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What are you studying today, /mg/?

https://en.wikipedia.org/wiki/Vladimir_Voevodsky

Previous thread >>9193069
>>
Kalman filters. Have to. I also have to learn C#.
>>
>>9209451
So, can someone explain to someone stupid what was this guy doing?

As I understood it, it was somehow related to a new foundation for mathematics that would be more useful for automated proof checking, is this correct?

And if it is, could this be used to see if the ABC proof is really correct?
>>
>>9209482
fun anon, i'm also learning kalman filtering for my new job. are you also compelled by occupation?
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That's a big proof...
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How tall was Vladimir?
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who here /categorytheoryonwindows/?
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>>9209451
[math]t\,e\;s~t[/math]
\mathbb{TEST}
[math]a^{test}[/math]

Just checking in to see if this works before using it
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Lately I've been playing around with the axiom of choice and its internal version in elementary topoi, and I'll see if I can prove the theorem by Diaconescu after I've slept:
>if an elementary topos satisfies IAC then it is boolean
Considering the categories of sheaves on topological spaces, I think one can show that the category of sheaves over a space is Boolean iff the space is discrete. Assuming I remember correctly, Diaconescu would then imply that the internal axiom of choice fails in such categories. I wonder if AC implies IAC. That is something I need to check as well.

>>9209634
Not on windows, but I tend to take the receipts every time I buy something so I can do category theory on them.
>>
What's the difference between calc and anal?
>>
WTF? WTF IS THAT?

Why no anime girl image on the OP? Why put a fucking random guy instead of a cute anime girl, you piece of shit?
>>
>>9209451
Hey, I'm a college student who does olympiad problems for fun. Today I came up with a new and really cool solution for a USAMO problem from 1984. Is there any kind of forum where I could just post the proof and have it be under my name? I just want people to know it was my idea.
>>
>>9209793
Right here buddy, just use a trip, faggot.
>>
>>9209808
>faggot
Why the homophobia?
>>
>>9209808
I'm not going to post it here. First because it will die, second because then I can't show it to my peers because remember that from the perspective of outside people, 4chan is le nazi hideout.
>>
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>>9209769
It can be shown that Voevodsky is homotopy equivalent to anime.
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>>9209793
no one really cares about a new proof for a math Olympics problem...
>>
>>9209812
Because most gays are annoying faggots, so deal with it.
>>
>>9209823
On which basis can you make and uphold that baseless and senseless claim? How many reasearches have you read or done on this particular subject that makes you so certain about its results?

Oh wait, you did nothing because you're a /pol/tard that likes to call everyone a nigger or a faggot in an attempt to ridicule those minorities because you yourself leads a pathetic life where you don't have the right to express those same opinions because you know you'll be even more humiliated than you already are.
>>
>>9209821
Many people do. They are really fun.
>>
>>9209847
Yeah, but not on the level of treating it like some kind of huge achievement. What do you think you'll get exactly for "claiming" that new proof as yours? Nothing at all, man, just post that proof wherever you like.
>>
9209812
9209833
>>>/t/umblr/
>>
>>9209853
I don't think it is a huge achievement. I just think it's cool. My idea is cool and I just want that in the future when olympiad students start desperately googling "USAMO PROOF" they see my name.

But you just gave me a great idea. I'm going to create a blog where I will submit these kinds of proofs. Thank you.
>>
>>9209756
nice taste in anime desu senpai
>>
>>9209812
Because tripfags are faggots

>>9209814
I think you've misunderstood me. Post it here, bucko.
>>
>>9209833
>believing empirical garbage
Fuck off to >>>/toy/ and take your dog-eating friend with you.
>>
>>9209860
That's a very egoistical way of looking at Mathematics and Science in general, you're just looking at the recognition for something that is not even worth that much. I'll just leave you with this beautiful phrase from Gravity Falls and hope you can reflect on it and change your thoughts somehow:

"Science is a horizon to search for, not a prize to hold in your hands"
>>
>>9209869
>"Science is a horizon to search for, not a prize to hold in your hands"
Wanna ask me how I know that phrase comes from a kid's show?

But my question for you is that if I know that there is barely any recognition in doing this, and you know it also, then what problem do you have with me wanting my name to be under it?

If I don't do my blog then I have two options. Option 1 is posting it here anonymously or with a trip but then the proof just dies and will never be available for students. The other option is going to a permanent math forum and posting it there but there is no dedicated math forum to just post proofs and if I were to do it at StackExchange or something then it would still be under my name, so nothing changes.

I will leave you with this quote that isn't a quote: "Paul Erdos' first published paper was an alternative proof he discovered for Bertrand's Postulate".

Obviously what I found is not as cool as Bertrand's Postulate, but that is also why I am not seeking publication either.
>>
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How do i prove this? I am struggling with this.
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>>9209890
>How do i prove this?
Try induction and Pascal's rule.
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>>9209892
Just noticed what I have been missing, I am very dumb and it was so easy to spot if I actually had eyes.
>>
>>9209882
>Wanna ask me how I know that phrase comes from a kid's show?
Go on, I wanna have a good laugh at your egoistical reasoning.

Nonetheless, I have nothing else to say to you, just do whatever you want, I don't care, I just don't like your kind of mentality of wanting to "claim" something as yours and doing science/math for recognition instead of pleasure and truth.
>>
>>9209890
Say you have n distinct objects o_1, ... ,o_n and you want to pick 3 of them.

o_1 o_2 ... o_n

you can pick o1 and then you can pick from the rest on the right side in n-1 choose 2 ways

or you can pick o2 and then pick 2 on the right side (picking on the left side would be double counting) in n-2 choose 2 ways

...

or you can pick o_{n-2} and be forced to pick the two only objects on its right (o_{n-1} and o_n)

these are obviously exactly all the ways you can pick 3 objects out of n.

This proves it.
>>
>>9209927
>wanting to "claim" something as yours
It's impossible, what he wants to "claim" isn't even a physical thing.
>>
>>9209950
Somebody asked you anything, pal? Why butt in on other people's conversations like that?
>>
>>9209956
Is something confusing you?
>>
>>9209793
What about stackexchange
>>
>>9209958
No, you're the one confused here since no one was even talking to you... But you still felt the need to say something that no one cares...
>>
>>9209882
>Wanna ask me how I know that phrase comes from a kid's show?
>I'll just leave you with this beautiful phrase from Gravity Falls

Uhhh, because he literally told you?
>>
>>9209451
>tfw fell for the bc calc transfer credit meme
i'm still discovering new gaps in knowledge
>>
>>9209833
You're awfully annoying, do you happen to be a gay?
>>
>>9209968
Speak up. I can't hear you when you trail off like that.
>>
>>9209634
me since I do not have blackboard.
>>
>>9209761
"the virgin anal": rigor circlejerking and proofs of statements that are intuitively obvious to infants (IVT)
the chad calc: what the modern world runs on, intuition and infinitesimals
>>
>>9209451

Any good stats and probabilities problem sets?
>>
In the category of linearly ordered sets, which object is initial?
[math](\mathbb{N},<)[/math] ?
>>
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>>9211646
The answer is quite disappointing and depressing: [math](\emptyset, <_\emptyset)[/math]. Why? Because there are no non-related elements in the empty set, and so it is linearly and well orderded, and the empty function preserves this ordering, so it is an arrow in the category of linearly ordered sets. Moreover, the always existing empty function [math]\emptyset \to A[/math] is unique for any set [math]A[/math], and so we have an initial object. Next, let [math]0[/math] be an initial object in that category. There is then a function [math]0 \to \emptyset[/math], but this means [math]0= \emptyset[/math].
>>
>>9211646
>which object is initial?
You're saying as if it has to have an initial object.
>>
Why isn't analysis ever taught before Calculus?

In programming, there's a pedagogical dispute between whether to start bottom up (assembly, c, etc) or top down (java, Python, etc) and this situation of analysis after calc seems analogous, yet I see no one vouching for analysis before or even in parallel to calc
>>
>>9212005
you can argue there's no point in teaching calculus to mathematicians. it's hard to reach a conclusion either way. but calculus is easier to teach, because you're teaching it to all the engineers anyway.
>>
>>9212005
Both are garbage and should be mostly ignored.
>>
>>9212009
>dont teach calc to math students
I think I'm beginning to agree. Though I don't regret learning calc, I wish my school would've allowed me to learn analysis before or during calculus, and did not require taking a whole year of calc.

I feel like I'm learning so much more on my own, and having so much more fun doing it. It's going to be hard to return to school.
>>
>>9212005
>Analysis/Calculus
What the difference? What's each thing exactly about? We don't seperate them in Greece.
You get taught the following in high-school: limits (without a strict definition), continuity, derivatives, integrals, fundamental theorem, rolle's, mean value, bolzano, intermediate value, basic differential equations, etc.
And in the final exams (which decide where you can go for higher edu) the problems presented are pretty damn hardcore.
And then in uni you see ε-δ, sequences, etc.

How would a high-school student benefit from having to prove stuff with ε-δ? I personally see it as an obstacle. You don't need it for basic stuff.
>>
>>9212151
yes, you separate them in greece. if you don't know the difference, you don't know what analysis is.

terms like compacity, uniform continuity, connectedness are at the heart of the theory you need to formally develop calculus, and they aren't even mentioned in calculus
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>>9212157
>if you don't know the difference, you don't know what analysis is.
I know the "difference". Both are analysis.

>terms like compacity, uniform continuity, connectedness are at the heart of the theory you need to formally develop calculus, and they aren't even mentioned in calculus
Why the hell would you ever teach that to a high-school student? It's like saying, "hey let's teach those 7 year olds ZFC set theory so that they can understand what a number is.
>>
>>9212181
they're not both analysis. I never commented on high school, I ignored that part because this is an 18+ board
>>
>>9209451
trying to prove an necessary and sufficient condition for density of smooth compactly supported for generalized Orlicz spaces.
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>>9211878
>but this means [math]0 = \emptyset[/math]
This actually follows from assuming the existence of an initial object in [math]\mathbf{Set}[/math]. In fact you can even conclude [math]A = \emptyset[/math] for any set [math]A[/math].
>>
>>9212184
>I never commented on high school, I ignored that part because this is an 18+ board
huh? you were talking about teaching and high school is where you introduce analysis.

>they're not both analysis
They are. Just like high-school algebra and abstract algebra are both algebra. One is just a level higher than the other.
If you want to say they are not, whatever.. those are just names. You might as well call it all topology.
>>
>>9212181
>let's teach those 7 year olds ZFC set theory
Honestly I wouldn't teach that garbage to anyone, let alone kids.
>>
>>9212194
>Just like high-school algebra and abstract algebra are both algebra.
Actually this is provably false. It's similar to how "applied math" isn't mathematics.
>>
>>9212194
>you were talking about teaching and high school is where you introduce analysis.
>You might as well call it all topology
you need to be 18+ to post here. I was quite content to reply before you went full nonsense
>>
>>9212198
>provably false

>being able to prove that something can't be called algebra
>algebra isn't well defined
interesting
>>
>>9212203
>you need to be 18+ to post here. I was quite content to reply before you went full nonsense
Oh I see, makes sense.
>>
>>9209861
>>9209756

this is not engineering general
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>>9212215
You'd know, wouldn't you?
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>>9211878
Thx, makes sense. Indeed disappointing.

>>9211897
Yes I know that existence is not guaranteed, but thx for the correction!

Two follow up questions:
1. What if we take the subcategory of sets at least countable infinite?
2. This should be generelazible, isn't it? For a well founded relation [math] E [/math] which is connex,
is [math](\emptyset,E_{\emptyset})[/math] always initial?
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What letters do I pick to denote reflections in a dihedral group?
>>
relatively basic for some here but just learning about the axiom of completeness, pretty cool stuff
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>>9212524
It's false though, what exactly is cool about that?
>>
Is homotopy type theory useful for people who aren't just masturbating over topology?
>>
>>9212576
It got me into masturbating over subjects related to algebraic topology, so I guess it is.
>>
>>9212518
r for rotation, s for reflections
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>>9212864

1. Neither. Interior: nothing. Closure: S plus (0,y) where y is in [0,1]. Boundary: S plus (0,1) and (0,0).

2. Neither. Interior: nothing. Closure: Everything. Boundary: Everything
>>
>>9212518
μ or m for "mirrorring"
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anyone want to help a brainlet out?
>>9212903
/sqt/ is dead right now
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>>9212917
if x isnt zero then 0< x < x/2
>>
can anything be an axiom?
>>
>>9212952
What do you mean by this?
>>
>>9212985
can an algorithm be an axiom?
>>
Why are proofs regarding properties of the real axioms so difficult for undergrads?
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>>9213162
I'm not sure I understand you. Can you elaborate?
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>>9213162
>can an algorithm be an axiom?
Yes
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How do I reduce an equation to a linear form and determine the values of two of its constants using logarithms? I know how to do it for one constant but two is fucking with my head.
>>
>>9212952
Any proposition can be taken axiomatically to be true.
Axioms are merely the basic building blocks of a mathematical model.
An algorithm is a set of functions. You should try to make a proposition about this algorithm to take it as an axiom.
For example:
* Algorithm A will always output FALSE
* Algorithm B always terminates
* Algorithm C is green
* Algorithm Z is a dog preying on the weak

After establishing your axioms you can begin to see what their logical entailments are.
>>
>>9213326
Logic is not usually used by most people.
>>
>>9209793
Post it in yo mama's butt, everyone will see it
>>
>>9213326
Because they are not used to it. You have to essentially learn a new language. Some people just tunnel-vision and can't think about stuff in a new way.
>>
>>9209939
thats a really nice intuitonal way of proving the statement anon, thanks for that
>>
Redpill me on fibre and vector bundles.

>What are they intuitively?
>what are they used for?
>what is the intuition for them?
>what are some important theorems regarding them?
>>
>>9211447

Anyone?
>>
>>9211447
>>9213928
https://ocw.mit.edu/courses/electrical-engineering-and-computer-science/6-041-probabilistic-systems-analysis-and-applied-probability-fall-2010/assignments/
https://ocw.mit.edu/courses/mathematics/18-05-introduction-to-probability-and-statistics-spring-2014/assignments/
>>9213914
https://terrytao.wordpress.com/2008/09/27/what-is-a-gauge/
>>
hello fellow patricians, I'm seeking a script, program or application that will throw a problem at me from a pool of problems from a pool of selected topics
>>
>>9214084
>open libgen
>search for book on that topic
>go to exercise section
>>
What are some rigorous texts in discrete math and related topics?

I know of only Lovasz, Epp and Rosen, and none of these strike me as particularly mathematically 'rigorous'.
>>
>>9213659
This ofc works for [math] \binom{n}{k} [/math] for any [math] 1 \leq k \leq n [/math] .
You can prove [math] 1+2+...+n= \frac{n(n+1)}{2} [/math] this way for example.
>>
>>9214235
>What are some rigorous texts in discrete math and related topics?
Stanley - Enumerative combinatorics
>>
>>9214279
What is included in discrete math that isn't in combinatorics? They always appear synonymous to me
>>
>>9214316
Maybe number theory? I think discrete mathematics is a pretty terrible/misleading term.
>>
I'm always into Real Analysis and any kind of analysis I got time to chew on and get into.
But I'm thinking about setting up a probability and measure course for my school to be taught over summers.
>>
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>>9214362
>analysis
Please don't litter.
>>
>>9209756
You're so cute homo :3
>>
>>9214357
I agree with the term being terrible, despite it being true (discrete rather than continuous). I just wish they all fit under a sexier name like combinatorics. Even combinatorics and number theory sounds better
>>
>>9214235
check out Laszlo Babai's discrete math lecture notes at the University of Chicago
undoubtedly one of the best professors i've ever had
>>
does /sci/ have a recommended scientific calculator?
>>
anyone know nay good math instagrams
>>
>>9214653
TI 36X
>>
>>9212558
>an axiom
>false
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>>9209756
>I wonder if AC implies IAC. That is something I need to check as well.
This was actually true. A topos [math]\mathscr{E}[/math] satisfies AC if every epimorphism [math]p[/math] has a split in [math]\mathscr{E}[/math], and [math]\mathscr{E}[/math] satisfies IAC if, for every object [math]E[/math] of [math]\mathscr{E}[/math], the functor [math](-)^E\colon \mathscr{E} \to \mathscr{E}[/math] preserves epimorphisms. Now, assuming AC is satisfied, for any object [math]E[/math] and any epimorphism [math]p[/math] and its section [math]s[/math], we have [math]p^Es^E = (ps)^E = 1^E[/math], so [math]p^E[/math] is an epimorphism and IAC holds.

>>9214414
Aww, thanks~
>>
>>9214316
Numerical math, graph theory, algebra, theory of computation, logic, game theory...
>>
>>9214653
Yes, your phone.
>>
Failed a test and feeling pretty down, especially since it was so fair. Any of you have any stories of saving your semester after a bad start?
>>
>>9215266
>Failed a test and feeling pretty down, especially since it was so fair. Any of you have any stories of saving your semester after a bad start?
just work harder (i.e. look at your textbook instead of 4chan)
>>
>>9214653
math stack exchange
>>
Sorry if this is the wrong place to post this. Can someone help me with this?

"Prove that, if y and z are irrational numbers such that y < z, then there exists
some x ∈ Q such that y < x < z."

Don't give me the answer, just need a hint. From what I understand, I ultimately want to prove that there is an infinite set of rational numbers between any two irrational numbers. How can I prove that?
>>
>>9215803
I'm not sure what you're allowed to use to prove this and it's hard to hint without giving the answer but I would 'spread' y and z far enough apart to find an integer between them if you catch my drift
>>
>>9215817
So I could for example say that y is an irrational number and z = y + 1. x can be any rational number between those, but then my proof doesn't cover a case where z = y + 0.1. In fact, it could be that z = y + n where n can be infinitely small. That's what I'm stuck on. Need to prove that a rational number exists between any two irrational numbers, regardless of how far apart they are spread
>>
>>9215828
>So I could for example say that y is an irrational number and z = y + 1
No, z was an arbitrary irrational greater than y, not necessarily y+1.

>but then my proof doesn't cover a case where z = y + 0
This case is irrelevant since z is assumed to be greater than z.

>Need to prove that a rational number exists between any two irrational numbers, regardless of how far apart they are spread
If z-y > 1 then there exists some integer k between z and y.
Otherwise z-y < 1 and there exists some integer n such that n(z-y) > 1...
>>
>>9215831
>This case is irrelevant since z is assumed to be greater than z.
greater than y*
>>
>>9215831
>z = y + 0
>This case is irrelevant since z is assumed to be greater than y
That's what made it click. Thanks
>>
Shieet, Vladimir's death will surely send us back to the stone age.
>>
>>9215831
>Otherwise z-y < 1 and there exists some integer n such that n(z-y) > 1...
and what the rational in between them then? y+1/n isn't rational.
>>
>>9215976
nvm I got it
>>
Can someone explain to me why pic related is true?
>>
>>9215985
which equality do you not understand?
>>
>>9209580
yes
>>
>>9209451
Been studying mathematical linguistics, which so far is pretty much algebra and computational theory, applied to natural language.

I know it's not as sexy as pure mathematics, but I think it's pretty cool, and I always enjoy the more abstract algebraic concepts finding some kind of practical application outside math.
>>
>>9215985
I don't get how we go from the first to the second. I imagine the key behind that step is the same one behind the remaining equalities.
>>
>>9216268
Oops, this was for (You) >>9215989
>>
>>9214738
Please learn basic mathematics before posting such retarded garbage.
I can literally prove AC (the "A" in the name should tell you something) is false assuming some other axioms.
>>
>>9216193
>"applied"
>"practical application outside math"
Grow some balls or get rid of them. You pathetic lowlife.
>>
Group cohomolgy, in particular Bar resolutions. I would prefer been studying more algebraic geometry though.
>>
>>9216283
>X is false
>how come?
>assume the opposite
idiot
>>
>>9216431
>X for propositions
You are literally retarded, I wouldn't surprised if you are physishit.
>assume the opposite
Even this actually works, but here it's unnecessary. Assume that excluded middle is false, now AC is false as well.
>>
>>9216441
>You are literally retarded
>muh arbitrary notation
>>
>>9216447
Not a constructive reply, feel free to delete it.
>>
>>9216451
>Not a constructive reply, feel free to delete it.
What for?
>>
>>9216457
Is that so?
>>
>>9216465
>Is that so?
Trivially yes.
>>
>>9216177
neat man, what do you do? i'm in aerospace
>>
https://www.nytimes.com/2017/10/06/obituaries/vladimir-voevodsky-revolutionary-mathematician-dies-at-51.html

>Nadia Shalaby, his former wife, said he was found dead in his home by friends, whom she had called when she had not heard from him. They then called the police. He had been ill and had apparently collapsed, she said, but the exact cause of death had not been determined.
>>
>>9209451
Harmonics and Musical Octaves
>>
>>9209451

what's the best method to optimize a simple regression (y=mx) for maximum robustness with a small sample?
>>
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>>9214977
What is a good introduction to topos theory? I want to learn some after I finish my category theory book.
>>
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>>9216486
https://arxiv.org/abs/1204.3216
>>
Hey fags I have some questions.

I'm currently studying bachelors of finance/economics at the moment, and I want to extend the mathematical component of it to set me apart from other grads - looking at working in an IB or consulting.

In any case, I'm looking at a masters of econometrics program. Subjects include Baysian econometrics, Time series forcasting etc. I've already studied calc 1,2,3 and linear algebra, then some undergrad stats subjects too.

How much harder is post-grad econometrics compared to undergrad calc and stats?
>>
Anybody have good suggestions on where to go to strengthen my calculus skills? I've recently been learning implicit differentiation but am having trouble with that specifically.
>>
>>9209451
Is a pic related a good first calculus book? How is it different than other '''''standard''''' texts?
>>
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>>9217034
Forgot pic
>>
>>9217038
looks like a meme. the standard stuff works well, but anything should to. just stay away from memes.
>>
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>>9217073
Every book is a meme. I'm asking what I'd be missing specifically, if at all, should I decide to go with this instead of the standard route (think Kline, Lang or Thomas, hell even Stewart) since this book certainly takes a different approach. I should mention that I eventually plan to read Apostol once I develop some intuition and better conceptual understanding. Hopefully somebody who's read this text would be kind of enough to provide some insight.
>>
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>>9216637
I like Mac Lane-Moerdijk a lot. Another good book is the one by Johnstone, but it was too hard for me to get into, so I'd recommend you pick up "Sheaves in Geometry and Logic".
>>
>>9217177
The "infinitesimal approach" part sets off alarm bells. Sounds kinda like it might be one of those watered down, hand-wavy books designed for engineering students. I'd recommend reading Amazon reviews, though. Not sure why you would come to /sci/ with an obscure book no one here has probably used.
Any particular reason for not just using a standard textbook?
>>
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>>9216473
I'm in augmented reality, so the Kalman filter is for making the device know where it is from image & IMU data. But now I'm also doing GNSS (GPS) and IMU.
But I worked in aerospace too, I did my PhD at the DLR.
But I'm a theoretical physicist and so a bit of the Homotopy type theory Wikipedia article is by me as well, for example. I'd rather talk about that :^)

https://www.youtube.com/channel/UCcrSMnEYhIPX_p127jI23qw/videos

>>9216655
go away with your rookie-level autism

https://www.amazon.de/Topos-Music-Geometric-Concepts-Performance/dp/3764357312
>>
>>9216803
Depends on your foundations and how long it takes you to develop """maturity""" and your own intuition. I'm sure you will, but you definitely need to learn Analysis. Calculus by itself isn't sufficient. Some elementary topology wouldn't hurt either, although chapter 2 of Baby Rudin should be enough. It's difficult to judge how much harder it will be, but after you learn Anal you'll have a better idea.

I'm understanding that your curriculum is mainly focused on econ. I would suggest learning stochastic processes too.

Here's a pretty good reading list if you want to get good:
https://phd.chicagobooth.edu/alexander.zentefis/wp-content/uploads/projects/book_list.pdf
>>
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>>9216803
>>9217247
As a matter of fact I have a friend who studies math and finance and I'll have her over and present the very basics of Technical Analysis in the next weeks. I'm writing bad stock market bots sometimes.
Kalman filters are used in the Quant world to, actually.

I think there's a way to bridge all of those. I'll start by writing a parser from a neat functional languageto an existing platform for smart contracts (digital financial contracts), pic related (or any other meme protocol, Cordano, Ethereum). If anyone is interested in dependent types, please reach out.
>>
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>>9217234
>The "infinitesimal approach" part sets off alarm bells.
Care to elaborate?

>Sounds kinda like it might be one of those watered down, hand-wavy books designed for engineering students.
Honestly that just comes off as being unnecessarily elitist and arrogant. I apologize if that wasn't your intention.

>obscure book no one here has probably used.
I learned about the book through the /sci/ guide so I'm sure there's somebody here who has read it.

>Any particular reason for not just using a standard textbook?
I'll most likely end up using the standard text but infinitesimals approach seemed quite interesting after reading about it (see Non-standard analysis).
>>
>>9217323
You say elitist like it's a bad thing.
>>
>>9217323
You could do either one, analysis is hand-wavy garbage either way.
>>
>>9217363
You guys mean to say "Constructive Elitism".
>>
>>9217366
Go to bed, Wildberger.
>>
>>9217378
Why would Wildberger treat "hand-wavy" as an insult?
>>
>>9217234
nonstandard analysis can be done rigorously and doesn't have to be the handwavy shit engineers get served.
there's a reason why it's called nonstandard though, so if you want to have a good foundation for more advanced analysis I'd suggest to don't focus too much on the infinitesimal meme
>>
>>9209968
>implying this board/thread is based around private conversersations

Stop
>>
What are some good basic math books? A few I've heard good things about are:
>Basic Math, Lang
>Precalculus, Axler
>Numbers and Geometry, Stillwell
>What is Mathematics?, Courant

Any other GOAT tier stuff out there?
>>
>>9218169
Algebra chapter 0
>>
>>9218173
thanks, forgot about that one
>>
>>9218173
this is a graduate text, no?
>>
>discover programming freshman year in HS
>focus 90% of my time on said programming
>think rigorous math is stupid stuff, I can make my computer do cool things
>four years later and I have the mathematical maturity of a potato
>>
>>9218216
Forgot to add, I've started working through Spivaks calculus. Is there anything else I can do to unfuck myself before college? I feel like a brainlet around all my friends who are doing high level maths.
>>
>>9218223
Learning how to properly prove things as well as some linear algebra certainly wouldn't hurt
>>
>>9214653
ur bren
>>
>>9214977
How's it going?
>>
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>>9218681
Pretty nicely. I've taken a break of a few days and I've been walking quite a lot and went to an arts museum to see a vaporwavy exhibition. After I wake up, I will start doing math again and I'll make sure I'll know the Lawvere-Tierney topologies thoroughly. Also, I can't wait for it to start snowing. How about you?
>>
>>9209451
What can I do with a degree in Math?
It seems interesting to me but I'm not sure that beyond the theory the jobs are that interesting.
>>
>>9218720
Be a lecturer, become a doctor in math, write papers, give talks.
Maths has almost no application in industry, in case you are looking for it.
>>
I figured a prime generating formula based on dubs.

Where should I publish this?
>>
>>9218723
Mathematical Journal of 4chan
>>
>>9218721
>Be a lecturer, become a doctor in math, write papers, give talks.
>Maths has almost no application in industry, in case you are looking for it.
welp, that's what I feared.
I might study it anyway, I guess I'll have to think about it
>>
>>9218732
Study stats, you will still be able to slide to pure math if you decide later.
>>
>>9218734
If i grad in physics, will I become 2d girl?
>>
>>9218733
>Study stats, you will still be able to slide to pure math if you decide later.
pure math from the get go seems more interesting to me
>>9218734
>Go to trade school kid
you have to take that into consideration. you may choose to ignore it (which I might) and study it anyway, or find something you both like and has potential, or ignore the having fun part completely and just go for something that gives you the best jobs.
>>
>>9218739
Nope. I tried it and it didn't work.
>>
>>9218740
What is your level?
>>
How does your uni approach giving the definition of integrals?
>>
>>9218216
>>9218223
You'll be better off then most people if you keep at this, so don't worry too much about it. If you think you're really interested in CS, you could read an intro discrete math book; it would probably serve as a better intro to proofs than Spivak anyway.
>>
>>9218720
The other post may have misled you. While the only job which lets you do pure math is academia, doing math can get you into plenty of other industry jobs. You can also do it in undergrad and then go to some sort of professional graduate school. The truth is that a math degree is more likely to make you generally smarter than other degrees tend to, so if you have an interest in doing it, it's probably a good idea to get a degree in math.
>>
>>9218743
Did you remember to vote for Trump? Anime isn't real unless you voted for Trump.
>>
>>9218763
Well no I mean you have to get a PhD too, or the anime world would collapse. It needs physicists, but it can only take physicists that voted for Trump. You'll have to go back in time and vote for Trump. You can even do it illegally because Trump has vowed to deal with voter fraud anyway, and since he did get elected you won't even cause a time paradox.
>>
>>9218752
pre image of single variable differentiation
>>
>>9218778
How do you connect it with the area then?
>>
>>9218788
Can you even prove that non-rectifiable entourages on quasi countably tight uniform spaces are F-sets?
>>
>>9214730
thank you for the only non-shit answer

>>9215154
>>9215394
>>9218288
shit answers
>>
>>9218802
That doesn't seem relevant at all to my endeavor.
>>
>>9218816
>not usin g you are bren
上笑い
>>
>>9218788
It's 2D so the physics are easier to deal with. You just have to create the image of something for it to exist. Plus there's already a ton of calibration data on this side of the pencil, so you just have to prevent the collapse of an entire universe. And you never have to work alone unless you're the one character at the end of the universe whose sole responsibility is to save it. If you're really good at your job you can get some fool protagonist to do save the universe for you.
>>
>>9218816
HP50G, don't listen to that texas instruments cuck
>>
>>9209761
calc isn't physically painful
>>
>>9214653
Online scientific calculator or wolfram alpha
>>
>>9218720
the same things you could do without a degree in math
>>
>>9218858
It'll be 3D since I need to take into account time.
>>
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Can someone explain to me why >>9215985
is true? I don't get how we go from the first to the second (or from the second to the third and so on). I imagine the key behind the second step is the same one behind the remaining equalities.
>>
>>9218937
Oh shit I forgot time. There'll probably be like 20 time dimensions too, fuck.
>>
>>9218734
>>9218763
>>9218788
>>>/r/dogs/
>>
>>9218946
Right and wrong. Those mathematicians that dislike the supposed "lack of rigor" in physics should also reject statements proven assuming generalized RH/CH.
>>
>>9218946
Assuming anything that is not proven (except axioms lol) cannot yield a proof. Any mathematician thinking otherwise is an idiot.
>>
>>9218719
I miss the snow, it's so hot here.
>>
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Brainlet here who skipped calculus wanting to revisit it with decent background in algebra, what is the holy bibles of Calculus books? which one do you recommend? multiple books would be nice
>>
"I realized that mathematics is on the verge of a crisis, or rather, two crises.

The first is connected with the separation of “pure” and applied mathematics. It is clear that sooner or later there will be a question about why society should pay money to people who are engaged in things that do not have any practical applications.

The second, less obvious, is connected with the complication of pure mathematics, which leads to the fact that, sooner or later, the articles will become too complicated for detailed verification and the process of accumulating undetected errors will begin. And since mathematics is a very deep science, in the sense that the results of one article usually depend on the results of many and many previous articles, this accumulation of errors for mathematics is very dangerous.

So, I decided, you need to try to do something that will help prevent these crises. For the first crisis, this meant that it was necessary to find an applied problem that required for its solution the methods of pure mathematics developed in recent years or even decades." -Voevodsky

What are you doing about these crises, /mg/?
>>
>>9219277
In all honesty my solution was to create an AI to master paradoxes and let it use a combination of genetic algorithms and n-dimensional metalogic to process the errors in our reasoning and tell us about them. Is that lazy or genius?
>>
>>9219277
I'm trying to actively cause them. It's a small part of my plan to destroy set theory.
>>
>>9219291
idiot
>>
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>>9219220
Honestly fuck calculus, it's a waste of time.
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>>9219494
b) and c) are not provable. a) is trivial.
>>
>>9219497

Are you trolling?

F[x] is a PID, so [math]I_\alpha[/math] is generated by a single polynomial, which may be chosen to be monic. If [math]\alpha = 0[/math] you have [math]g_\alpha = 1[/math].
>>
>>9212184
You seem to be a complete shithead. But congrats on knowing the arbitrary difference your university made up on analysis vs calculus, I'm sure you'll be recognized in time.
>>
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>>9219541

sqrt(1) is just 1

x - 1 - sqrt(3)
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>>9219541
>>9219543
Oops, that should read " Determine the minimal polynomial of sqrt(1+sqrt(3)).."
>>
>>9219572
square it
should be easy from there
>>
>>9219541
>>9219572
Don't repost your garbage here.
>>
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>>9219320
It probably is but I would still like to learn about it to advance, I just can't find the right book
>>
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Threadly reminder to work with physicists.
>>
Threadly reminder that dog-eating is disgusting.
>>
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>>9219661
dog's actually pretty good (depends how it's cooked obviously), very flavourful
>>
>>9219669
I'm sure the physishits in this thread would agree.
>>
>>9219712
the what?
>>
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Need some tiips/tricks/hints for this little bugger of a problem
>>
>>9219732
what have you tried?
>>
>>9219732
(a) infinity
(b) 2
pretty fucking obvious
>>
>>9219733
I tried working out the irreducible polynomial for (a), then writing out the basis, which has 4 elements I believe. Not sure if that's the write idea though
>>
>>9219739
The dimension is equal to the degree of the irreducible polynomial.
Read the theory before you do excercises ffs.
>>
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How do I prove that shit by mathematical induction?? help
>>
>>9219836

Clearly v_1 < 3/2. And v_n < 3/2 implies that v_{n+1} < (3/2 + 3)/3 = 3/2
>>
>>9219841
holy shit im a fucking brainlet, thanks tho
>>
>>9219846
wait but why did you replace vn by 3/2
>>
>>9219854
(not him)
induction hypothesis
>>
>>9219864
how does induction work if it's just a hypothesis (a geuss)?

does that mean the riemann hypothesis also works?
>>
>>9219867
It works like a domino.
You prove that "if a number works, then the next number works". That's setting up the domino pieces.
Then you prove that the first piece works. That's starting the domino.
>>
>>9219867
how can mirrors be real if our eyes arent real?
>>
>>9219220
>>9219597
The answer to this question depends on if you have any interest in learning pure proof-based math (you should, it's fun and way more interesting!). Even if you do want to do pure math, it is probably a good idea to do some computational calculus first, just to build a bit more mathematical maturity before learning proofs, it's very difficult. But if you really think you'd like to skip computational calculus, you'd probably be fine.
With all that said, here are my recommendations.
>Computational Calculus
Stewart's book is the standard, and I don't think you can really go wrong with this. That said, there are lots of other Calculus books out there that are pretty much just as good, if you want to use the one that's free at your library, that should go just as well.
>Rigorous Calculus
I think the best book in this area is Analysis I by Tao. It spends time actually trying to introduce the reader to proofs in general properly, and then goes on to do rigorous calculus. I another good feature is that Tao is actually willing to introduce more advanced analysis where it's appropriate. I think this cleans up the presentation a lot and is more useful in the long run. Lastly, he leaves a fair amount of the results as exercises, which is useful when you're trying to self-study the material.
The other books around this level that are commonly mentioned are the books by Spivak and Apostol, both titled Calculus. Many people have learned successfully from these books, so if you don't like Tao, you can give them a shot as well. I have some opinions about Spivak if you want them, but I don't think it's as good for self study as Analysis I. I haven't read Apostol, maybe someone else can give an opinion.
I hope this helps, good luck with your studies!
>>
>>9219867
>how does induction work
Well ordering.
>>
>>9220044
Subhuman engineer detected.
>>
https://youtu.be/REeaT2mWj6Y?t=1416
based on the logic wildberger uses here for extending the rationals to include algebraic representations of such things as [math]\sqrt(2)[/math], how can you define [math]\sqrt(7)[/math] ? I can't seem to come up with it at all.
>>
>>9220111
here is how he does it
>>
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>>9219642
How do mathematicians cope with the fact that invariants of 4-manifolds are constructed by using quantum field theories?
https://arxiv.org/abs/1705.01645
>>
>>9219867
consider the following two propositions:
>if some domino piece falls, then the next one falls also
>the first domino piece will surely fall
if we know these two things are true, what can we deduce from this ? necessarily all domino pieces will fall. this is precisely induction.
>>
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>>9220029
Yeah, I'm very interested in pure mathematics and that's the main reason I'm coming back to it with regret of not taking the classes necessary.
What does computational calculus imply? Lots of head calculations?
I do not understand why you recommended Analysis I by Tao when I haven't even took Calculus I class yet
>>
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not exactly math related but I need to typeset a me assignment and I want to typeset this less of a pain in the ass. wat do ?
>>
>>9220235
*in latex
>>
>>9220235
[eqn]\gamma_{3} \left( \frac{lbf}{ft^{3}} \right) = \frac{mg}{V} = \rho g = \left(\frac{55.2 \hspace{0.2cm}\text{lbm} }{\text{ft}^{2}} \right) \left( \frac{32.2 \hspace{0.2cm}\text{ft}}{\text{s}^{2}} \right)\left( \frac{\text{lbf}\cdot\text{s}^{2} }{32.2 \hspace{0.2cm}\text{lbm}\cdot \text{ft}}\right) = 55.2 \hspace{0.2cm}\text{lbf/}\text{ft}^{3} [/eqn]
trivial
>>
>>9220251
Can I see the source code? How did you do it?
>>
>>9220267
\gamma_{3} \left( \frac{lbf}{ft^{3}} \right) = \frac{mg}{V} = \rho g = \left(\frac{55.2 \hspace{0.2cm}\text{lbm} }{\text{ft}^{2}} \right) \left( \frac{32.2 \hspace{0.2cm}\text{ft}}{\text{s}^{2}} \right)\left( \frac{\text{lbf}\cdot\text{s}^{2} }{32.2 \hspace{0.2cm}\text{lbm}\cdot \text{ft}}\right) = 55.2 \hspace{0.2cm}\text{lbf/}\text{ft}^{3}

couldn't read your picture well enough to see if it was [math]\gamma_{3}[/math] or [math]\gamma_{s}[/math], but you can change that accordingly
>>
>>9220272
do you know a package that will help me in typesetting to this style of units tracking http://www.katmarsoftware.com/articles/railroad-track-unit-conversion.htm
>>
>>9220282
use tables and \usepackage{cancel} (http://muug.ca/mirror/ctan/macros/latex/contrib/cancel/cancel.pdf ) . there's probably a more elegant way to do it but that'll get the job done.
>>
>>9220292
thanks dude
>>
>>9220298
no prob
>>
Just started on permutation groups

Any tips on finding the centralizer of such groups?
>>
>>9220368
>centralizer
What's that? The center? The commutator subgroup?
>>
>>9220390
https://en.wikipedia.org/wiki/Centralizer_and_normalizer
>>
>>9220390
For g in a group G, C(g), the centralizer of g, is all of the elements in G that commute with g
>>
>>9220397
>>9220444
Oh I didn't know this thing had a name.
>>
>>9220467
Center is just the centralizer of the whole group.
>>
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>>9220233
Computational calculus means you're focusing on how to do computations and solve numerical problems using the tools of calculus. For instance, you'd learn in a computational calculus course how you'd learn how to find the area under the curve of a function (pic related). You would not prove anything rigorously (at best you'll have some intuitive idea of why things makes sense).
In an introductory analysis course, you'd prove that the techniques from calculus are valid (analysis is a much broader subject, but this is usually the starting point). If you look at the table of contents of Analysis I, you'll see that the first four chapters are focused on the basics for doing proofs in general, while the rest of the book is focused on proving the theorems of calculus. As such, it's a good book to learn calculus from the mathematician's perspective.
My recommendation would be do some computational calculus first, before trying to dive into proofs. If you'd like, you could also try reading the beginning of Analysis I while you read something like Stewart, like I said above, the beginning has more to do with proofs in general than calculus in particular.
>>
For a lie group G and G-module M, is the group cohomology [math]H_{{\text{grp}}}^k\left( {G,M} \right)[/math] in any way related to the singular cohomology [math]H_{{\text{sing}}}^k\left( {G,M} \right)[/math] ?
>>
>>9220496
proof: think
>>
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>>9220552
>weeps visibly while using approximations
meirl
>>
>>9220535
there is nothing to prove
>>
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does anyone else get autistic joy from reading Euclid's Elements?
>>
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>>9218946
they separate the 7/9 *10^n+2 and write it as 70/9 * 10^n+1 and just add with 8 *10^n+1 . that leaves you with 3/9*10^n+1 which can be written as -7/9*10^n+1 + 1/9 * 10^n+2
>>
>>9220769
Use the fucking definition.
>>
>>9209882
Tone down on the egoism and you may end up discovering something worthwhile.
>>
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TIps/tricks/hints for part b?
>>
>>9220979
It's trivial, where do you get stuck?
>>
>>9220979
Take 1,a,a^2, ...
Let k to be the smallest number such that 1,a,a^2,...,a^k are linearly dependent.
You can write a non-trivial combination of 1,a,a^2,..,a^k and get 0 (make the coefficient of a^k 1).
If you replace a with x, you can easily see that this will be the minimal polynomial of a in F and it will satisfy the properties required in (b).
>>
>>9220979
ok I'll complete it:
Let g be a non constant polynomial in F with g(a)=0.
Divide g by f.
g=qf+r with degr<degf
r=g-qf
r(a)=0
Because f the minimal polynomial, r must be 0, which means that f divides g, which means that g is in fF[x].
Therefore I_a is a subset of fF[x].
Obviously fF[x] is a subset of I_a.
Thus, they are equal.
>>
>>9218732
Assuming you have at least a BS in mathematics, you could probably get an MS in accounting in a year and then get CPA certification.

Alternatively, you could study some statistics and financial mathematics and that take your first two actuarial exams.

Either way, you should start off making high 5-figures or low 6-figures, depending on your market - and if you can climb your way up to partner, you can easily make well into 6-figures range, or even 7.
>>
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So this proof isn't giving me any grief but my professor hinted at using the "eventual comparison test" but I feel the limit comparison would be easier. Here is a pic of question and proof I did. If my proof is invalid, why? I can also post the limit comparison test given in my book if needed
>>
>>9221524
>If my proof is invalid, why?
Because it involves analysis, which is not well-defined.
>>
>>9221524

Eventual comparison is easier. Since a_n --> 0, it is eventually less than 1; and when a_n < 1, a_n^2 < a_n.
>>
>>9221548
The largest number set we are dealing with in this course are the reals. Also, we are not dealing with matrices nor rings etc so I am pretty sure we can assume that an is well defined. If I am off, could you provide a counter example to help make it more clear for me? Also if you are trolling me I have autism and this constitutes as cyber bullying my dude

>>9221562
I am struggling with how is it easier than what I posted. Yes what you said is right but I would have to formally declare some N such that (a_n)<1 for all n>=N and that seems like slightly more work. Honestly, I am mostly trying to see why my professor pushed using the eventual comparison
>>
>>9221574
>The largest number set we are dealing with in this course are the reals.
Which can't be shown to be well defined as of right now. Actually you could even prove their non-existence if you assume some pretty intuitively clear axioms.
>Also, we are not dealing with matrices nor rings
Rings do not form a set, but neither do the so-called "reals".
>>
>>9221562
>Since a_n --> 0, it is eventually less than 1
>"limits"
>eventually
The engineering thread should be somewhere nearby.
>>
>>9221583
why u bullying me bro
>>
>>9221583

Let R be the set of subsets X of the rationals that have no largest element, are non-empty, are not equal to the entire set of rationals, have the property that if x is in X and y < x then y is in X.

Then R can be made into a field, which is the field of real numbers.

Alternatively there is a construction of a completion of a topological group in Bourbaki's Topology which can be applied to the rationals.
>>
>>9221601
>Let R be the set of subsets X of the rationals that have no largest element, are non-empty, are not equal to the entire set of rationals, have the property that if x is in X and y < x then y is in X
Prove that such a set is well-defined.
>Then R can be made into a field
Prove it.
>>
>>9221612
master troll do we need to prove the rationals are also well defined and that subsets of well defined sets are also well defined
>>
>>9221617
Absolutely, but that is already fairly well-established so there is no need to do it here.
>>
>>9221612

By powerset axiom, the powerset of Q is a set.

The less than relation on Q is given by a first-order formula in the language of set theory. So by the axiom of comprehension we can pick out the subset R of P(Q).

To make R into a field, define X + Y = {x + y : x in X and y in Y}, 0 = { rationals less than 0}, 1 = {rationals less than 1}, X * Y = {x * y : x in X and y in Y} if X, Y are both >= 0, and -X = {-x : x rational but not in X}. Multiplication extends to the negative numbers, and it is easy to see that the distributive, commutative, and associative properties hold.
>>
>>9221626
>By powerset axiom
>by the axiom of comprehension
In what system are you working? Assuming it is ZF, prove that these axioms are independent of ZF.
>it is easy to see that the distributive, commutative, and associative properties hold
Prove that these properties in fact hold.
>>
>>9221626
>To make R into a field
Also prove that this field is isomorphic to the so-called "field of real numbers".
>>
>>9220552
>refuses to touch calculator
>insists he works alone on assignments by choice
>double checks work
>makes arithmetic mistakes
Me
>>
>>9221656
Seperation is independent of all axioms except replacement, look at the axioms satisfied by the class of ordinals. Also I believe the constructable universe satisfies not power set, since definiability can be formalized without powerset.
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Need to find the center of the general linear group of 2x2 Matrices
I barely passed linear algebra so I have no idea how to do this when suddenly this appears in group theory class
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>>9221663

http://planetmath.org/everyorderedfieldwiththeleastupperboundpropertyisisomorphictomathbbrproofthat

X + ( Y + Z ) = { x + y + z : x in X and y in Y and z in Z} = (X + Y) + Z

(X * Y) * Z = {x * y * z :x in X and y in Y and z in z} = X * (Y * Z) if X, Y, Z are nonnegative.

X + Y = {x + y : x in X and y in Y} = Y + X

X * Y = { x * y : x in X and y in Y} = Y * X
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>Proof: omitted
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>>9221730
Google you faggot
https://groupprops.subwiki.org/wiki/Center_of_general_linear_group_is_group_of_scalar_matrices_over_center
https://math.stackexchange.com/questions/299626/the-center-of-operatornamegln-k?noredirect=1&lq=1
https://math.stackexchange.com/questions/960342/center-of-general-linear-group
https://math.stackexchange.com/questions/737592/find-the-center-of-the-group-gln-r-of-invertible-nxn-matrices
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>>9219732
I haven't even studied this shit lmao
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doing differential equations

/blog
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>>9222514
complex plane is now 4d, get newspaper on the phone
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>>9222514
>irreducible real quartic
no shit you haven't studied it
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>>9222587
Brainlet, where do you think it went wrong? I'll guide you through it


>>9222601
Describe the solutions to the given equations please
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>>9222625
>Describe the solutions to the given equations please
You can find them using Wolfram if you're that lazy, or just use the quadratic formula

protip: all real quartics are reducible
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>>9222625
You can break that polynomial of 4th degree into two irreducible polynomials of 2nd degree.
For the reals specifically the only irreducible polynomials are those of 2nd degree with negative discriminant.
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>>9222639
Oh hehe did it over Q
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Theoretical Computer Science for the Working Category Theorist
https://arxiv.org/pdf/1710.03090.pdf
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>>9222639
>protip: all real quartics are reducible
Sure, if real numbers exist. This should already sound fishy to you.
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>>9223308
>Category theory
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>>9223579




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