifolds later.
>>11059882
Not particularly hard.

>>11059858
Dear math faggots, you will never be able to figure the universe out with it. Accept your fate and become my meal.

Sincerely: God LOL

>>11059882
Why would you ""hope"" for that that and then immediately proceed to make it shittier?

>>11059919
>Sincerely: God LOL
You don't exist, LOL.

>>11059919
You are subhuman and you and your enablers unironically deserve to be stung up.

>>11059858
Ahem......Fuck category theory

As a person of certain descent, what's the easiest maths for me? I have tried learning Linear Algebra and Matrixes, but I find them hard to wrap my head around.

>>11059930
>>11059939
LOL PRETEND FOR AS LONG AS YOU CAN
>>11059935
LOL YOUR CUTE IDEOLOGY OF "DESERVE" IS PRECIOUS, KEEP IT PLZKTHX

>>11059941
You should play videogames for living and live off patreon bucks donated to you by the followers you gained responding to donald trumps twitter account

>>11059947
Me and my wife on that photo can't live off video gaming. I need to learn Matrixes or Calculus to get a good job.

>>11059941
why are they not attacking him?

>>11059950
holy fuck this anon crushed it

>>11059950
You should learn ML libraries while not knowing what a likelihood function or gradient descent is.

This knowledge along with your community college degree, severe mental retardation, and insufferable personality should get you a job at google as an AI researcher making $200,000 per year.

>>11059965
Well, I married my wife and I need to support our family with good maths knowledge but it's very hard for me. I have a fine personality but I am of certain descent.

>>11059965

Ehm hello. Are there books you can recommend to help understand math? We're talking pretty basic math compared to this board, but still the hardest course you can pick as an 18 year old. I know i should probably just stick to problem solving, but my motivqtion is a lost cause

>>11059873
It depends on how you interpret logic. Both interpretations can be justified depending on what you're after.
Are you concerned with truth or constructive provability?

>>11059982
Shouldn't true truth be independent of interpretations?

>>11059910
I've been working on this https://arxiv.org/abs/1907.08204.. First step into generalizing the classification of SPTs and SETs that isn't complete abstract nonsense (e.g. a bunch of stable homotopy computations with [math]MTH_n[/math]'s a la Freed-Hopkins) is to understand obstructions to gapped symmetric ground states of defect networks, which generalizes and in fact unifies Lieb-Schultz-Mattis-type theorems in many strongly-correlated systems. Once this is achieved, we can study the bulk-edge equivariant Gysin map in more detail in order to extract hints of a generalized Atiyah-Singer in the many-body context.

>>11059873
If youre a dirty Formalist, that is. But if you are a real mathematician you realize that LEM is real and even though you can describe formal systems without LEM, It is only a formal approximation: that is, you are simply playing around with a string of characters

>>11060043
>you realize that LEM is real
How so?

>>11060043
>Formalist
What do you mean? As opposed to what?

>>11060043
How can something be real if it does not exist mathematically and non-axiomatically?

>>11060062
I conceive of set x, therefore I can either only conceive of x or not conceive of x
>>11060067
Realists, Platonists, Empiricists, Constructivists the list goes on

Wth is LEM?

>>11060074
>Realists, Platonists, Empiricists, Constructivists the list goes on
What makes them superior to Formalists, empirically and rationally speaking?

>>11060073
it exists a priori, and if you 100% deny that, then you also dont 100% deny it.

>>11060074
>I conceive of set x, therefore I can either only conceive of x or not conceive of x
I thought this space wasn't inclusive to absolutely everyone on the IQ spectrum.

>>11060082
Some of them are, some of them arent, read up on them yourself

>>11060084
Does your mind have some sort of special third property? This is what most philosophers talk about when they say the essence of all thought is negations. You either conceive of something, or you dont conceive of it. Its literally that simple.

>>11060083
>it exists a priori
How can it exist a priori when it cannot be shown to exist via mathematical means (you can only do it via axiomatic means)?

>>11060080
Law Exclusion middle
Something can be true or false, no middle solution.

intuitionistic logic, remove idea LEM, existing some topological space between true and false and replace set theory with topos.

>>11060080
law of the excluded middle.
says that for any predicate P, we have [math] P \vee \neg P[/math]. So P is true or not P is true.
What this means is that [math] \neg \neg P \implies P[/math] which is obvious to anyone with a brain but is apparently not justifiable for the morons arguing about it in this thread.
(Hint: All of mathematics hinges on LEM).

>>11060091
>Does your mind have some sort of special third property?
No, that's what mathematically provable double negation of LEM implies, not LEM (which is non-mathematical in essense). I thought this space wasn't inclusive to absolutely everyone on the IQ spectrum.
>>11060095
>no middle solution
That's not LEM, strictly speaking. "LEM" is just a heuristic name for a non-mathematical axiom, what you mention is the double negation of this axiom which is provably true with no philosophical objections. Learn to be higher on the IQ spectrum and learn to spot obvious double negations.

>>11060095
what a horrifically indecipherable post
and is that really what topos theory is? schizo math?

>>11060100
>when you finally understand something in maths
Well, you're a fair distance away from acomplishing that judging by your post, haha.

>>11060102
ok, then what is LEM? if these are just the double negation?

>>11060093
>How can it exist a priori
because it does
>it cannot be shown to exist via mathematical means
it cant, its a fundamental piece of logic used in math and all rational thought though
>>11060102
are you fucking dumb? you cant comprehend what people are saying and all you can do is throw the IQ card
>Well, you're a fair distance away from acomplishing that judging by your post, haha.
but he also potential is, because apparently LEM dosent exist

>>11060107
perhaps it is so natural and intuitive to accept LEM, so much so that it is stated as its own double negation by everyone who deigns to understand it, that we should stop questioning it and move on to bigger and better things?
avatarshitting with le epic meme man isn't coming across as ironic by the way - in fact, based on this, you can conclude that is coming across as very, very sincere. you fucking disgusting piece of shit.

>>11060100
>(Hint: All of mathematics hinges on LEM).
What is the ontological basis for this statement?
>>11060108
LEM is *(by definition)* the non-mathematical (as in not provable mathematically, only axiomatically) axiom that
[math]\forall P : P \vee \neg P[/math]
Its *double negation* is what prevents there being a third possibility, while LEM merely *assumes* that every P is one of these things. You can thank the philosophically illiterates (such as most people in this thread) for this confusing naming scheme.

>>11060114
>because it does
Back this up with some solid ontology or GTFO, as we say.
>>11060116
You should not immediately assume things that are in nature non-mathematical. This level of thinking should be possible for anyone mathematically inclined.

>>11060117
oh fuck he used the word "ontological"
it's this guy, /mg/, it's the one who used to refer people to /lit/

well guess what MOTHERFUCKER!!! DISCUSSION OF FUCKING NONMATHEMATICAL FOUNDATIONS GOES ON FUCKING >>>/lit/ SO FUCK OFF!!!

>>11060087
Can you give me a quick rundown of your opinion since you seem to have such a strong one?

>>11060124
Ontological is a very common word in circles where almost all people lie in the higher range of the IQ spectrum.
LEM is non-mathematical, I agree, but I'm not the one encouraging it. I'm just clearing up the confusion caused by the philosophical illiteracy of most so-called mathematicians here.

>>11060124
>no argument
That's fine, kid. Not everyone can be so intelligent so as to understand basic double negations.

>>11059882
Lad, I'm scared.
Tell me it's gonna be alright.

>>11060128
I dont have a strong opinion, really, Im just pointing out that any system of axioms must, at the end of the day be reducible to LEM. Much in the same way all multi-valued logic is reducible to two vauled logic, and how every formal system about N is incomplete.

>>11060121
>Back this up with some solid ontology or GTFO, as we say.
I have a better idea, how about you prove it is and it isnt.

>>11060140
>how about you prove it is and it isnt.
>any system of axioms must, at the end of the day be reducible to LEM
>"reducible"
What did he mean by this?

>>11060133
ontological is not a fancy word, but the only /mg/ poster who used it consistently was that guy and you've now used it 3 or 4 times in one thread
this tells me that you're either that guy or new. there is no third option.
>>11060136
i don't need an argument, my claim is a non-mathematical axiom

>>11060139
oh it was fine until you decided to post
go back to your fucking stupid question circle jerk

>>11060140
>pepeverymuchamusedlol.jpg
Thanks for outing yourself as a vapid mouthbreather who probably doesn't even understand the distinction between epistemology and ontology. This isn't a discussion for the feeble-minded, so you probably shouldn't join in.
>>11060147
>there is no third option.
According to what?
>i don't need an argument
You are officialy BTFO in this debate then. Next.

>>11060147
>my claim is a non-mathematical axiom
Refer to >>>/lit/.

>>11060157
>second response
i was making jokes you autist, i'm not debating you

>>11060144
Give me any formal system. Anyone and I can give you an equivalent one with LEM. Its really not that hard to understand.

>>11060168
But I was under the impression that I was an illiterate? What would I gain from visiting >>>/lit/?

>>11060169
Sure, it's just a joke, "bro". It's just a joke when you lose a debate due to your utter incompetence and ignorance of basic mathematics. Actually, you might be right. It's a joke. Nobody can legitimately be this stupid.

>>11060171
>equivalent one
What do you mean by that, in an ontological sense?

>>11060144
>>how about you prove it is and it isnt.
If you believe LEM does not exist then you are open to the possibility of it also existing. The fact that you cant comprehend this is insane.

>>11060139
>it's gonna be alright.
Given how the thread has progressed over the past hour, I doubt it.

>>11060095
>Something can be true or false
>no middle solution
>implying these are equivalent statements
lmfao. is the level of logic understanding here really this pathetic? now i understand what my prof meant by mathematicians being fucking garbage at logic.

>>11060179
isomorphism

>>11060177
yes, of course it was a joke. i made it obvious enough i was joking by repeating some of the ridiculous phrases from the thread in context where they weren't totally applicable.
and i'm not your "bro," "dawg."

>>11060186
What do you mean by isomorphism, in an ontological sense? Isn't that about groups? Lol, you don't know what you're talking about - this isn't group theory.

>>11060183
>If you believe LEM does not exist
I don't believe, I KNOW it does not exist.
>you are open to the possibility of it also existing
What does that have to do with anything, you drooling retard? I can comprehend it not existing due to the simple *mathematical* reality that the double negation of LEM is *mathematically* true and on a solid ontological basis. Neither of these statements hold for LEM.

>>11060186
Please learn your words properly before using them. This space does not promote vapid undergrads butting into conversations way out of their league, intellectually speaking.

>>11060196
This space does not promote that? Are you saying that means the space denounces it? I don't think that's what you're saying.

>>11060191
Yeah, "dog', it was totally a joke and you were totally not BTFO in a debate by an individual much smarter than you.

>>11060199
Using the Double Negation of LEM, we see that the space can only EITHER denounce it or promote it. The rest should be pathetically obvious to most people on the IQ spectrum.

>>11060195
>I KNOW it does not exist.
which means it might exist aswell

>>11060206
No, that would be forbidden due to the double negation of LEM being mathematically and ontologically self-evident. Just apply it to your statement and realize that you're not intelligent enough to even take part in this conversation.

>>11060211
does the double negation of LEM not imply LEM itself?

>>11060211
>double negation of LEM being mathematically and ontologically self-evident
explain this

Is is possible to find an elementary function that maps the set of natural numbers onto the set of primes? Could such a function exist? Do we have any idea?

>>11060228
list the primes in order

>>11060216
This is equivalent to LEM itself, so no. It would be an obvious contradiction, because LEM is not valid both mathematically and ontologically.
>>11060224
What is there to explain, your vapid undergrad? It is ontologically and mathematically immediate that there is no predicate which is neither true nor false.

>>11059919
>faggots
Why the homophobia?

>>11060232
>LEM is not valid both mathematically and ontologically
yes it is

Does anyone else find that all "logicians" should be crucified and left to die painfully?

>>11060232
your obsession with calling others undergraduates outs you as a first year graduate student

>>11060239
This mistaken *assumption* (much like LEM itself) demonstrates that you aren't intelligent enough to participate in this discussion.

LEM a spook

>>11060228
define elementary

>>11060242
Truth is the truth. There is not much you can do to deny this when it's obvious to anyone who took (and passed) a basic Ontology 101 course.

Threadly reminder to work with physicists.

>>11060244
prove that is isnt a spook aswell
>>11060243
I think youre just stuck in your shitty formalist head canon

Wait, so you guys are arguing over whether or not to drop the thing that prevents the principle of explosion from getting in the way?
Is the board infested with guys who have confused gender binaries and true/false binaries the same way that conservapedia confused cultural relativism and general relativity a decade ago?

>>11060252
>formalist
What is the ontological groundwork for this claim when I don't identify as formalist? Can you present some actually valid points to back this up? Surely you learned this in Debate 101, right?

>>11060256
Brainlet who doesn't understand the ontological distinction between LEM and its double negation detected. Next.

What's the cardinality of [math] Hom_{Ax}(LEM,LEM) [/math] where [math] Ax [/math] is the category of axioms?

>>11060267
Neither of these terms seem to be well-defined.

>>11060267
>category of axioms
What did he mean by this?

>>11060278
>What did he mean by this?
I'm not a "he".

>>11060250
in the ontology department?

>>11060279
My bad. What do you identify as so I can refer to you correctly?

>>11060270
>seem
?

>>11060282
he identifies as "it"

>>11060279
Actually he is a neutral pronoun

>>11060288
ontologically untrue

>>11060283
"seems" as in "appears to be ontologically indistinguishable from the truth value "True" for all intents and purposes"

>>11060293
>ontologically
This is a meaningless notion.

>>11060282
>What do you identify as so I can refer to you correctly?
She.

>>11060278
it

>>11060282
The only pronoun other than "he", smartass.

Isn't Lem basically saying that there is an Abrahamic God out there who can fully see every truth value of every proposition and he guarantess the binaryness of every proposition, i.e. that every proposition is either true or false?

Isn't Lem basically saying that there is an Abrahamic God out there who can fully see every truth value of every proposition and he guarantess the binaryness of every proposition, i.e. that every proposition is either true or false?

>>11060301
The space of pronouns isn't a binary entity these days.

>>11060301
>only
pronouns include I, we, me, us, you, she, her, he, him, it, they, them, that, which, who, whom, whose, whichever, whomever, whoever, this, these, those, anybody, anyone, anything, each, everybody, either, everyone, everything, neither, nobody, no one, nothing, one, somebody, something, someone, both, few, many, several, all, any, most, none, some, myself, ourselves, yourself, yourselves, himself, herself, itself, themselves, what, my, your, his, her, its, their, your, our, mine, yours, hers, ours, yours, theirs.
Not sure what exactly it is that you mean?

>>11060313
Yes, but under this interpretation LEM is profoundly heretical in that it collapses the Holy Trinity to include as God only either the Father or the Son, leaving out the Holy Spirit. Instead, you should use its double negation, which is canonically valid and merely states that both the Father and the Son are God, nothing more, nothing less.

>>11060313
undergrad here. does this have any weight? i'm a staunch atheist and now i feel bad about using it.

>>11060440
>i'm a staunch atheist
Big Yikes.

>>11060251
>>11055211
Because the picture shows physical tools becoming important in mathematics over the past few decades and vice versa. Examples include Seiberg-Witten monopoles, the KZB equations and string theory. In addition, many mathematical conditions can be translated to "existence" statements in physics (e.g. existence of vortex solutions to HYMH is equivalent to the Deligne stability of the line bundle).
>>11055136
Not quite. The reason that string theory, as inherently a CFT, admits such nice descriptions is that the theory itself has a very structured and well-controlled algebra of quantum operators (viz. Virasoros and affine Lies). This doesn't solve any open questions regarding convergence issues in general QFTs, where the quantum operators form general von Neumann nets over spacetime geometries. In other words, string theory and CFTs in general are very special cases of QFTs where we may leverage the massive conformal symmetry group to explicitly evaluate physical quantities.
From a TQFT perspective, the reason why we can evaluate [math]Z[/math] explicitly for strings and SUSYstrings is because TMFs has the conformal nets of free fermions as geometric realizations (similar to how [math]ku[/math]-theory has Clifford-module bundles as geometric realization). This allows the TQFT with target into the 3-category of vN alg. of boundary conditions to be expressed in terms of topological/geometric invariants such as TMF Euler classes. This, as well as an explicit non-Abelian localization formula for the partition function, is still not proven, but we have seen numerous examples in which this is true. Hence why we suspect that the string theory partition function does indeed allow localization (the so-called "finite dimensional functional integral" in your words).

LEM is obvious, either X is true or not X is true: "either this apple is red or this apple is not red" I don't know what caused you fags to make such a ruckus over it.

>>11060527
can you explain? i'll seriously consider your opinion if you are not an undergrad. i want to devote my life to this so i'd like some experienced views.

Don't you dare call me a "he". I am a pure Categorical being who belongs to no gender category.

>>11060619
>LEM is obvious
?

>>11060632
what? LEM is as obvious as the conjunction rule: if you have "A and B" then you have A and you have B separately. How it isn't obvious to you?

>>11060657
Please refrain from posting in this space if you lie to the lower ends of the IQ spectrum.

>>11060669
good luck proving (an intuitevely obvious fact) that every subset of a finite set is finite without lem, idiot

>>11059910
>What are you studying?
Conditions for a group ring to be semiperfect. I found some Turkish guy's paper or dissertation or whatever on the subject.

>>11060031
I've often wondered what the physicists think of all that Freed-Hopkins stuff.

>>11060746
Link to the paper

>>11060788
http://library.iyte.edu.tr/tezler/master/matematik/T001253.pdf here you go, lassie.

>>11060256
>getting in the way
There's logics that don't have LEM but still have explosion, e.g. intuition logic.
If you drop explosion, you get Minimal logic
which is actually weaker than classical/intuitionist logic.
https://en.wikipedia.org/wiki/Minimal_logic

>>11060619
That's just one example. LEM says that it holds for all proposition.
For one type of interesting proposition, the Mortal Matrix problem shows that it's undecidable, if you're given any two 15x15 matrices A and B, whether they can be multiplied in some way (possibly with repetition, e.g. as AABBABBAAABB), such that they yield the zero matrix. There's provably no algorithm that would correctly work for all matrices, to decide whether it's true that they can be multiplied to zero or not.
https://en.wikipedia.org/wiki/List_of_undecidable_problems#Problems_about_matrices
If you now say that LEM holds, you make the claim about some propositions (those involving some of the matrices where it's not possible). You make a statement that's inaccessible to any human proof system.
But the computationally undecidably variant of proposition is only one point of criticism that relates to it.

E.g. >>11060144 says
>Give me any formal system. Anyone and I can give you an equivalent one with LEM.
But that's not the case. There's axiom systems (say that axioms are "a","b","c") such that if you also adopt "lem", then some particular axiom "d" would make the system inconsistent (i.e. "a","b","c", "d", "lem" is an inconsistent system), while at the same time, the system given by the four axioms "a","b","c", "d" is an interesting theory. That is to say, adopting "lem" means you restrict the range of theories you can work with. E.g.
https://en.wikipedia.org/wiki/Synthetic_differential_geometry

Meanwhile, "lem" doesn't help you prove more, from a classical interpretation.

>>11060105
No, Topos theory just don't necessitate hard compliments, but see
https://ncatlab.org/nlab/show/Boolean+category

>>11059965
faggots seething so hard that the jobs that earn the most aren't necessarily the most rigorous
for how smart mathlets are they can be really dumb

What incantation do need to I pronounce to free myself from the shackles of LEM and truly see math for what it is?

>>11060851
as if who

chemist here

just wanted to thank you all mathfags for loving math and doing great things with it. i for one appreciate math but im certainly not good at it and have been too far removed from it.
i recently read an article on some statistics shit i didnt understand that my coworker was babbling about and i was able to understand it by the thoughtful and intuitive explanation written by some mathautist.

once again, thank you all.

>>11060843
Great post as always.

t. A constructivist that has been observing these threads for quite a while

>>11060843
Straight up batshit. If you can't answer computationally indecidable problema that's on your not having an oracle, not LEM. LEM is above the tower of oracles.

>>11060858
Basic intelligence on the level of a five-year-old should be enough. As you can see, most of the thread lacks even this much.

>>11060626
>can you explain?
The case that no higher force than humanity exists is absurd, not only is there zero evidence for such an absence but logicality it is almost completely incoherent.

In fact studying logic without a belief in such a higher power, which shaped the meta universe of logic in some coherent manner, seems quite insane.

Kind of a blog but dont hate please,

Im a first semester math student and I dont know how to learn math really. I have a final appointment for my ADHD diagnosis in 4 weeks. Apart from that I check many marks for Aspergers too imo (very bad with social stuff as in i dont understand, sensory issues, bad at keeping friends due to neglecting friendships even though i like them, generally feeling like being on a different wavelength than most other people).
During highschool I generally got good grades without doing anything, so I never developed good habits to learn stuff.
That being said, based on my grades in highschool I dont feel I do have a solid foundation in math. Im not very confident.

I do have some stimulants on hand which are very helpful, but I dont know how to make use of that time. I can sit down for hours, but at the end of the day I feel I havent learned anything new. I have no structure on how to approach this. Ideally I want to follow some sort of algorithm that I can repeat for every new concept I have to learn.

In Germany (probably every other decent math program too) you do Linear algebra and Analysis in the first semester.
We are provided with a script, book recommendations and weekly practice problems you have to submit.
I go to the lectures and copy whatever the professor writes on the board. Then at home I go trough them and try to do the problems from the weekly sheet. This went semi well in the first week. While my understanding of these subjects is greater than before the first day of university, I doubt I will get a good grade at the end of the semester if I get better at the current speed. I also didnt manage to complete all problems. I feel I sometimes get so lost in the problems that I spend 45 minutes without really progressing and then only going further with help from an online source. Then even after "completing" the problem I dont feel I really grasped it.

cont

Our Analysis course is structured like this: Proof by induction -> axiomatic characterization of real numbers -> sequences, limits, Supremum, Infimum -> ...
Linear Algebra: R^n -> vectors -> linear equations -> ....

Pretty basic like most other universitys, everything with proofs and so on.

Idk I feel scared and my confidence is really low. Im anxious and I dont know how to approach this with a clear head. I refuse to give up so early though.

So do you have some advice? Maybe some sort of algorithm on how I should approach all these topics from the lectures. Im lost

>>11060031
Will read later, promise.

>>11061006
It really is hard to judge after one week whether or not your learning is effective, it only really shows after a few months if you can (or can't) easily connect new material to old one.
The problem sheets should be your best indicator, if you can do them you are fine, if you can't do at least half of the exercises you are in serious trouble.

In general I think what you are doing is fine, but I would approach the exercises differently, because the point at which you learn are the exercise sheets.
If you can't do them you should go back to your notes, or the script of the professor and review the relevant sections, trying to see how they fit in with the exercise, that, in my experience, is much more beneficial then a pure review of the materials.
Invest time in the exercises, but don't try to force them in a single day, you have an entire week, use it wisely.

>>11061007
>Pretty basic like most other universitys
I don't think the definition of the real numbers is very common, especially at such an early point, even before the most essential ideas of analysis.

>Maybe some sort of algorithm
Look at the exercise, if you can't do them, review your notes on the subject, if that doesn't help look on the internet and if that still doesn't help go the tutorials and try to understand what went wrong.

But the general advice I would give you that it's all right, pretty much everyone has troubles at the start and if you put in the effort of doing the exercises, going to classes and doing a bit of review you are certainly in the upper half of participants.

>>11059882
>anime picture of girl
>here's to hoping this thread is like last (great (anti-tranny)) thread
Yeah, go get fucked in the ass, sissy.

Bros, how do I become a better math student? I'm definitely not dumb and would go as far as saying that I'm at least above average intelligence. I'm three years into my math degree and I'm doing good thus far, but I know I can do better. I'm an A- average student and I know I can do better. How can I develop the mental fortitude and drive to get there?

>>11061007
Worst case scenario (assuming you can drive) you can just become an electrician (lineman or joiner), gas engineer or phone line repairman. Non-plumbing utility companies always take math dropouts who like the outdoors, even in recessions.

>>11061129
i have a 4.0 and don't even try while going to work 60 hours a week and btw im doing my degree in 2.5 years and am double majoring and have 4 hours of daily commuting and no internet at my house to study with

you are stupid as fuck

How feasible is it to publish a paper independently?
Would applying for presentation at some conference like the ICFP be a good approach? Although I'm not sure how hard it is to get your paper accepted at those conferences.

Asking here

My room is 5 meters long and 3 meters wide
Each plank is 129 cm long and 19 cm wide

How many planks do I need to fill the room floor?

>>11061007
>algorithms
not going to make it
>how to know if I’m alright
First exam, can you do the proofs the author supplies on your own, how often do you spend more time than your peers working on the homework. Talk with your professor at office hours on a weekly basis if you’re worried, we can’t help you.

>/mg/ - stupider questions thread and logic discussion

>>11061232
About 40.

can I ask a discrete maths question here? math stackexchange is fucking stupid with all its formatting

>>11061167
>publish independently
For what purpose?

>>11061278
you can admit you’re retarded anywhere you’d like anon, its the internet we judge you before you make your presence known

>>11061010
Never mind, the physics is ilegible.
Be back in~3 months.
>>11061278
If it's a good question, of course, please do.
If it isn't, try >>>/sci/sqt

Any calculus logic tips? All the questions feel like brain teasers and less math

>>11061278
No. If you attempt to ask such a question 4chan will automatically permaban you.
Only LEM discussion, Touhou "look how smart I am" wanking and category theory is allowed here.

>>11061295
idk what a "good" question is because I already know the correct answer to it but idk WHY it's the correct answer. I know it's not a difficult question but I'm just stuck. anyway, here goes:

>Let F denote the set of functions from ℕ to ℕ. Define the relation R on F×F as follows:

>(f,g) ∈ R if f(n) ≤ g(n) for infinitely many n∈ℕ

>Which of the following properties does R have?
(have to pick from reflexivity, anti-reflexivity, symmetry, anti-symmetry and transitvity; it's only reflexive BTW)
so during the lecture, when the professor explained it, he used f(n) as a function that maps to 0 when n is an even number. it maps to 1 when n is odd. g(n) is the opposite: maps to 1 when n is even and 0 when it's odd. pic related
so I get that it's reflexive (and thus not anti-reflexive). but I don't get why it's not symmetric. f(n) <= g(n) for infinitely many values of n (= 0, 2, 4, etc.) and g(n) <= f(n) for infinitely many values of n (= 1, 3, 5, etc.)
so IMO fRg and gRf so it's symmetric, right?

>>11061322
That one isn't good.
>>11061296
>tips for logic
Logic exercises aren't randomly generated, they're made by people to be solved. Just go with the flow.
>>11061297
>touhou look how smart I am
Woe would be me if everyone started posting cute Touhous and I was hidden, as a tree within the forest, with my meek genius uncapable of shining through.

>>11061351
well ok then

>>11061363
lol at you fag

>>11061322
>so I get that it's reflexive
But your above writing has literally nothing to do with it being reflexive or not.
fRf always holds, because for all n f(n) <= f(n) thus it is reflexive.

The example of the the professor is why the Relation isn't total.

>but I don't get why it's not symmetric. f(n) <= g(n) for infinitely many values of n (= 0, 2, 4, etc.) and g(n) <= f(n) for infinitely many values of n (= 1, 3, 5, etc.)
so IMO fRg and gRf so it's symmetric, right?
This is pure nonsense.
It has to symmetric for ALL f and g, finding one example where it is symmetric means absolutely nothing.
You can't prove that all cars are red by proving that a red car exists.

>>11061367
oh sorry, I didn't mean to imply the things I wrote above proved reflexivity. I have a bad habit of saying "so"
so what's the counter-example for symmetry then?

>>11061378
>have a bad habit of saying "so"
>the very next word is "so"
unintentional

>>11061378
not going to make it

>>11061390
thanks for the help

>>11061378
f constantly 0, g constantly 1.
fRg is certainly true, gRf certainly isn't.

>>11061006
>>11061006
Hi bro,
Im 5 semester Ba math in germany so maybe I can give you advice.
Feeling like you dont think anything for 45min is normal id say, although I dont know how strong the effect is for you. It can help to take a 10min break or change location (study at home instead of library).
You probably have 3 lectures, 3 exercises per week. If you spend a lot of time on the weekend (10 hours in the library trying to solve 1-2 of the hard problems) you can probably do it.
If you want reassurance that you dont suck then look at old exams. The exams tasks arent as hars as the weekly exercises.
Go to the tutorial sessions and ask lots of questions if you dont understand smth.

any new developments regarding mochizuki's proof of the ABC conjecture?

>>11061398
ahhh, I see. I was under the impression that symmetry doesn't hold for the pair of functions I used in the example because the professor just used that one example to talk about the properties but he wasn't really explicit as to WHY symmetry doesn't hold as if it were obvious and he merely mentioned it in passing
I get it now though. thank you!

>>11061406
>You probably have 3 lectures, 3 exercises per week
Where on Earth do you study that that is 30 ETCS?

>>11061007
the closest to an algorithm I can give you is this:
Learn ALL the definitions by hard and by understanding. If you dont know a definition you cant solve the exercise.
When you see a problem write down all the definitions that appear. Apply, combine and do algebra to get new statements. When you dont know where to continue, look if you can apply a definition or statement you already know.

Get comfortable with forall and exists. When you want to prove for all x something you write:
Let x
to show: something
When you want to prove there exists x such that "something" you write:
I choose x = or I choose x such that
then you leave a gap
and use your x to try and get "something"
You will see how you need to pick your x.

Use your visual iamgination. In 1st year analysis and LA EVERYTHING can be understood with plain visual/spacial intuition.

>>11061417
understand me gaussian elemination/jordan normal form or that V\Ker(A) is isomorphic to Im(A) with visual intuition, brother

>>11059978
Thomas calculus is pretty good

>>11061396
its not anyone else’s job to complete the coursework you are expected to be able to do on your own idiot.

Why do girls succeed in math? This really hot blonde girl got a higher mark on our linear algebra midterm and there is no way she is smarter than me

>>11061426
the second one is easy to visualize

>>11061439
My guess is that math is fundamentally unattractive to females so the females in mathematics are usually above the average of all math students.

Aside from that, brute Force learning can get you good grades in pretty much any 1st or 2nd year course.

>>11061447
how to into brute force learning?

>>11060229
that doesn't map anything, dullard

>>11061443
which one?

>>11061452
>>11060228
But of course there is:
1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,19,19...
2,3,5,7,11,13,17,19,23,29,31,37,41,43,47,53,57...

>>11061451
Do exercises. Everyone you can find on the subject, preferably from previous semesters.

>>11061406
Im in Bonn, we have analysis, linear algebra and algorithmic mathematics for 9 credits each. 27 credits chill first semester.

>>11061437
I'm not asking anybody to complete my coursework though?

>>11061232
About 61

>>11061426
sorry I meant first semester. In first semester linear algebra understanding vector spaces visually works pretty well.
In 2nd semester not so much anymore yea. But even then you can still use visual intuition with things being orthogonal, things being greater or smaller than eachother, parallel etc. sometimes.
But that's exactly the reason I am not good at algebra because I cant imagine anything. I struggled in 4th semester algebra.
Now Im only doing analysis and it's still very effective to imagine things.

>>11061460
To answer his question, there isn't a combination of elementry function that spits out all the primes with naturals as input, or anything as input really
(2^p)-1 where p is prime spits out more primes though

>>11061487
how do you know there isn't one? maybe it's just that we have not found it yet

>>11061509
Primes are distributed randomly, elementary function cannot produce random numbers

>>11061439
girls study by doing every single exercise in the book till 2AM while guys consider this a waste of time and they shitpost on /sci/ instead. ask her to prove the rank nullity theorem if you want to know if she's smart. you'll come off as a total autist, but at least you'll know.

>>11061475
You're asking basic questions that your professor could easily have answered during office hours, not contibuting to the thread in any meaningful capacity. People come into this thread and instead of lurking until they have something worthwhile to say, or a really difficult interesting question to ask, will immediately submit to their base instincts and spam questions about how to organize their major, what books should they read, how to think properly, can you do my homework /mg/? your post is no different and doesn't warrant careful inspection, fuck off.
>>11061453
2nd concept, read carefully.
>>11061524
>girls study math until 2 AM
women don't study math.

>>11061515
>Primes are distributed randomly
Proof?

>>11061614
fuck off it's not your thread
not him btw

>>11061614
jordan normal form? and what is your geometrical intuition that helps you find it?

>>11061633
swallow a bag of nails faggot
>>11061638
>V\Ker(A) is isomorphic to Im(A)

>>11061524
I'm pretty sure that 0% of girls can do actual proofs and research by their own

>>11061614
>wah wah your post doesn't fit my requirements
>doesn't warrant careful inspection
then don't reply to it, faggot. what the fuck are you gonna do about it

>>11061647
>0% of girls
I mean there ARE female mathematicians

Did they finally sort through this guy's shit? Crackpot or genius?

>>11061647
its a meme from women taking easy classes in majors that depend largely on attendance, lab grades, and grinding practice problems. not applicable to physics and mathematics.

>>11061645
hmm, I don't see how drawing down V\Ker(A) would help find an isomorphism, maybe because it is a particularly trivial one.

>>11061656
>"""female mathematicians"""
lmao

>>11061426
>V\Ker(A) is isomorphic to Im(A)
this is easy to visualize desu

>>11061447
xd

How do I learn Logic, Quantifiers and Proof? I can't find good resources online

>>11061670
okay, take V = R^3, A:V->V, A(x,y,z) = (x,y,0)
what would the V\Ker(A) and Im(A) be and how can you see that they are isomorphic?

>>11061674
because there is none
You can ask in the logc room at mathstackexchange.com here:
https://chat.stackexchange.com/rooms/44058/logic

>>11061718

injectivity: if A(x) = A(y) then A(x-y) = 0, and x-y must be a member of the kernel

you just take out all the stuff that gets sent to zero.

>>11061738
what

>>11061718
[math]\ker A[/math] is the [math]z[/math]-axis. therefore the quotient space [math]V/\ker A[/math] consists of all lines parallel to the [math]z[/math]-axis, i.e. all lines orthogonal to the [math]xy[/math]-plane. if you look at this from the top, a line orthogonal to the [math]xy[/math]-plane will look like a dot in the [math]xy[/math]-plane. addition in [math]V/\ker A[/math] using representants will look like a regular vector addition in the [math]xy[/math]-plane. this is the isomorphism since [math]\text{Im} A[/math] is precisely the [math]xy[/math]-plane.

>>11061748

Ker(A) are exactly the elements of A's domain that make it a non-injective mapping. A(V\Ker(A)) = Im(A), so you don't lose anything by only considering the subset V\Ker(A)

>>11061751
right except this give me no untution whatsoever about why this isomorphism is true
>>11061738
>>11061756
this anon gets it but I don't quite get his explanations, I'll reread it and give it some thought

>>11061771
so what exactly do you want, visualization or algebra ?

>>11061674
http://www.personal.psu.edu/t20/notes/logic.pdf

>>11061781
what I want really is the intuition why V\Ker(A) =^~ Im(A)

>>11061782
I'm pretty sure this guy just wants to learn rules of logic and how to write proofs, not a book on mathematical logic equipped with systems such as hilbert-style and hentzen-style systems that are the complete opposite of systems that are actually being used in proofs

Could you all give me some suggestions on math ideas/topics I could explore and create interactive visualizations. Examples of projects already would be dunce hat, 3d fractal convergence, and sphere eversion visualizations. I'm looking for something not worn out already and preferably outside of topology.

>>11061793
The elements of [math]V/\ker A[/math] are lines parallel to [math]\ker A = z[/math]-axis. Each such line can be written as [math](x,y,z) + \ker A = (x,y,z) + t(0,0,1)[/math]. Clearly if the [math]z[/math]-coordinate is changed in [math](x,y,z)[/math] it will define the same line and conversely two vectors give the same line if and only if their difference is a multiple of [math](0,0,1)[/math], the generator of [math]\ker A[/math]. So we see that it's completely irrelevant what we write in the [math]z[/math]-coordinate, can write the lines as [math](x,y,z) + \ker A = (x,y,*)[/math]. The addition in the quotient space works via representants: [math](x_1,y_1,*) + (x_2,y_2,*) = (x_1+x_2,y_1+y_2,*)[/math], this is well-defined because different representants differ by a different [math]z[/math]-coordinate which is them disgregarded anyway. It is now clear that all that happened is that we started to ignore the [math]z[/math]-coordinate and we compute just with the [math]x,y[/math] coordinates. The actual formula for the isomorphism is now [math](x,y,*) \mapsto (x,y)[/math]. This doesn't depend on the representant chosen, since the differ by something which is thrown away. Surjectivity is clear. And the only thing which goes to zero is [math](0,0,*) = \ker A[/math] which is zero in the quotient space. Therefore injectivity.

>>11061854
http://libgen.is/book/index.php?md5=52A2C985A2C5C87B0669BD34F7CCDBEE

>>11061672
?

>>11061657
Turbo genius
Just happens math community don't want read thousand pages in niche topics instead of just continue langrangs program

>>11061883
Understanding this example thoroughly is kind of all that's needed. In the general case [math]\ker A[/math] is some subspace in [math]V[/math] and elements of [math]V/\ker A[/math] are all affine subspaces parallel to [math]\ker A[/math]. Addition works using representants. An affine space [math]u + \ker A[/math] gets send do [math]Au[/math] and this is well-defined because [math]u + \ker A = v + \ker A[/math] if and only if [math]u-v \in \ker A[/math] and this implies [math]Au = Av[/math] immediately. It's injective because the only thing that gets send to zero is [math] 0 + \ker A[/math] which is zero in the quotient space. Surjectivity doesn't need a comment.

You can also look at it this way. Pick any complement [math]W[/math] of [math]\ker A[/math]. Then the rank-nullity theorem says that [math]A[/math] restricted to [math]W[/math] is a injective, therefore an isomorphism onto [math]\text{im } A[/math]. Geometrically if you picture [math]V/\ker A[/math] as a set of parallel affine planes, [math]W[/math] is any subspace which transversely pierces through all of them. Clearly each [math]u + \ker A[/math] is uniquely specified by its point of intersection with [math]W[/math]. This gives an isomorphism [math]V/\ker A \cong W \cong \text{im }A[/math]. In your example [math]W[/math] was the orthogonal complement to [math]\ker A[/math], namely the [math]xy[/math]-plane. Coincidentally, [math]W[/math] was actually also the image, but this works in general.

>>11061937
>arithmetic geometry
>niche
Really?

>>11061657
Mochizuki is like an ascended Tooker

what math do I study if I want to hate everything

Why are "e" and "0" the same? it's a basic set theory question desu but it's stumped me.

>>11062050
>Why are "e" and "0" the same?
Why would they?
e appears to be Euler's number, which is non zero.

>>11062050
draw a picture

>>11062054
the soluton

>>11062067
Yes?
This is what one would expect given e being Euler's number, which is larger than zero, but smaller than pi.

I think I'm missing something big.

Let [math]X[/math] be a scheme (or a prevariety for that matter) and [math]U\subset X[/math] a non-affine open subset. Apparently, [math]U[/math] is a scheme in a natural way, but I just don't see it. What is the affine cover?

Suppose [math]X_i[/math] is the affine cover of [math]X[/math]. We already have that [math]X_i\cap X_j[/math] is not necessarily affine, therefore there's even less of a chance that [math]U\cap X_i[/math] will be affine, therefore that doesn't give an affine cover.

>>11062103
never mind, figured it out

>>11060787
The first problem is that practicing physicists regard the entire classification of topological orders as already solved by Kitaev's periodic table. The rationale being that topology (in Fermi/Majorana liquids), as a mean-field first-order effect, is independent of higher-order perturbations coming from many-body phenomena, hence extensions to Kitaev's free fermion program to interacting systems is inherently uninteresting. Not to mention the abstract machinery employed in the Freed-Hopkins paper is a big turn-off, especially since they had not made any effort in attempting to realize concrete models exhibiting the topological orders displayed in their periodic tables. This is actively being worked on by mathematical physicists, however.
The second problem is that there is no agreed-upon definition of "topologically equivalent phases". There are currently three major definitions:
1. the ground state manifolds are weakly homotopic,
2. the Hamiltonians are related via local unitaries, or
3. the ground states are connected by finite-depth quantum circuits,
all competing with one another, despite being extremely similar but have different domains of application. The second works very broadly with free fermions, while the third works for defect networks on pointed CW's, for instance.
As a consequence, an "invertible topological phase" is itself a fuzzy word; in Freed-Hopkins and the TQFT circle, invertible means [math]Z[/math] maps every bordism to invertible linear maps, while in more QC circles it means the anomalies in the defect network can be cancelled. There is currently no definitive proof (only demonstrations in restricted cases) that these definitions coincide, and some physicists do not seriously regard the Freed-Hopkins result simply because of this fact. There's nothing much that can be done about this one unfortunately.

I feel like Calculus is bullshit because they use like riddles in the question. Linear Algebra is very straight forward and there are no "gotcha" questions. Calculus is dishonest

>>11062118
tell us the, what did you figure out?

>>11062145
Although [math]X_i\cap U[/math] is not affine, it is an open subset of an affine scheme, and therefore has an open affine cover (since notably, the basic open sets [math]D(f)[/math] are affine and are a base of the topology)

>>11062131
but linear algebra is the only math which is this straight forward. everythign else is all about "gotcha": when you write a conjecture and find out that you can't prove it because it's ultimately wrong, it's always wrong because there's some "gotcha" case which you haven't thought about when writing the assumptions. not because it's "obviously" wrong, otherwise you wouldn't have tried to prove it in the first place.

I took intro to topology (point set topology, homotopy, covering spaces a bit) and I have this conflict that the subject seems so cool, yet it feels so shitty. Im someone that really likes proofs which are done all the way through and the amount of words used in topology proofs Ive seen outs me off. But I really feel like topology is so important and read about it everywhere. At the moment I am not taking another topology lecture but I might in my masters or in self study.
Why do topology proofs have to be so unrigorous, was it just my professor? When correcting homework it was the same.
And then some of the pronlems can be solved with "this one weird category theory trick" and our tutor rants on about functors and I dont know what' the more effective way to think of these matters.
I usually like spatially imaginable maths so I want to like topology :(.

>>11062188
>Why do topology proofs have to be so unrigorous, was it just my professor? When correcting homework it was the same.
that's because if you were to prove everything into full details, your course would cover 1/4 of the material
>I usually like spatially imaginable maths so I want to like topology :(.
if you want "visual topology", try differential topology

How do I go about being a researcher at my school? How did you get into research?

Is it based on GPA, etc? Do I have to know the Professors?

>>11062188
"intros" to topology suck because you don't have the tools yet to do anything useful unless you take multiple courses on it, but then suddenly you have a toolbox to do a bunch of cool shit in other classes.
>unrigorus
this isn't true and your prof sucks, or is dumbing it down since they only have you for the semester. Try proving the book stuff on your own time, maybe ask someone else in your department to look at it then you can be as wordy as you want.

>>11062213
>How do I go about being a researcher at my school?
You get into a PhD program.

>Do I have to know the Professors?
No, talking to the magic fairies is enough.

>>11062224
is it enough to be in a masters program
i want to be research assistant

Hi guys :3

>>11062188
give us a taste of what you consider an unrigorous proof, perhaps from your lecture notes.

The only thing I can think of that most books/lecturers usually just handwave are some homeomorphisms of concrete objects, like S^2 being homeomorphic to the tetrahedron, or somethings like collapsing subsets, but I feel most of them can be actually be given a rigorous argument

If I have 52 cards and I want to deal 5 per player to 4 people, how many ways are there to do this when order of the players matters but the order they get the cards in doesn't?
So if player A gets 4 aces instead of player B that matters but the order in which he gets them doesn't.

My intuition says (52 choose 5)(47 choose 5)(42 choose 5)(37 choose 5)*4! but I don't know how to verify these things.

>>11062327
so the configuration of the players also matters ? is ABCD the same as BCDA ?

>>11062283
yes I mean the hand waving, of coufse the proofs can be done rigorously, but what frustrated me was that it was so incredibly annoying to prove even simple things about homotopies. You just want to say okay I can pull the path along this face obviously but actually showing it means you have to make a stupid parametrization construction or smth.

>>11060184
based
>>11060139
It'll all be over soon

>>11062425
>>11062425
>incredibly annoying to prove even simple things about homotopies
Oh, yeah. Sort of. There are all sorts of cheats to doing it.
Try to prove that the n-sphere for n>0 is path connected.
Tip 1: prove manually for n=1 and prove the suspension of something path connected is still path connected.
Tip 2: prove it's homotopic to R^{n+1}/{0} and build a path in R^{n+1}/{0}.
Tip 3: Jesus Christ don't attempt to build paths in S^n through their polar coordinates.

>>11061771
>right except this give me no untution whatsoever
You don't expect intuitions to be "given" to you. You need to make them yourself if you have any worth whatsoever.

>>11061751
>>11061883
>>11061942
very nice

>>11061162
are you trolling or youre serious right now?

>>11062213
>Immortals of Math
>pic has exactly one(1) mathemtician
What did he mean by this?

>>11062697
That situation be very common here in Africa.

>>11062641
>Jesus Christ
Tip 4: He did not exist.

>>11062727
>He did not exist.
Except he did. Whether or not he was the son of God is another question.

>>11061129
>I'm definitely not dumb
The picture you attached to your post begs to disagree.

>>11062731
He did not. You can not disprove this as it happened literally in 0 AD. If he did, he might as well be the Son of God.

>>11062736
There are plenty of non-biblical sources of him existing in history. Try looking for some. Unless your bias is getting in the way?

>>11062740
I've looked and couldn't find anything but an old fiction book called the Bible and some old sheets of paper from 300AD, which is long after he supposedly died. I'm a hard-core rationalist in my leanings so I'm entirely unbiased.

>>11062749
Here are some names: Tacitus, Lucien, Suetonius, Thaullus, Pliny, The Talmud, Mara Bar-serapian, Celsus, Josephus. Figure it out yourself.

>>11059858
just got an undergrad in math and i dont know what the fuck a limit is

>>11062820
in what context?

>>11062820
Closest number you can approach without getting there. They are found in functions, sometimes you cant approach the limit (ND)

>>11062820
A limit is just an object that factors maps to the cone.
Or was it from the cone? Definitely one of those.
There might also have been an inverse cone somewhere.

>>11062758
>religious gobbledigook names
Nah, thanks. I don't listen to extremely biased sources.

>>11062990
Low effort troll. Don't you have homework to finish for your high school classes?

>>11062927
don't worry, a colimit is just a limit in op so you're right either way

>>11063033
I don't understand how anyone with even slight logic/maths and reasoning skills can believe in Jesus Christ. I have a hard time respecting anyone's intelligence that believes in a fictional being that rules over their life.

some of you are alright, don't look for zeroes of the zeta function in a neighbourhood of [math]\infty[/math]

>>11062731
>I will declare the decree: the LORD hath said unto me, Thou art my Son; this day have I begotten thee.(Psalm 2:7)
David is the begotten Son of God according to Psalm 2:7.

>>11062820
I have had an undergrad in math for over a year and I couldn't tell you what a ring is.

>>11062820
>>11063518
many such cases!

>>11063518
a ring is an abelian group (the addition) which also has a multiplication operation which is COMMUTATIVE and HAS AN IDENTITY.

>>11063545
>matrices don't form rings
lol

>>11062641
Tip 4: Sn minus a point is Rn

>>11063545
>multiplication operation which is COMMUTATIVE
brainlet

>>11063227
I understand your general sentiment, but in fact, convincing oneself that logic observed in place A carries over to any place is a logical fallacy. There's no way of arguing away non-logical things from empirically finding evidence on how practical logic is.

>>11063227
someone believes in jesus, someone believes in infinity. big deal man

>>11063565
it's Sn plus a point you fucking irredeemable moron. it's just the one point compactification of Sn. jesus christ why do they let idiotic undergrads like you on our board? literally the disease killing /sci/
fucking draw it, it's so god damn obvious

>>11063227
If god doesn’t exist then how come the universe have a beginning? How come the entropy is lower at the beginning of the universe?

What other explanation could there be other than god created this universe?

>>11063607
read my post again, then read your post again.

>>11063644
i don't get your point. maybe you're not smart enough to communicate with people in this thread?

>>11063652
n-sphere minus a point is R^n. you seem to disagree.

>>11063545
If I wanted to know I would read the Wiki article.

>>11063227
>can believe in Jesus Christ.
What does "believe in Jesus Christ" mean and what does it have to do with logic?

Logic is about deducing claims which follow from certain axioms, I do not see a connection to having faith (you know the thing that isn't based on pure logic) in the divinity of Jesus Christ.

>fictional being that rules over their life.
The belief in the absence of a higher being than humanity is much more absurd than that.

>>11062749
>I'm a hard-core rationalist
You seem a hard core idiot and extremely emotional about issues of religion.

>>11062990
>Nah, thanks.
The classical rationalist who disregards everything that disagrees with his biases, lmao.

>>11061751
>>11061883
>>11061942
this is the first instance of strong intuition unobscured by self-fellating grad brain spam I've seen for lin alg in this general, what a great series of posts.

>>11063655
you keep saying minus when you mean to say plus. i'm just going to give you the benefit of the doubt and assume you're fucking up and that you're not actually this fucking stupid.

>>11061657
Crackpot who used to be a genius.

>>11063781
>what is stereographic projection

>>11063805
>what is RP^n
jesus fucking christ

>>11062043
Analysis

>>11063815
see >>11062727

>>11063781
n-sphere with a point removed is R^n. Are you saying that n-sphere with a point attached is R^n ?

>>11063855
sad!

I think I can prove the Erdos-Straus conjecture.

>>11063607
It's both, tho.
Add a point and you get one point compactification.
Remove a point (0 for convenience) and you have R^n/{0}-> (x/|x|, |x|) homeomorphic to S^(n-1) x R+. R+ is contractible, so it's homotopic to S^n.

>>11063948
>homeomorphic
>homotopic
can you define this with full rigour?

>>11063948
I mean this guy >>11063607 mentions one point compactification of Sn (the sphere), that's a good indication that he has absolutely no clue what he's talking about

>>11063545
What about coomutative operations?

>>11064119
The sphere is already compact. The 0 point compactification of the sphere lmao

>>11063890
her name has only one "H", while the proposed anagram has two.

>>11063545
Rings do not have to be commutative. They do lose a fair bit of arithmetic properties by doing that.

Linear operators are an example of a non-commutative ring (technically, an algebra)

>>11063781
>>11063607
You're fucking retarded. Go back to elementary school.

Is the set of uncomputable numbers dense in the set of real numbers?

>>11064180
Of course

>>11064180
I can think of Q(pi), of which all members are uncomputable* (except 0) and which is dense in R.

*if by uncomputable you mean non-algebraic

>>11064181
How would you prove it? I don't see how you could construct a sequence of uncomputable numbers, so I guess you have to use the axiom of choice?

>>11064186
That would be transendental tho.
https://en.m.wikipedia.org/wiki/Computable_number

>>11064191
Proof by contradiction.
That is, you don't need to characterize the uncomputables, showing that the computables have empty interior is enough.

>>11064191
Take a single uncomputable number x. Then x/10^n is also uncomputable for all n. Take any open interval. There is a computable number in that interval, call it y. Then y + x/10^n is uncomputable and in that interval for large enough n.

>>11064194
I didn't know about these. I'm not sure if I understand them right.
Basically, they are numbers which are solutions of "unstable dynamical systems", right ?

Just need to show that unstable systems are dense in the set of all determinstic systems, maybe.

What is happening to this thread?
Undergrads that dont know what limits or rings are, topologists that cant tell the difference between S^n and R^n. Debates about Jesus.
Is this the power of US education?

OT: Anyone have a good resource on the geometry of four manifolds? I tried the book of the guy in the OP but are there any other standard textbooks?

>>11064302
>Undergrads that dont know what limits or rings are
HEY.
I actually have a degree and do not know what a ring is.

>>11064208
I don't know what you mean by "numbers are systems". This is about numbers where you can/can't compute their digits

>>11064180
It's gonna be stronger and probably easier to show that any interval is densely filled with indefinable numbers.
In any arbitrary small interval, the cardinality of indefinable numbers is uncountable.

>>11064208
How is the solution of an unstable system a number? What does that even mean?

>>11064302
>>11064484
I doubt anyone knows what a ring is, in some books it must be associative with an identity, in other identity is not required yet in other even associativity is not required! It seems that no one knows the right definition of a "ring"

>>11064569
No, no, no.
Ring is always associative and may not have an identity.
You're thinking of an algebra. An algebra isn't necessarily unital or associative.

>>11064569
I don't know, I think the standard terminology is to call associative unital things rings and call the rest algebras.
It is very easy to produce examples of rings that are not commutative (take the endomorphism ring of a typical abelian group), but I have very rarely seen naturally occurring nonassociative things aside from maybe Lie algebras and octonions.

new thread

>>11064752

>>11064752

>>11064752

>>11064752

>>11064752

>>11060897
>LEM is above the oracles

What did he mean by this?