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# /sci/ - Science & Math

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Pure Mathematics edition
Talk maths
Prior >>12275236

 >> Anonymous Wed Oct 28 19:01:19 2020 No.12283975 >>12283965>premature ejaculating a new thread fifteen posts too early
 >> Anonymous Wed Oct 28 19:03:59 2020 No.12283986   File: 405 KB, 685x497, 654654.png [View same] [iqdb] [saucenao] [google] [report] >>12283975Tell us how you really feel.
 >> Anonymous Wed Oct 28 19:57:39 2020 No.12284227 File: 57 KB, 600x600, 7ecde3bf.jpg [View same] [iqdb] [saucenao] [google] [report] I was gonna make the hyperglyph edition :{Anyway, are there any fundamental properties that govern relations or algebras, that require more than 3 inputs? Associativity, order, commutativity, and equivalence are all 2 input. Transitivity is three. I see it relating to dimensions, with 2 dimensions you have a symmetry between objects, and with 3D, you have transitivity which lets you flesh out interactions throughout the space. But are there any other base level properties that require a fourth dimension?
 >> Anonymous Wed Oct 28 19:58:41 2020 No.12284233 >>12284227Oh and distributive is 3 as well
 >> Anonymous Wed Oct 28 20:20:41 2020 No.12284305 File: 31 KB, 500x375, 1603646149050.jpg [View same] [iqdb] [saucenao] [google] [report] Can someone explain this to me, I'm having a hard time wrapping my head around the concept.27 - -16 = 43Why do the two negative signs here cancel each other out?My brain is taking this to mean that I'm "subtracting" the negative sign from the value of -16?
 >> Anonymous Wed Oct 28 20:27:53 2020 No.12284334 >>12284227Your question is not really clear because it's not obvious what should count as fundamental. People consider identities and relations involving arbitrarily many variables all the time.
 >> Anonymous Wed Oct 28 20:28:25 2020 No.12284337 >>12284305A negative number is an anti. You're removing anti units. If negative is below sea level, you're removing depth, going the opposite direction. That means height.
 >> Anonymous Wed Oct 28 20:29:58 2020 No.12284340 >>12284334Some property of reals or other simple, intuitive sets, that requires >3 elements to describe, that the set would look unusual without
 >> Anonymous Wed Oct 28 20:33:22 2020 No.12284355 How they know outliers are Q1-1.5 X IQR and Q3+ 1.5 x IQR?
 >> Anonymous Wed Oct 28 20:34:06 2020 No.12284357 >>12284340Well you can't really take a property away from a structure, it either has it or it doesn't. Abelian groups are medial magmas, which means that they have (xy)(zw)=(xz)(yw)
 >> Anonymous Wed Oct 28 20:34:29 2020 No.12284358 >>12284355It's the definition of outlier They chose it to be that way
 >> Anonymous Wed Oct 28 20:36:11 2020 No.12284367 >>12284357>abelian groupsThanks thats interesting. Although less powerful than others imo because it relies on position very strongly
 >> Anonymous Wed Oct 28 20:39:03 2020 No.12284375 >>12284357But wait aren't they commutative so that's trivial?
 >> Anonymous Wed Oct 28 20:40:01 2020 No.12284378 >>12284337That's a good way of conceptualizing it, thanks.
 >> Anonymous Wed Oct 28 20:53:20 2020 No.12284409 >>12284375Well it's a thing that is true for any abelian group by an easy argument. If you don't know that you have an abelian group it can be useful though, see the Eckmann-Hilton argument.
 >> Anonymous Wed Oct 28 21:17:15 2020 No.12284449 File: 200 KB, 1024x931, Pacfc3.jpg [View same] [iqdb] [saucenao] [google] [report] Any songs for the feel of pic related + writing symbols/definitions? Here's one example:https://www.youtube.com/watch?v=TY5Hq_5FbT0
 >> Anonymous Wed Oct 28 21:18:17 2020 No.12284452 >>12284409Thanks nonny
 >> Anonymous Wed Oct 28 23:54:16 2020 No.12284859 >>12284305For any number x, -x is (by definition) the unique number y satisfying the property that x+y=0. But this defining property tells us that x = -y = -(-x).
 >> Anonymous Thu Oct 29 00:11:40 2020 No.12284895 Suppose there is an idempotent $f: M\to M$ such that $Im(f) = A$I'm trying to prove that the map $A\bigoplus B \to M$ is an isomorphism. I would greatly appreciate a hint in the right direction. I can't seem to figure out why the induced homomorphism would have anything to do with the idempotent.
 >> Anonymous Thu Oct 29 00:59:16 2020 No.12285011 >>12284895Can someone actually clarify what the notation MM means?
 >> Anonymous Thu Oct 29 02:17:36 2020 No.12285147 >>12285011What do you mean by MM?
 >> Anonymous Thu Oct 29 02:24:54 2020 No.12285160 >>12284895Also I should’ve mentioned these are modules. Let f’ denote the induced homomorphism. I’ve thought about it a little more and I think it comes down to coming up with a $g:M \to A \bigoplus B$ such that f’g = 1_M and $gf’ = 1_{A \bigoplus B}$. Coming up with the right g is not obvious to me tho.
 >> Anonymous Thu Oct 29 02:59:58 2020 No.12285214 File: 216 KB, 1660x860, image.png [View same] [iqdb] [saucenao] [google] [report] Does someone know why Poincaré's inequality for a ball ends up with the constant in the upper bound scaling with the radius?It seems like since you're doing the same COV in the last step, the Jacobians would cancel. I'm sure this is really trivial but it's driving me crazy.
 >> Anonymous Thu Oct 29 03:03:11 2020 No.12285220 File: 59 KB, 1554x333, F7ECCF84-796D-443D-9850-7C8DE22853D1.jpg [View same] [iqdb] [saucenao] [google] [report] Solve this
 >> Anonymous Thu Oct 29 03:28:17 2020 No.12285261 >>12285214Because along the way you use Holders inequality for the function on rhs and the characteristic function of the ball.
 >> Anonymous Thu Oct 29 03:39:14 2020 No.12285287 >>12285261Are you speaking in general, or is that what's actually happening in the last step here in the screenshot? Thanks for the help.
 >> Anonymous Thu Oct 29 04:01:36 2020 No.12285308 >>12285147Sorry, the entire f: m --> m, notation.
 >> Anonymous Thu Oct 29 04:04:31 2020 No.12285314 >>12285287Just look at this:https://ocw.mit.edu/courses/mathematics/18-152-introduction-to-partial-differential-equations-fall-2005/lecture-notes/lecture4.pdfI know it is in 1 dimension and only for C^1 functions with 0 values on the boundary, but the general idea is similar, just more involved.
 >> Anonymous Thu Oct 29 05:19:25 2020 No.12285451 >>12285308Function f from set M to set M.
 >> Anonymous Thu Oct 29 05:20:54 2020 No.12285457 >>12285451Oh, and for the armchair cat theorists, I deliberately called it a function because that anon will have no use of knowing that it's a morphism or an arrow or a mapping or whatever.
 >> Anonymous Thu Oct 29 05:23:44 2020 No.12285465 How are you supposed to prove that 0 < 1 just from the ordered field axioms? He says you can prove it in my book but I think he might be forgoing to mention some assumptions or something
 >> Anonymous Thu Oct 29 05:26:34 2020 No.12285469 >>12285465What are the axioms?
 >> Anonymous Thu Oct 29 05:31:14 2020 No.12285473 >>12285469There exists operators + and * and an order relation < such that>x+y=y+x>x*y=y*x>x(y+z)=x*y+x*z>x*(y*z)=(x*y)*z>x+(y+z)=(x+y)+z>if x>y, x+z>y+z>if x>y and z>0, x*z>y*z
 >> Anonymous Thu Oct 29 05:32:47 2020 No.12285478 >>12285469Oh wait sorry there's more>0 exists and x+0=x>1 exists and x*1=x>there exists y such that x+y=0>there exists y such that x*y=1 unless x=0
 >> Anonymous Thu Oct 29 05:47:46 2020 No.12285498 >>12285473>>12285478Doesn't it specify that the order is total?
 >> Anonymous Thu Oct 29 05:50:39 2020 No.12285503 >>12285498It has to be, i.e. the symbol < is misleading and he should have used $\leq$ instead.As it stands, his axiomatization of field division doesn't even rule out 0=1.
 >> Anonymous Thu Oct 29 05:51:46 2020 No.12285504 Bros... Holy shit... I just invented something... Cyclical commutativity. Just arrange x y and z in a circuit like a triforce, and it goes so that (x*y)*z = x*(y*z) = x*)*y*(z* where it would loop around, and you put x in back as y*(z*x) because y is the new open position and is first in line in the cycle, and then this becomes (y*z)*x which gives you associativity for free!
 >> Anonymous Thu Oct 29 05:53:02 2020 No.12285506 >>12285498>>12285503What is a total order, he hasn't used that word. Also the symbol < is just to denote an arbitrary order relation in general
 >> Anonymous Thu Oct 29 05:57:37 2020 No.12285513 >>12285503Yes I know, I was mentioning that to see if that was enough for him to come up with a proof. >>12285506It means that for all two members of the field it must be that xy.
 >> Anonymous Thu Oct 29 05:59:20 2020 No.12285516 File: 102 KB, 1920x1080, WIN_20201029_05_59_00_Pro.jpg [View same] [iqdb] [saucenao] [google] [report]
 >> Anonymous Thu Oct 29 06:01:26 2020 No.12285520 >>12285513Ah yes, his order relation is total although the = symbol only refers to x and y that are equivalent in the system of discourse
 >> Anonymous Thu Oct 29 06:15:08 2020 No.12285541 >>12285513>It means that for all two members of the field it must be that xy.No, that's called something else, "connected" or "connex" or something like that (the constructivists may have yet another word).Totality is specifically "x < y or y < x" and entails reflexivity (the "connex" relations are precisely those whose reflexive closure is total), which is why I suggested that writing the order relation symbol as < was misleading, as it suggests irreflexivity even though only the reflexive interpretation is correct (in the sense of being consistent with 0 < 1, because the axiomatization is satisfied by the field with one element).
 >> Anonymous Thu Oct 29 06:45:19 2020 No.12285599 File: 652 KB, 2414x1706, 20201028_043404.jpg [View same] [iqdb] [saucenao] [google] [report] I'm gonna do it anyways, but will studying pure geometry have any carryover to university level mathematics?It seems that nowadays most geometry is done analytically
 >> Anonymous Thu Oct 29 06:55:08 2020 No.12285613 >>12285599It'll help you learn basic proof structure if you're new to maths. Other than that pure geometry is pretty niche.
 >> Anonymous Thu Oct 29 06:58:13 2020 No.12285616 >>12285613I already understand proofs for the most part.But I just really like geometry.and by pure geometry I don't necessarily mean euclid only, I was studying projective geometry
 >> Anonymous Thu Oct 29 07:02:19 2020 No.12285622 File: 1.26 MB, 640x480, hacker.gif [View same] [iqdb] [saucenao] [google] [report] >>12285616Just do it friend, maybe it will give you a new perspective that people don't get doing analytic geometry.
 >> Anonymous Thu Oct 29 07:05:46 2020 No.12285626 >>12285622Thank you for the support bro :)
 >> Anonymous Thu Oct 29 07:09:01 2020 No.12285630 File: 284 KB, 824x1200, geometry provides us with many expressions.jpg [View same] [iqdb] [saucenao] [google] [report] >>12285599 (checked)I am also curious about this. Geometry seems to be the most "controversial" branch of mathematics (at least according to my limited knowledge of the subject). There are a few people like Coxeter who try to keep pure synthetic geometry alive, and at the other extreme you get people like Dieudonne who reportedly said, "A bas Euclide! Mort aux triangles!" ("Down with Euclid! Death to triangles!").Compared to other branches of modern mathematics synthetic geometry feels very much out of place. The other branches of math seems more or less unified whereas pure synthetic geometry seems to proceed in its own particular way. Maybe its because pure geometry is such an old subject. Do the big brains of /sci/ know how we ended up with this state of affairs? Does pure geometry have a future besides being a quaint curiosity taught in a high school course and then forgotten?
 >> Anonymous Thu Oct 29 07:24:32 2020 No.12285649 >>12285630set theory is the ultimate cause of our modern degeneracy. embrace type theory, embrace topos theory... embrace synthesis
 >> Anonymous Thu Oct 29 07:25:30 2020 No.12285651 >>12285630I'm not entirely sure. I think a lot of it is derived from Hilbert iirc, when he started the shift from geometry as being the foundation of mathematics to logic, and geometry was kind of thrown to the side as being a lesser derivation from logic."Hilbert once remarked that instead of points, lines and planes one might just as well talk of tables, chairs and beer mugs"I'm not quite sure if I really agree with that though. Anyways, It still seems really strange to me to exclude pure geometry from modern mathematics since it still seems that much modern mathematics is derived from geometry, e.g. the real numbers which are essentially just an attempt to describe a line on which you can choose any point you would like, no?
 >> Anonymous Thu Oct 29 07:27:57 2020 No.12285654 >>12285649Are these the salvation for would be pure geometers?I recall seeing something about topos theory while reading about synthetic geometry.
 >> Anonymous Thu Oct 29 07:30:16 2020 No.12285657 >>12285649>topos theoryNo, no, don't embrace topos theory. It's like dialectical materialism, a fad claiming novelty when it's just old crap in disguise. Topoi are a failed attempt at type theory that was clinging too much to set theory.> embrace synthesisThere is not only one synthetic approach. But yeah, please embrace types and computation.
 >> Anonymous Thu Oct 29 07:33:24 2020 No.12285661 >>12285651>real numbers which are essentially just an attempt to describe a line on which you can choose any point you would like, no?Euclidean geometry can get away with real numbers. You just need "constructible numbers" which is the closure of $\mathbb{Q}$ by taking square roots. It's a strict subset of algebraic numbers, and in particular it is a countable set with decidable equality.
 >> Anonymous Thu Oct 29 07:44:53 2020 No.12285676 >>12285651Is it really Hilbert's fault? Ultimately Hilbert's system was merely a correction of Euclid's. That quote about tables and chairs was really meant to say that we should not accept any "intuitively obvious" fact about points, lines, and planes except for those explicitly stated in the axioms. I think Hilbert's work was ultimately a continuation of a long tradition of refinement in the foundations of geometry going back to von Staudt, Pasch, and others. Hilbert's being overly autistic about rigorous logic may be a turn off for most people interested in pure geometry rather than mathematical logic per se, but I think ultimately his work was in line with the geometric tradition up to that point, it was only that it took hairsplitting to a new level. (Which is not a bad thing in itself, so far as it is limited to courses in the foundations. Trying to implement Hilbert into an elementary textbook would likely lead to failure, as George Bruce Halsted exemplifies.)I suspect that the big shift in geometry came when linear algebra came to the forefront as a possible foundation for geometry, and so the "relational" axioms of pure geometry were substituted with more "operational" (algebraic) axioms, as it is done in the definition of a vector space.
 >> Anonymous Thu Oct 29 07:45:33 2020 No.12285677 Does anyone know the following topological property? I noticed that it shouldnt be possible to decompose S^n into a disjoint union of arbitrarily many images of closed paths. Formally, can you find paths $\gamma_i: [0,1] \rightarrow X$ so that $X = \bigcup_{i \in I} \gamma_i ([0,1])$ is a disjoint union?A space which has this property is clearly $[0,1]^2$. But for $S^n$ it seems impossible! It would be obvious to try the paths which go from a point in the boundary towards 0, but just intuitively I don't know how to resolve the situation at 0 then because all the paths interfere with eachother. It reminds me of the hairy ball theorem, as in that there must be a point where the paths circle or meet, both situations which would leabe that point not in the image of the paths...Furthermore given such a collection of paths, one could factor $X$ into a family of subspaces$A_t = {\gamma_i(t) : i \in I}$ which reminds me of the product measure, because there an integral in R^2 decomposes into integrals over lines...
 >> Anonymous Thu Oct 29 07:46:02 2020 No.12285679 >>12285616Euclidean geometry has already been solved by Tarski-Seidenberg, so unless you're interested in the computational efficiencies of geometric constructions, or an acolyte of Wildberger, you won't find much theoretical insight from it anyway.>>12285622 >maybe it will give you a new perspective that people don't get doing analytic geometryI was going to say that this is the best reason to study geometry, aside from artistic purposes. But "gaining a fresh perspective" sounds pretty artistic as well.And in the wake of the mechanization of geometry and automation of constructions, "artistic insights" may be the only way to advance the subject. I don't keep up with what they're doing at Erlangen, but Hilbert axiomatization (really, Godel's completeness theorem) didn't put an end to logic, nor did the Turing machine put an end to computability theory. If these are any indication, geometry will return to being an "applied math", with its development guided by advances in other subjects like cosmology, geography, and maybe even art.>>12285541Turns out the proof isn't quite as simple as I expected: to prove $1 < 0 \implies 0 < 1$, show that 0 is absorbing, then multiply both sides by -1, and then add 1.
 >> Anonymous Thu Oct 29 07:46:23 2020 No.12285680 >>12285661Well yes, euclidean geometry can be done with just constructable numbers of course. I saw a little bit about geometry with field extensions of the rationals. But I was just trying to say that the real number system is an attempt to "fill in" the line, originally, right?Like we can take the rational numbers plus some constructable irrationals, but then you have "numbers" like pi which obviously are not algebraic and not constructable, but there is some idea of its range. And then the real numbers say that we can continually approximate this an infinite number of times.Not necessarily saying I feel the real numbers are necessary, just trying to say that the idea of real numbers doesn't really make sense without geometry as the foundation, I feel.
 >> Anonymous Thu Oct 29 07:52:58 2020 No.12285693 >>12285661Sounds like something of a cop out. And you still have to deal with irrational numbers, even if it's a countable subset of them. And even the ancient Greeks weren't so strict about compass and straightedge. They came up with a lot of curves that can't be constructed just with compass and straightedge. Even something as simple as the conic sections can't be constructed that way in their entirety (you can only construct conics point-by-point with compass and straightedge, not a whole continuous curve). The obsession with compass and straightedge was just something of a curiosity and a desire to reduce geometric constructions to the simplest tools, but it's not like it was illegal for Greek mathematicians to work with curves which involved non-constructible numbers.And Dedekind cuts really are a refinement of Eudoxus' theory of proportion as described in Euclid's fifth book, which arose as a nned to dela with irrational quantities after the Pythagoreans found out about incommensurable geometric quantities.
 >> Anonymous Thu Oct 29 08:00:40 2020 No.12285708 >>12285680>Not necessarily saying I feel the real numbers are necessary, just trying to say that the idea of real numbers doesn't really make sense without geometry as the foundation, I feel.I feel the same way, but there may be more to it. For example, Euler's number and the exponential function arise when dealing with compound interest, so we have a fairly concrete application of mathematics involving real numbers (even transcendental numbers) and yet pretty much unrelated to geometry. Then again, the underlying issue is the same: the assumption that space (in the case of geometry) and time (in the case of compound interest) are continuous. And this assumption may or may not be true, but it works well enough in practice, so it's a good enough approximation for most purposes.
 >> Anonymous Thu Oct 29 08:34:21 2020 No.12285760   File: 52 KB, 511x416, DynamicHedging.jpg [View same] [iqdb] [saucenao] [google] [report] >>12285708>pretty much unrelated to geometryOn the contrary, it demonstrates a fundamental dependence on the geometry of continuous-time, and this is a sticking point for mathematical finance, where the actual trading and information updating can only ever happen in discrete time steps.>>12285677Decompose into a disjoint union of spheres, and take the latitude lines for each?
 >> Anonymous Thu Oct 29 09:00:22 2020 No.12285814   >>12285677I think you can skewer the sphere through its diameter, and then for each $r\in (0,1]$ form the radius-r sphere (minus the two punctured points at the poles, which are part of the axis) out of its latitude lines (great circles).
 >> Anonymous Thu Oct 29 09:40:09 2020 No.12285878   >>12285677Does $e^{2\pi it}$ count as a closed path for $S^1$?If it does, then you can skewer $S^2$ along any axis, and then decompose it as this axis plus a concentric series of radius-r spheres (minus the pair of antipodal "poles") for $r\in \left(0,1\right]$. Each sphere decomposes in turn into a series of $S^1$ "latitude lines", indexed by their angle with the north pole, and for which the decomposition is "known".The case for general $S^n$ should follow inductively.
 >> Anonymous Thu Oct 29 11:11:10 2020 No.12286048 >>12283965What do you call the idea that if you choose an infinite number of things from a finite set, some element gets chosen an infinite amount of times?I know I've seen this before in Ramsey theory
 >> Anonymous Thu Oct 29 11:13:32 2020 No.12286052 >>12286048Pigeonhole principle or (sometimes) the Dirichlet principle
 >> Anonymous Thu Oct 29 11:14:02 2020 No.12286053 >>12285214never mind I'm retarded! This is why I shouldn't do math at 3am
 >> Anonymous Thu Oct 29 11:44:07 2020 No.12286141 >>12285677>I noticed that it shouldnt be possible to decompose S^n into a disjoint union of arbitrarily many images of closed pathsIt is possible, use the constant paths.
 >> Anonymous Thu Oct 29 12:10:08 2020 No.12286209 Have you guys ever printed off an entire textbook PDF? I'm thinking about starting with Lang's basic mathematics but I have a hard time focusing on a computer and I don't want to pay \$60 for the book. I was thinking about just going somewhere to get it printed off and just throwing it into a binder. Has anyone done this before and how much did it cost?
 >> Anonymous Thu Oct 29 12:15:49 2020 No.12286226 >>12286048>>12286052is this contradiction - m elements in set, N = max{n|n= times element e_i chosen i=1,...,m}then finite mN+1 > inifinity choicesor is that the pigeonhole
 >> Anonymous Thu Oct 29 12:18:02 2020 No.12286235 Just lost my 4.0 because the shittily made chink spyware that my Uni forces everyone to install decided to crash in the middle of a proctored test.
 >> Anonymous Thu Oct 29 12:21:13 2020 No.12286249 >>12286209I did this for the first courses. I think it was around 6 dollars with binding included for each, but I'm not american.
 >> Anonymous Thu Oct 29 12:30:23 2020 No.12286276 File: 2.39 MB, 2277x1867, ClXItsR.png [View same] [iqdb] [saucenao] [google] [report] >>122862496 dollars would be amazing. I'm looking at printing it at my local staples and it's 5 cents for each page if you print over a thousand pages which isn't too bad. But If I have to print at least 1000 pages I'll have to print multiple textbooks but I don't really know which ones to get. Should I just follow the main texts on this meme chart?
 >> Anonymous Thu Oct 29 12:32:07 2020 No.12286284 >>12286276Just print off Napkin and Lang, that'll be over 1000.
 >> Anonymous Thu Oct 29 12:35:00 2020 No.12286290 >>12286276Book of Proof and Spivak are high quality textbooks, too.
 >> Anonymous Thu Oct 29 12:38:31 2020 No.12286304 >>12286048Common sense.
 >> Anonymous Thu Oct 29 12:43:40 2020 No.12286326 >>12286284>>12286290By napkin do you mean guesstimation? So I should go Lang's -> proofs -> napkin -> Spivak?
 >> Anonymous Thu Oct 29 12:46:14 2020 No.12286335 >>12286326Evan Chen's Napkin. Look it up.
 >> Anonymous Thu Oct 29 12:46:48 2020 No.12286339 >>12286209That's somewhat standard practice in my country. Can't tell you about prices but just to let you know it's not that out there as an idea.>>12286276I never noticed the background on that image, hah.I'm noone to say, but personally for "precalc" stuff I just kept some pdfs or googled when I had forgotten something while reading other courses. For proofs I just kinda went by feeling/learning what the book used, but maybe a book on that isn't bad.Spivak is a neat book, I didn't complete it. But it's clear and very readable. Cool exercises.Shilov I couldn't quite get through. I used Friedberg and I loved it.D&F always gets criticized for being more of a reference than anything, but I'll let someone else comment on that.>>12286326He means Evan Chen's Napkin Project: https://web.evanchen.cc/napkin.html
 >> Anonymous Thu Oct 29 12:49:04 2020 No.12286351 >>12286326The infinitely large napkin, by Evan Chen https://venhance.github.io/napkin/Napkin.pdfYou could also print off Fuchs Fomenko, another top tier book
 >> Anonymous Thu Oct 29 12:50:19 2020 No.12286357 >>12286326He means the napkin by Evan Chen.
 >> Anonymous Thu Oct 29 12:51:21 2020 No.12286361 >>12286326I think he means Evan Chen's napkin. You can read it at https://venhance.github.io/napkin/Napkin.pdf
 >> Anonymous Thu Oct 29 12:53:10 2020 No.12286369 >>12286335>>12286339Jesus christ that napkin project looks seriously impressive. Do I just start that after I'm done with calc?
 >> Anonymous Thu Oct 29 12:54:43 2020 No.12286379 File: 57 KB, 1266x680, I am so proud of this community.jpg [View same] [iqdb] [saucenao] [google] [report] >>12286335>Evan Chen's Napkin. Look it up.>>12286339>He means Evan Chen's Napkin Project: https://web.evanchen.cc/napkin.html>>12286351>The infinitely large napkin, by Evan Chen https://venhance.github.io/napkin/Napkin.pdf>>12286357>He means the napkin by Evan Chen>>12286361>I think he means Evan Chen's napkin. You can read it at https://venhance.github.io/napkin/Napkin.pdf
 >> Anonymous Thu Oct 29 13:05:48 2020 No.12286424 >>12286369In all seriousness tho, don't actually print off Napkin (unless you want to ). Use it during your summers (I assume you're actually a student, and not a hobbyist. If you are read it whenever you want to find a new topic to learn) to wet your appetite for future topics that you'll find interesting
 >> Anonymous Thu Oct 29 13:06:43 2020 No.12286428 File: 10 KB, 149x533, sq.png [View same] [iqdb] [saucenao] [google] [report] I simplified this square root without calculator
 >> Anonymous Thu Oct 29 13:12:42 2020 No.12286455 >>12286424I am a student but the reason I'm considering printing it out is because I have ADD so it's hard for me to study at my computer.>>12286379Kek
 >> Anonymous Thu Oct 29 13:20:25 2020 No.12286496 >>12286369I mostly used it to fuck around and learn neat thingsSome of it you don't even need calc for>>12286455Napkin has a graph inside of chapter dependenceYou could print something that appeals to you and its related chapters
 >> Anonymous Thu Oct 29 13:50:37 2020 No.12286636 File: 367 KB, 322x445, 60C6D0BF-0DC2-40AF-BC7C-CEDA41906755.png [View same] [iqdb] [saucenao] [google] [report] I'm a mathlet. Can I pass Calculus 1 by memorizing problem types? It's the only thing that works for me and I end up reverting back to it. For example I'm learning logarithms right now so I just memorize what certain problems look like and I copy the steps on homework/quizzes/exams.
 >> Anonymous Thu Oct 29 13:52:47 2020 No.12286646 >>12286235Email the professor. Heavily suggest in the email that you will contact the dean if they do not permit you to retake the exam.
 >> Anonymous Thu Oct 29 13:53:29 2020 No.12286649 >>12286636it's easier just to do the practice.
 >> Anonymous Thu Oct 29 13:56:37 2020 No.12286658 >>12286428Impressive
 >> Anonymous Thu Oct 29 14:00:23 2020 No.12286673 Feeling a bit disappointed lads. Is all math really just abstract nonsense? I thought it was supposed to describe reality.
 >> Anonymous Thu Oct 29 14:00:26 2020 No.12286674 >>12286649No that's what I'm saying, I practice and I end up just mentally categorizing everything into types of problems because that's the only way I learn/complete my work. It's the only way I ""learn"" math, I don't understand jack shit otherwise.
 >> Anonymous Thu Oct 29 14:07:48 2020 No.12286710 >>12286428>>12286658You know the trick for when something is a multiple of 3 right?
 >> Anonymous Thu Oct 29 14:11:04 2020 No.12286723 >>12286674doomed to fail the moment you encounter a problem that isn't in one of these categories (which will happen). what's so difficult about reading the definitions and theorems?
 >> Anonymous Thu Oct 29 14:18:21 2020 No.12286752 Why do we focus so much on arbitrary categorizations of objects and existence theorems? Why don't mathematicians work more on computational structures and methods, on making structures that represent physics, and of finding their numerical/elemental properties? I know some theorems can come to be useful but the majority of them seem in the wrong direction.
 >> Anonymous Thu Oct 29 14:18:43 2020 No.12286756 >>12286674That's not the "only way you learn". There's no way you can't understand calculus, except if you're actually retarded.I am 100% sure that you jump straight into solving problems without having even looked up the theory.That just won't work.Read the theory to understand what you're doing.
 >> Anonymous Thu Oct 29 14:19:52 2020 No.12286759 >>12286752because abstract, in time, leads to the tangible.
 >> Anonymous Thu Oct 29 14:20:28 2020 No.12286763 >>12286752the answer is because most of them want to intentionally avoid that so that they don't feel like watered down physicists
 >> Anonymous Thu Oct 29 14:21:28 2020 No.12286769 >>12286710What trick?
 >> Anonymous Thu Oct 29 14:22:50 2020 No.12286774 >>12286752Because mathematics is not engineering. It's truth-seeking.
 >> Anonymous Thu Oct 29 14:22:54 2020 No.12286775 >>12286769Add the digits. If what you get is divisible by 3, the number is divisible by 3.
 >> Anonymous Thu Oct 29 14:31:52 2020 No.12286792
 >> Anonymous Thu Oct 29 14:34:14 2020 No.12286797 >>12286792Yep. Another slightly less useful one is that if a number is divisible by 3 and by 2, it's divisible by 6.
 >> Anonymous Thu Oct 29 14:34:31 2020 No.12286799 >>12283975How else was he gonna get the thread for some basedboy Nazi LARPer that decided to die young in the Eastern Front rather than doing mathematics?
 >> Anonymous Thu Oct 29 14:41:07 2020 No.12286813 I have a family of operator $C(\dot):[0,T]\times\mathcal{S}\to\mathcal{S}$ with $\mathcal{S}$ some Schwartz space such that for a fixed $f\in\mathcal{S},\; C(t)f$ is smooth in $t$. I managed to find the estimate $\lvert\lvert C(t)f\rvert\rvert_2\leq e^{Kt}||f||_2$ in $L^2$. Is the unique continuous extension also smooth or at least continuous in $t$?
 >> Anonymous Thu Oct 29 14:48:11 2020 No.12286833 >>12286813$K$ is a positive constant just to clarify.
 >> Anonymous Thu Oct 29 14:53:41 2020 No.12286844 File: 104 KB, 647x478, 1595188917036.png [View same] [iqdb] [saucenao] [google] [report] >the one guy in class who asks 'are we using the axiom of choice here'?
 >> Anonymous Thu Oct 29 15:00:15 2020 No.12286861 >>12286752Many of them do. I think because we start off learning "pure" math as undergrads and many people here then either graduate and stop doing math or go on to do pure math as postgrads, we tend to underestimate how many applied mathematicians there actually are.At my uni, the applied math department is several times larger than the pure math department. They are the ones bringing the money in
 >> Anonymous Thu Oct 29 15:00:52 2020 No.12286863 >>12286844Do we have a choice?
 >> Anonymous Thu Oct 29 15:01:49 2020 No.12286866 >>12284895Splitting lemma
 >> Anonymous Thu Oct 29 15:03:51 2020 No.12286880 2+2=46*8=4832-1=31.Kneel faggots
 >> Anonymous Thu Oct 29 15:11:21 2020 No.12286898 >>12286880I KNEEL
 >> Anonymous Thu Oct 29 15:18:20 2020 No.12286926 >>12286874Oof, hope it wasn't too tedious.
 >> Anonymous Thu Oct 29 15:23:25 2020 No.12286936 >>12286880wtf how did you discover this?
 >> Anonymous Thu Oct 29 15:23:32 2020 No.12286937 >>12286141no constant paths, I forgot to mention.
 >> Anonymous Thu Oct 29 15:30:13 2020 No.12286956 >>12286844I am that guy lol. What about it?
 >> Anonymous Thu Oct 29 15:30:32 2020 No.12286958 >>12286880>6*8=48prove it
 >> Anonymous Thu Oct 29 15:37:27 2020 No.12286976 File: 295 KB, 1080x1099, 1600130676116.jpg [View same] [iqdb] [saucenao] [google] [report] >>12286844>the one guy in class who asks 'are we using the Zorn's Lemma here'?
 >> Anonymous Thu Oct 29 15:40:09 2020 No.12286986 >>12286937Do the paths have to be injective? If they can be a line that goes back and forth along itself then you can do it. Otherwise I think it's impossible because if you remove finitely many paths you get a bunch of disks and annuli, possibly some things like annuli with multiple holes, but there's always at least two disks and the intersection of an infinite descending sequence of disks is a point that can't be covered. Hmm, unless the diameters din't converge to zero... but the intersection should still be simply connected... but so is R3 and you can cover that with disjoint circles... hmm
 >> Anonymous Thu Oct 29 16:10:18 2020 No.12287047 >>12286797that's true in generalif n is divisible by r and s, and r and s are relatively prime (i.e. they have no common divisors besides 1, i.e. their gcd is 1), then n is divisible by rs as well.
 >> Anonymous Thu Oct 29 16:29:43 2020 No.12287098 >>12285677by closed you mean gamma(0) = gamma(1) ?
 >> Anonymous Thu Oct 29 16:38:15 2020 No.12287124 File: 8 KB, 247x250, 1603125119147s.jpg [View same] [iqdb] [saucenao] [google] [report] Can somebody help me with the proof of this?Show that every quotient space of a locally path connected space is locally path connected
 >> Anonymous Thu Oct 29 16:54:20 2020 No.12287183 File: 143 KB, 1224x1316, help.png [View same] [iqdb] [saucenao] [google] [report] can somebody explain to this mega-brainlet what i need to learn in order to understand this? i took a machine learning class because i thought it would be fun but i'm starting to think i made a mistake since i'm shit at math
 >> Anonymous Thu Oct 29 16:56:50 2020 No.12287194 $\bullet$What textbooks, papers or text did you read today?$\bullet$What non-textbooks did you read today?$\bullet$Did you write something today?$\bullet$Did you do some programming today?$\bullet$Did you build something today?$\bullet$Did you clean up something today?$\bullet$Did you plan something today?$\bullet$Did you manage to work off some bureaucracy/paper work today?$\bullet$Did you practiced any skills today? If so, which?$\bullet$Did you do sports/cardio/weightlifting today?$\bullet$What were you eating today?$\bullet$How much sleep did you get yesterday?
 >> Anonymous Thu Oct 29 17:00:47 2020 No.12287215 >>12285504>Just arrange x y and z in a circuit like a triforce, and it goes so that (x*y)*z = x*(y*z) = x*)*y*(z* where it would loop around, and you put x in back as y*(z*x) because y is the new open position and is first in line in the cycle, and then this becomes (y*z)*x which gives you associativity for free!I tried to read this 3 times but I don't get it. Write better sentences
 >> Anonymous Thu Oct 29 17:07:43 2020 No.12287242 >>12285676Where do you take these historical facts and references to rather obscure mathematicans?I'm not saying that's a bad thing, but I'm surprised where this comes from. In partcilar since we talked about synthetic geometry a few threads ago.
 >> Anonymous Thu Oct 29 17:09:20 2020 No.12287249 >>12287194what i read today-The Real Projective Plane-Apollonius' Conics
 >> Anonymous Thu Oct 29 17:09:41 2020 No.12287251 I've been having fun doing mathematics
 >> Anonymous Thu Oct 29 17:18:29 2020 No.12287278 >>12287124What have you tried?
 >> Anonymous Thu Oct 29 17:20:02 2020 No.12287283 >>12287183This book is for people like you: https://mml-book.github.io/You mostly just need linear algebra and vector calculus.
 >> Anonymous Thu Oct 29 17:30:23 2020 No.12287311 has /mg/ ever worked through textbooks together? if not would it be something of interest?
 >> Anonymous Thu Oct 29 17:31:25 2020 No.12287315 File: 83 KB, 1491x1118, 0.jpg [View same] [iqdb] [saucenao] [google] [report] >>12287278This is what I have so far. I'm not sure if my approach is correct
 >> Anonymous Thu Oct 29 17:37:11 2020 No.12287338 >>12287315I think your approach will work but I find it a weird way to think about things. Here's my intuition: the quotient space is more connected since we can attach things but not disconnect them. Paths that worked before will still work. Open sets that worked before will still work.All you need to do is formalise this idea by talking about the quotient topology.
 >> Anonymous Thu Oct 29 17:40:50 2020 No.12287347 >>12287315>>12287124>>12287278Retard here, wouldn't the entire $\mathbb{R}^2$ plane be a quotient group of itself?
 >> Anonymous Thu Oct 29 17:43:39 2020 No.12287358 File: 7 KB, 436x179, Capture2.png [View same] [iqdb] [saucenao] [google] [report] >>12283965i dont even know what to do with thisi know cos(0)= pi/2 but after that is where i get lost
 >> Anonymous Thu Oct 29 17:44:53 2020 No.12287363 >>12287347You mean under the trivial quotient where you don't change anything? In that case yes.
 >> Anonymous Thu Oct 29 17:45:15 2020 No.12287365 >>12287358Solve the equation cos(x)=0, then find what makes e^y+1.2 =x for some y>>12287363Elaborate?
 >> Anonymous Thu Oct 29 17:48:26 2020 No.12287373 >>12287365why would i solve for y now? im super confused
 >> Anonymous Thu Oct 29 17:49:06 2020 No.12287376 >>12287365Elaborate?Let ~ be the trivial equivalence relation where x~y if and only if x=y. Then $\mathbf{R}^2/\tilde \cong \mathbf{R}^2$. Or if you want to think of $\mathbf{R}^2$ as a group then consider the quotient group $\mathbf{R}/0 \cong \mathbf{R}$. This is a trivial statement that is true for any topological space (or group).
 >> Anonymous Thu Oct 29 17:50:08 2020 No.12287383 >>12287376Oh that notation go really messed up, I mean $\mathbb{R}^2/~ \cong \mathbb{R}^2$
 >> Anonymous Thu Oct 29 17:52:27 2020 No.12287392 >>12287376I made the mistake of reading the wikipedia article, what's a good source on this?>>12287373I used y the second time to show that it's a different variable than x
 >> Anonymous Thu Oct 29 18:06:21 2020 No.12287432 >>12287392https://www.youtube.com/watch?v=aO9l7zteKlEAny introductory topology course will cover the quotient topology construction. If you haven't seen topology before then make sure you understand metric space analysis first (for example definitions of continuity, compactness, connectedness, etc in terms of open sets). Otherwise everything will seem really abstract and unmotivated.
 >> Anonymous Thu Oct 29 18:12:28 2020 No.12287453 >>12286844I hope it's you. Stop living in the past, make a contribution. Get rid of Choice and the lie of excluded middle.
 >> Anonymous Thu Oct 29 18:13:43 2020 No.12287460 >>12287249>Apollonius' Conicsnicethe Burger always keeps talking about him
 >> Anonymous Thu Oct 29 18:15:11 2020 No.12287464
 >> Anonymous Thu Oct 29 18:15:49 2020 No.12287466 >>12286976>Zorn's Lemma>not Kuratowski's Lemmafucking plebs
 >> Anonymous Thu Oct 29 18:16:04 2020 No.12287468 >>12287283thanks anon, going through it right now
 >> Anonymous Thu Oct 29 18:17:11 2020 No.12287476 What do you call a sequence f(i):N-> S where S is some finite set that is defined by a set of rules for what symbol can come next?For example, S = {A,B,C}B can only come after CC can only come after Asome sequences would be:AAAAABC...AAAABA...AAAAAAA...ABABABC...
 >> Anonymous Thu Oct 29 18:19:05 2020 No.12287484 >>12287476whatever i got the rules rong fuck it doe
 >> Anonymous Thu Oct 29 18:20:55 2020 No.12287487 >>12287476finite automata?
 >> Anonymous Thu Oct 29 18:21:05 2020 No.12287490 >>12287476regular expression.
 >> Anonymous Thu Oct 29 18:32:03 2020 No.12287517 >>12287392got itln((pi/2)-1.2))could you walk me through this last problem?
 >> Anonymous Thu Oct 29 18:33:06 2020 No.12287519 File: 47 KB, 1280x496, Capture3.png [View same] [iqdb] [saucenao] [google] [report] >>12287517forgot pic
 >> Anonymous Thu Oct 29 18:37:27 2020 No.12287532 Please rate this curriculum:1st Semester:>Introduction to Calculus>Math Lab 1 (problem solving)>Arithmetic Fundamentals>Quantitative Geometry 12nd >Calculus 1>Quantitative Geometry>Analytic Geometry>Introduction to Combinatorics and Probability3rd>Physics 1>Calculus 2>Math Lab 2>Linear Algebra 1>Seminars4th>Physics 2>Calculus 3>Linear Algebra 2>Linear Analysis>Algebra 15th>Probability and Statistics>Algebra 2>Introduction to Topology>Ordinary Differential Equations>Computational Math Lab6th>Physics 3>Calculus 4>Analysis 1>Differential Geometry>Numerical Methods7th>Physics 4>Topology>Complex Variables>Thesis 18th>Introduction to Galois Theory>Computational Science>Partial Differential Equations>Thesis 2
 >> Anonymous Thu Oct 29 18:38:20 2020 No.12287535 >>12287532cringe
 >> Anonymous Thu Oct 29 19:06:07 2020 No.12287633 >>12287532Forgot Analysis 2 on the 7th
 >> Anonymous Thu Oct 29 19:09:22 2020 No.12287644 >>12287466>Kuratowski's Lemma>not well ordering theoremsuper pleb
 >> Anonymous Thu Oct 29 19:11:19 2020 No.12287649 >just introduced Taylor series in my math classholy smokes. am i gonna be okay?
 >> Anonymous Thu Oct 29 19:20:15 2020 No.12287677 >>12287649They're fun
 >> Anonymous Thu Oct 29 19:46:30 2020 No.12287797 >>12287649taylor series are your friend.
 >> Anonymous Thu Oct 29 19:49:18 2020 No.12287811 >>12285473Use the second to last property, let z be 0, x be 1, and y be 0.
 >> Anonymous Thu Oct 29 20:43:31 2020 No.12287936 File: 103 KB, 1280x720, trump_dab_election_night.jpg [View same] [iqdb] [saucenao] [google] [report] why do elementary divisibility proofs trip me up so much number theory brosalso>masturbating>start thinking about number theory problem>become interested in problem and not in boobs>stop masturbating>solve problem>no longer feel like masturbatingsend help
 >> Anonymous Thu Oct 29 20:55:21 2020 No.12287971 Physical books all the way right?
 >> Anonymous Thu Oct 29 21:01:27 2020 No.12287991 >>12283965What's the fastest way to multiply two n digit numbers w/o a forrier transform?
 >> Anonymous Thu Oct 29 21:02:36 2020 No.12287995 >>12287936/sci/ - science and math
 >> Anonymous Thu Oct 29 21:08:27 2020 No.12288014 Can /sci/ help me with this gay ass fucking stats problem? Don't know where I'm going wrong.Suppose that Θ is a random variable that follows a gamma distribution with parameters λ and α, where α is an integer, and suppose that, conditional on Θ, X follows a Poisson distribution with parameter Θ. Find the unconditional distribution of Y = α + X.So I try and solve for the mgf of X because I can use that to get the mgf of Y so I can fucking be done with this. Since I want the mgf of Y, I'm gonna use the iterated expectation formula, which relies on me getting th expectation of e^{Xt}. That is:[eqn]M_X(t) = E[e^{tX}] = E[E[e^{tX} \ | \ \Theta]]= \int_{-\infty}^\infty e^{xt} \frac{\theta^x e^{-\Theta}}{x!}dx [/eqn] but this fucking integral doesn't give me anything... wolfram alpha can't even evaluate it. Am I fucking up somewhere?
 >> Anonymous Thu Oct 29 21:10:20 2020 No.12288018 >>12288014sorry, that integral is $E[e^{tX} \ | \ \Theta]$, not the expectation of this.
 >> Anonymous Thu Oct 29 21:11:31 2020 No.12288024 File: 689 KB, 2300x1618, 20201028_045105.jpg [View same] [iqdb] [saucenao] [google] [report] >>12287532>calculus 4
 >> Anonymous Thu Oct 29 21:28:04 2020 No.12288064 >>12286866I'm not particularly sure how that helps me here. Are you saying I can construct a SES using my idempotent f?
 >> Anonymous Thu Oct 29 21:30:37 2020 No.12288072   File: 42 KB, 300x421, 1601379061509.jpg [View same] [iqdb] [saucenao] [google] [report] >>12287532How's UFSC treating ya?
 >> Anonymous Thu Oct 29 21:51:01 2020 No.12288130 >>12287315you write like a bitch, let me fuck your girlfriend
 >> Anonymous Thu Oct 29 21:54:17 2020 No.12288142 I saw your postIt's treating me wellI saw the archives and apparently it has a 90% drop rate, is this true?
 >> Anonymous Thu Oct 29 21:54:49 2020 No.12288145 >>12288018>Am I fucking up somewhere?Yes.>have expression with $x!$ term>decide to integrate it rather than summing*>starting from the lower bound $x = -\infty$Bluntly put, you should be thinking about what you're calculating. In fairness to you, this is not something that comes naturally to people, it has to be honed by practicing problems.* For the puremathfags: in this case, the urge to generalize by writing $\Gamma(x+1)$ everywhere instead of x!, ends up working against you by obscuring the error of integrating against the wrong measure.
 >> Anonymous Thu Oct 29 21:58:02 2020 No.12288156 >>12288142No idea. Probably? Wouldn't surprise me.
 >> Anonymous Thu Oct 29 22:11:04 2020 No.12288191 >>12288156Why so? Apparently it kinda sucks? It's hard to get information with this pandemic so I'm not sure about transfering. I'm pleasantly surprised someone in /mg/ recognized the curriculum though
 >> Anonymous Thu Oct 29 22:11:28 2020 No.12288192 >>12288145thanks homie. bluntly put, it's a stupid mistake that reflects badly on my competence of the material. then again, this is an online class that meets once a week about my least favorite subject. I do needa learn stats eventually, but I'll do this over winter break when i don't have any class.
 >> Anonymous Thu Oct 29 22:33:19 2020 No.12288244 >>12288192>competence of the materialThis isn't incompetence, it's carelessness resulting from unfamiliarity. Being incompetent would be if you were unable to rectify the mistake, even after it was pointed out to you.Protip: Redefine your probability distributions to be multiplied by a {0,1}-valued indicator function (or "Iverson bracket") that explicitly marks their support, e.g. [eqn]p_X = \mathbf{1}\{ x\in \mathbb{N} \} \cdot \theta^x \cdot e^{-\theta}/x![/eqn]or [eqn]f_X = \mathbf{1}\{ x\in\mathbb{R}, x > 0 \} \cdot x^{a-1} \cdot e^{-x/\lambda} \cdot \lambda^{-a} / \Gamma(a)[/eqn]Then you no longer have to keep track of the integration bounds, since the indicator variables do that for you. They combine according to Boolean logic, e.g. $\mathbf{1}\{ x\in A \} \cdot \mathbf{1}\{ x \in B \} = \mathbf{1}\{ x \in A \text{ and }x \in B \} = \mathbf{1}\{ x \in A \cap B \}$, which is how you calculate the support of your final distribution.
 >> Anonymous Thu Oct 29 22:38:17 2020 No.12288261 >>12288191It does suck, yeah, and the first two semesters are filled with mem shit. IIRC it didn't cover much less than, say, USP, tho, so there's no big deal.>transferingA friend of mine once considered transferring to maths. I specifically told him not to because he'd get tired within the first two semesters and drop out. I stand by my opinion.
 >> Anonymous Thu Oct 29 22:38:23 2020 No.12288263 >>12287649He’ll fucking yes. Most interesting part of calculus. Super satisfying when you prove Taylor’s thm. One of my favorite parts of intro analysis. Speaking of, what’s everyone’s favorite result or technique from analysis?
 >> Anonymous Thu Oct 29 22:43:01 2020 No.12288276 >>12287936>>12287995I once stopped having sex with a girl to work on a problem relating to idempotent functions. It was really awkward
 >> Anonymous Thu Oct 29 22:45:21 2020 No.12288283 >>12287936This sounds like the origin to a very strange math related fetish.
 >> Anonymous Thu Oct 29 22:48:23 2020 No.12288290 >>12287811>if 1>0, 1+0>0+0>if 0>1, 0+0>1+0I dont get it
 >> Anonymous Thu Oct 29 23:02:37 2020 No.12288326 >>12288261Thanks man, I really wanted a opinion on this matter. Guess I'll just do CS and self study higher math
 >> Anonymous Fri Oct 30 00:46:49 2020 No.12288557 >>12288276Just have sex and think about math at the same time. It's not that hard, especially if you get the other person to do all the work.
 >> Anonymous Fri Oct 30 00:47:23 2020 No.12288560 >>12287242>Where do you take these historical facts and references to rather obscure mathematicans?There is plenty of books on the history of mathematics. You'll pick up some of these facts if you read a few of them.
 >> Anonymous Fri Oct 30 00:52:49 2020 No.12288563 >>12288276more like impotent functions
 >> Anonymous Fri Oct 30 00:54:08 2020 No.12288567 File: 122 KB, 720x720, 1481730293586.jpg [View same] [iqdb] [saucenao] [google] [report] >>12288563Savage.
 >> Anonymous Fri Oct 30 00:56:32 2020 No.12288576 File: 210 KB, 645x968, 1503241345483.jpg [View same] [iqdb] [saucenao] [google] [report] >Consider the subgroup $G=\left\langle \sigma,\pi \right\rangle$ of $S_{4}$...can someone clarify what this notation means?
 >> Anonymous Fri Oct 30 00:58:51 2020 No.12288578 >>12288563kek'd>>12288576The smallest (sub)group containing $\sigma$ and $\pi$. ie you're going to need the identity, inverses, and anything you can generate with the group operation.
 >> Anonymous Fri Oct 30 01:00:22 2020 No.12288582 File: 32 KB, 530x492, CF-k9JAUEAAhvqg.jpg [View same] [iqdb] [saucenao] [google] [report] >>12288578thanks
 >> Anonymous Fri Oct 30 01:45:37 2020 No.12288657 File: 207 KB, 1110x1600, 1569958429044.png [View same] [iqdb] [saucenao] [google] [report] >>12288263>what’s everyone’s favorite result or technique from analysis?Intermediate value theorem and >>12286048The triangle inequality may look like analysis but is really algebraic, as evidenced by its appearance in discrete math.
 >> Anonymous Fri Oct 30 01:56:09 2020 No.12288672 >>12288657>apperance in discrete mathWhich theorem? I've seen it in linear algebra but it was with inner products and norms, kind of definitional
 >> Anonymous Fri Oct 30 01:59:03 2020 No.12288684 >>12284895Just Karoubi complete, bro
 >> Anonymous Fri Oct 30 02:04:31 2020 No.12288693 >>12285220No, I'm lazy. But you square it first, multiply by the two, and then divide 8 by the resulting number.The two counts as part of the P step of PEMDAS. If they wanted 8 divided by the 2, they would've written it as a fraction, or put parenthesis around it.
 >> Anonymous Fri Oct 30 02:09:26 2020 No.12288700 >>12288672It's in the name: the triangle inequality is a theorem of Euclidean geometry, which is assuredly non-analytic as it predates the conception of $\pi$.In other words, the definitional character of the triangle inequality (as you've observed) is the evidence that it did not originate $from$ analysis; rather, it is being applied $to$ analysis.
 >> Anonymous Fri Oct 30 02:56:41 2020 No.12288765 Undergrad here. What course should I take next sem lads, an advanced PDEs course (that focuses on the theoretical stuff not just the solving bullshit) or combinatorial design theory? Leaning towards PDEs.
 >> Anonymous Fri Oct 30 04:01:34 2020 No.12288867 File: 118 KB, 994x340, Screenshot from 2020-10-30 07-59-43.png [View same] [iqdb] [saucenao] [google] [report] Can anyone take a quick look at this proof? I believe it is fine but would like to be sure.
 >> Anonymous Fri Oct 30 04:23:08 2020 No.12288900 Stupid anon here.I have a question about probability theory.Say, there are a soldier and tank. We know only that the probability to shoot an enemy for the first one is 0.7 and 0.4 for the second one.So, if we take these two together the probability to shoot an enemy EITHER by soldier OR tank is 1 - q1*q2 = 1 - 0.3 * 0.6 = 0.82.Is is right to say that tank gives additional credits of success to soldier = 0.82 - 0.7 = +0.17 and soldier to tank = 0.82 - 0.4 = +0.42? And how are these additions called officially?I try to understand the effect of support without any data about their real cooperation.
 >> Anonymous Fri Oct 30 05:24:12 2020 No.12288984 >>12288900>Is is right to say that tank gives additional credits of success to soldier = 0.82 - 0.7 = +0.17 and soldier to tank = 0.82 - 0.4 = +0.42? And how are these additions called officially?I suspect you want the probability ratios 0.82/0.7 and 0.82/0.4 (or equivalently, the log-probabilities log(0.82)-log(0.7) and log(0.82)-log(0.4)) instead. Those are called "(log) odds" or "odds ratios".>without any data about their real cooperation.No, your analysis is only valid if you explicitly assume that they are acting independently. That can be your null hypothesis though.>>12288867I don't see any problem either.
 >> Anonymous Fri Oct 30 05:24:16 2020 No.12288985 >>12288263Harmonic analysis as a whole.
 >> Anonymous Fri Oct 30 05:30:20 2020 No.12288994 Today I struggled with something for about 2 hours and it basically boiled down to the definition of the matrix representation of a linear transformation. I’m in the third year of my undergrad. Which method of suicide do you recommend?
 >> Anonymous Fri Oct 30 05:44:02 2020 No.12289024 >>12288984Thank you for your answer.>No, your analysis is only valid if you explicitly assume that they are acting independently. That can be your null hypothesis though.Is there any valid way to make a reasonable assumption about what will be the support of each other if they are NOT acting independently?
 >> Anonymous Fri Oct 30 05:54:21 2020 No.12289037 >>12288994Watch 3blue1brown
 >> Anonymous Fri Oct 30 05:56:41 2020 No.12289045 >>12288867I love mathscr so much bros
 >> Anonymous Fri Oct 30 06:17:06 2020 No.12289076 >>12286799contributed more to mathematics than you
 >> Anonymous Fri Oct 30 06:34:30 2020 No.12289100 File: 83 KB, 900x900, no.jpg [View same] [iqdb] [saucenao] [google] [report] >>12289024Is there any valid way to draw a reasonable map of a territory if you do NOT know what it looks like?(And do you actually know that they are not acting independently, or is that just an assumption? In certain situations, knowing that some event will occur with positive probability can be useful, but this is unlikely to be what you're looking for.)
 >> Anonymous Fri Oct 30 06:43:00 2020 No.12289122 >>12289100You have a point.Thank you again.
 >> Anonymous Fri Oct 30 06:43:28 2020 No.12289124 How to show?Let $[x]$ denote the equivalence class of $x \in X$. This is called the path-component of $x$and consists of all points that you can connect to $x$ by a path in $X$. Let $\pi_0(X) = X /\sim$ denote the set of path components of $X$. Give $\pi_0(X)$ the natural quotient topology and write the quotient map $q_X:X \w \pi_0(X), q_X(x) = [x]$. Show that if $f:X \w Y$ is a continuous function, then $f_0: \pi_0(X) \w \pi_0(Y), f_0([x]) = [f(x)]$is well defined and a continuous function.I think I can do it through showing the composition is continuous but I'm not sure?
 >> Anonymous Fri Oct 30 06:44:51 2020 No.12289127 >>12289124sorry \w is a shitty macro for \longrightarrow
 >> Anonymous Fri Oct 30 06:46:23 2020 No.12289130 >>12289045I too love it when half my letters look the same.
 >> Anonymous Fri Oct 30 07:57:41 2020 No.12289264 >>12289127Just use \to
 >> Anonymous Fri Oct 30 08:14:25 2020 No.12289293 Why are eigenvectors of AT * A and, conversely, singular vectors of A orthonormal? I understand why they are orthogonal (AT * A is symmetric) but I don't see how they are unit length.
 >> Anonymous Fri Oct 30 08:16:53 2020 No.12289297 >>12289293You can just choose them to have unit length. Do you understand what an eigenspace is?
 >> Anonymous Fri Oct 30 08:17:10 2020 No.12289298 >>12289293Eigenvectors can be made any length you want.
 >> Anonymous Fri Oct 30 08:18:27 2020 No.12289300 >>12289297>>12289298Yep, posted this and realized what an idiot I am, we don't care about their norm, we only care about direction, so you can just choose a unit vector in this "eigendirection". Silly me.
 >> Anonymous Fri Oct 30 09:01:21 2020 No.12289356 Guys. How come "if anon is a faggot, anon watches anime" is true?Also, listen to Tinariwen:https://www.youtube.com/watch?v=H1YIgwPsX5Q
 >> Anonymous Fri Oct 30 09:15:23 2020 No.12289389 >>12289124>>12289124>>I think I can do it through showing the composition is continuous but I'm not sure?yeah you don't have much else at your dispositionas usual with eq classes, just be sure your result is independant of the representant.
 >> Anonymous Fri Oct 30 09:16:39 2020 No.12289391 In the future the low IQ populations will look at us mathematicians and think it's all just a very elaborate meme or that we're all just pretending to be smart to boost our egos. This process will be accelerated by low tier diversity hire mathematicians similar to Piper Harron who will constantly publicly complain about the arrogance, the exclusivity of mathematicians, how they obscure their thoughts with obscure jargon, how they take pride in not being understood by PoCs and common people who want to get into the field, how they fail to take the historical mathematical achievements of various african tribes seriously. These voices will be amplified by the media on all fronts, continually diminishing the respect people hold for mathematics. There will be multiple websites like /r/iamverysmart dedicated to posting mathematical papers, excerpts from textbooks and our faces. The typical comments will be "yup, this guy needs to leave his room once in a while", "I bet he's fun at parties", the classic "Yikes", "Someone likes the thesaurus too much".
 >> Anonymous Fri Oct 30 09:21:28 2020 No.12289406 >>12283965Seeking advice here. What should I orient my graduate education if my goals are to learn useful things for my job (predictive modelling) but also specialize in an area where I can sit comfy writing interesting papers.I know analysis and stochastic analysis are good but is there anything more specific? Like specific classes that would aid? My goal is to become competent enough to produce independent research but I also want to become better at my job.
 >> Anonymous Fri Oct 30 09:29:33 2020 No.12289424 >>12289391>continually diminishing the respect people hold for mathematics.nobody respects mathematicians, even before the birth of nihilism. Also mathematicians are very few, all over the world. Cartier estimates the number at 10k.
 >> Anonymous Fri Oct 30 10:28:07 2020 No.12289552 >>12288563Kek nice one, I got btfo>>12288576The angle bracket section is what's called a "group presentation", and S4 is the 4th permutation group
 >> Anonymous Fri Oct 30 10:36:45 2020 No.12289566 >>12289552That's not a presentation you dweeb, there are no relations. And finite symmetric groups don't have free subgroups.
 >> Anonymous Fri Oct 30 10:43:42 2020 No.12289579 >>12287532>intro calculus>calculus 1>calculus 2>calculus 3>calculus 4>"math lab">quantitative/analytic geometry (high school math?)>arithmetic fundamentals (middle school math?)>physics classes just have numbers, no names>called complex "variables" instead of complex analysis>implying the differential geometry class is real differential geometry if taken simultaneously with analysis 1>intro to topology and topologycan you just start at 4th semester, cut out the bloat, and take grad classes for 2 years? i mean come on.
 >> Anonymous Fri Oct 30 10:44:01 2020 No.12289580 >>12289566Elaborate?
 >> Anonymous Fri Oct 30 10:45:59 2020 No.12289585 >>12288765advanced pde is fun
 >> Anonymous Fri Oct 30 10:50:16 2020 No.12289596 >>12288263>resultbanach fixed point theorem>techniquesumming things with increasingly bad properties /2^n to get something with really awful properties. simple example would be weierstrass functions.
 >> Anonymous Fri Oct 30 10:51:01 2020 No.12289599 File: 345 KB, 1280x720, Screenshot_20201030-174929.jpg [View same] [iqdb] [saucenao] [google] [report] >>12283965>messes up sentence>loudly exhales >repeats sentenceWhy does he always do this?
 >> Anonymous Fri Oct 30 10:54:39 2020 No.12289606 Is there a direct proof of the fact that there's no integer between 0 and 1? All proofs I've read use contradiction
 >> Anonymous Fri Oct 30 10:55:36 2020 No.12289611 >>12286209Printed off Pressley's Elementary Differential Geometry yesterday; school library for cost of tuition
 >> Anonymous Fri Oct 30 10:55:47 2020 No.12289613 >>12289580It's the subgroup generated by those two elements, not a presentation. If it was a presentation it would be the free group on two generators, which would be infinite. Do you know what the subgroup generated by a set is?
 >> Anonymous Fri Oct 30 11:22:49 2020 No.12289679 >>12289606Not sure if you can directly prove a negative, but perhaps you could show that $x \mapsto 2^x$ is an order-isomorphism from $\left\{ x\in\mathbb{Z} \mid 0 \leq x \leq 1 \right\}$ to the powerset of {0}.
 >> Anonymous Fri Oct 30 11:27:18 2020 No.12289693 >>12288244I came back to this problem and I still can't fucking crack it... Taking the sum in place of the integral does simplify, and then I'm left with[eqn]M_X(t) = E\left[\exp(\theta(e^t - 1))\right] [/eqn]as the mgf of X, but this is horseshit still. $\theta$ follows a gamma distribution, and so the expected value of that garbage is a mess (again, wolfram alpha doesn't evaluate it), so I'm at another fucking wall
 >> Anonymous Fri Oct 30 11:28:38 2020 No.12289696 >>12289679Wait no, $x\mapsto 2^x$ makes no sense.But $\mathrm{card}: \mathcal{P}(\{0\}) \to \left\{ x\in\mathbb{Z} \mid 0 \leq x \leq 1 \right\}$ seems like it should work.
 >> Anonymous Fri Oct 30 11:32:26 2020 No.12289712 >>12289693that's just a compound Poisson distribution bro
 >> Anonymous Fri Oct 30 11:35:59 2020 No.12289719 >>12289712I don't even know what that means familia, please elaborate.
 >> Anonymous Fri Oct 30 11:37:18 2020 No.12289724 >>12289606The integers are all R who are + or - by 1 from 1, and no others. 1-1 is 0. Any int that's +1 to 1 or -1 from 0 is greater than 1 or less than 0. So none of them fit 0 < x < 1. And of course 1 and 0 don't fit either.
 >> Anonymous Fri Oct 30 11:44:17 2020 No.12289738 >>12289719Let $\theta$ be Gamma-distributed. Now let $N \sim \textrm{Poisson}(\theta)$. Then the variable [eqn]X = \sum_{k=1}^{N} Y_k,[/eqn]where the variables $Y_k$ are iid, is compound Poisson distributed. Calculating the moment generating function of this variable would be a fun exercise for you and what you get is going to look like the function you have in >>12289693(Hint: the variables Y are allowed to be deterministically a constant)
 >> Anonymous Fri Oct 30 11:51:05 2020 No.12289752 >>12286209>Have you guys ever printed off an entire textbook PDF?lol yes, i printed loads, but from a lab and from a computer belonging to someone else, in order not to have my counter going upall printing jobs are tracked.
 >> Anonymous Fri Oct 30 11:52:54 2020 No.12289755 >>12289738>would be a fun exercisefor someone who likes stats maybe>and what you get is going to look like the function you have inAnd I'm stumped here. This compound variable stuff hasn't been discussed yet, so I'm unsure how to proceed after this expectation.
 >> Anonymous Fri Oct 30 11:56:44 2020 No.12289765 >>12289606I'd use proof by contradiction>>12289613I know what subgroups are, admittedly I'm still learning and permutation groups have been a thorn in my side
 >> Anonymous Fri Oct 30 12:07:18 2020 No.12289796 >>12289755You don't need any compound shit. Literally look up the MGF of a Poisson distribution and compare with what you have.
 >> Anonymous Fri Oct 30 12:10:27 2020 No.12289805 >>12289738>>12289755Alright, so [eqn]\exp(\theta(e^t - 1))[/eqn] is the mgf of a Poisson random variable w/parameter $\theta$, so the expected value of this is just[eqn]E[\exp(\theta(e^t - 1))] = E[E[e^{Xt}]] = E[e^{Xt}] =...[/eqn]wtf
 >> Anonymous Fri Oct 30 12:13:24 2020 No.12289809 >>12289606It follows from the usual construction of the real numbers and the definition of the naturals as a subset. What you have to understand is that mathematicians don't prove obvious shit because it isn't obvious, but to see if their particular axiomatic system works. There are many ways to construct the real numbers, and so you have to specify how you are defining the natural numbers in the real numbers. I'm going to assume you are using field axioms and so >>12289724 Is tthe usual definition because you only know you have special elements 1 and 0.
 >> Anonymous Fri Oct 30 12:21:59 2020 No.12289828 >>12289809All constructions of $\mathbb{R}$ I know start from the rational numbers (Cauchy sequences, Dedekind cuts, decimal expansions), and the rationals, as far as I know, are built from the natural numbers.
 >> Anonymous Fri Oct 30 12:24:59 2020 No.12289838 >>12289828You can start with an unspecified field with a total order and then afterwards construct all the subsets you know. Is the approach done in spivak and used by people who don't like set theoretic shit.
 >> Anonymous Fri Oct 30 12:29:08 2020 No.12289852 >>12289838I know, but that still doesn't answer my question. The proof you mention is only valid if $\mathbb{R}$ exist, which (as far as I know) can only be proven by the construction of the natural numbers. Then the proof would be redundant
 >> Anonymous Fri Oct 30 12:38:50 2020 No.12289892 >>12289852Again, the real numbers as defined through the axioms, not as a set theoretic construction. The real numbers "exist".
 >> Anonymous Fri Oct 30 12:43:21 2020 No.12289906 File: 28 KB, 480x480, anons second wife.jpg [View same] [iqdb] [saucenao] [google] [report] >>12289809We wants to prove$\neg \exists n. \big((0  >> Anonymous Fri Oct 30 12:46:33 2020 No.12289919 To spell it out in wordsIf [math]n$ and $j$ are two nonzero numbers, use the Peano axioms to derive contradiction (i.e. derive $(0=1)$) from the claim $n+j=1$.
 >> Anonymous Fri Oct 30 12:48:57 2020 No.12289931 Why is all math seemingly reduced to functions of two things rather than operators on >2 things?
 >> Anonymous Fri Oct 30 12:50:06 2020 No.12289934 >>12289931Think.
 >> Anonymous Fri Oct 30 12:52:20 2020 No.12289942 For the love of God someone please kill me. Posting again because fuck me.Suppose that Θ is a random variable that follows a gamma distribution with parameters λ and α, where α is an integer, and suppose that, conditional on Θ, X follows a Poisson distribution with parameter Θ. Find the unconditional distribution of α + X (Hint : Find the mgf by using iterated conditional expectations.
 >> Anonymous Fri Oct 30 12:54:12 2020 No.12289948 I suppose since 1 doesn't have more axioms than being singled out as the multiplicative unit, one must multiply (n+j)·x=x>>12289931It's called ternary operation fyi>>12289934I thought for a second but can't give a moral justification desu. Other than that it's easier. One can of course say all functions are only ever really functions of a single arguments and 2-ary arguments are 1-ary one's in disguise. But I suppose the underlying question is whether there's a reason 3-ary notation is rarely the setup in mathematical theories.I recall a SE thread on this.And there's also of course counterexamples, e.g. the associator or what's it called, where you studyx·(y·z)-(x·y)·z in its own right.But it's rare.
 >> Anonymous Fri Oct 30 12:56:57 2020 No.12289953 If x and y are two nonzero naturals, does x+y=1 lead to a contradiction? Why, formally?
 >> Anonymous Fri Oct 30 12:58:36 2020 No.12289963 File: 305 KB, 1048x1584, 1588079118725.png [View same] [iqdb] [saucenao] [google] [report] >logic and foundations
 >> Anonymous Fri Oct 30 12:58:58 2020 No.12289964 >>12289931What about tensors, multilinear maps, determinants?
 >> Anonymous Fri Oct 30 13:00:30 2020 No.12289972 File: 132 KB, 800x1200, nicola_cavanis4.jpg [View same] [iqdb] [saucenao] [google] [report] >>12289948found the thread I mentionedhttps://math.stackexchange.com/questions/94690/is-anybody-researching-ternary-groups>>12289963we're all deciding to live in our own personal hell
 >> Anonymous Fri Oct 30 13:05:16 2020 No.12289985 >>12289972>nicola cavanisi wonder how many men nicola cavanis picked up for anal sexwonder also how much easy is nicola cavanis lifewonder if nicola cavanis is a feminist and claims she has a hard life
 >> Anonymous Fri Oct 30 13:09:13 2020 No.12289995 >>12289948Redpill me on the associator
 >> Anonymous Fri Oct 30 13:09:19 2020 No.12289996 >>12284305Think of it this way, subtraction shows us the amount of steps between two numbers>27 - 16 = 11There are 11 steps between 27 and 16But how many steps are there between 27 and -16? The answer is 27 + 16Or just think of it this way, you have 27 apples. Now take 16 apples. You just grabbed some apples. But if you were to take -16 apples, what would you do? The opposite
 >> Anonymous Fri Oct 30 13:11:26 2020 No.12290002 >>12289934I would argue that it's because binary operations are the simplest form of interactions
 >> Anonymous Fri Oct 30 13:30:33 2020 No.12290053 >>12289995measures associativity
 >> Anonymous Fri Oct 30 13:30:58 2020 No.12290055   File: 1.18 MB, 1612x1186, brafe.png [View same] [iqdb] [saucenao] [google] [report] >>12289995https://en.wikipedia.org/wiki/AssociatorI only came across it in relation to the Star/Moyal product.Don't ask me to redpill you about the Star product.>>12289985she brave woman
 >> Anonymous Fri Oct 30 13:32:01 2020 No.12290059   Although admittedly it was a shit example, since it's probably never studied abstractly (but instead is defined just in terms of a binary operation)
 >> Anonymous Fri Oct 30 13:33:28 2020 No.12290063 File: 861 KB, 1548x830, b.png [View same] [iqdb] [saucenao] [google] [report] >>12289995https://en.wikipedia.org/wiki/Associator(Although admittedly it was a shit example, since it's probably never studied abstractly (but instead is defined just in terms of a binary operation))I only came across it in relation to the Star/Moyal product.Don't ask me to redpill you about the Star product.>>12289985she brave woman
 >> Anonymous Fri Oct 30 13:51:12 2020 No.12290119 >>12289942Oh hey, I see you're still at it.You've managed to get the MGF in >>12289693. I don't know why Wolfram doesn't recognize it, because that's exactly the expression for the MGF of $\theta$, but evaluated at $e^t-1$ instead of t. I.e.[eqn]M_X(t) = \left(1 - \lambda(e^t-1) \right)^{-\alpha}/\mathbf{1}\{ e^t-1 < 1/\lambda \}[/eqn]So all that remains is for you to recognize this MGF, for which it helps to rewrite the support as a radius of convergence $\mathbf{1}\{ t < \log( \frac{1+\lambda}{\lambda})\}$.This suggests the parameter transform $p = \frac{\lambda}{1 + \lambda}$, i.e. $\lambda=\frac{1}{1-p}-1$, so that after substituting$M_X(t) = \left(1 - (\frac{1}{1-p} - 1)(e^t-1)\right)^{-\alpha}/\mathbf{1}\{ t < -\log p \}$you can expect the numerator to simplify nicely (and you can probably already guess what the final distribution of X will be).
 >> Anonymous Fri Oct 30 14:10:15 2020 No.12290192 >>12290119I can tell by the way you talk that you have a big cock. Thank you very much for continuing to help me on this stupid problem anon.> that's exactly the expression for the MGF of $\theta$the MGF of a gamma distribution is the expected value of the MGF of a poisson distribution? Evaluating the expectation w.r.t. $\theta$ gets [eqn]E[\exp(\theta(e^t - 1))] = \int_0^\infty \exp(\theta(e^t - 1)) \frac{\lambda^\alpha \theta^{\alpha - 1}}{\Gamma(\alpha)} e^{-\lambda \theta} \ d\theta = \int_0^\infty \frac{\lambda^\alpha}{\Gamma(\alpha)} \int_0^\infty \exp(\theta(e^t - 1))\theta^{\alpha - 1} e^{-\lambda \theta} \ d\theta [/eqn]This part is incredibly confusing to me.
 >> Anonymous Fri Oct 30 14:11:17 2020 No.12290196 >>12290192ugh ignore the first integral in the third expression, why can't we edit posts on 4chin?
 >> Anonymous Fri Oct 30 14:18:31 2020 No.12290226 Friendly reminder that nobody has proved the smoothness of the Navier-Stokes equations. Over 100 years old and you get one 1 million bucks for the proof. Get going. I mean, you are as smart as you say you are on 4chan, right?
 >> Anonymous Fri Oct 30 14:20:41 2020 No.12290236 >>12289972Emil Artin wrote a 150 page book on n-ary group theory in 1940, initiating the discipline. It's still actively studied. People on StackExchange are so excited to answer even when they don't work in the area.
 >> Anonymous Fri Oct 30 14:21:36 2020 No.12290239 >>12290226tao is on the job
 >> Anonymous Fri Oct 30 14:35:04 2020 No.12290279 >>12290192No, I meant that the expression is of the form $M_X(t) = E_\theta[e^{u\theta}]$ for $u=e^t-1$ (or to be pedantic, $u(t)=e^t-1$).Protip 2: Subscript your expectation operators, so that you can see explicitly what you're integrating over. In this case, $E_\theta[e^{u\theta}]$ is the telltale pattern of an MGF, and $\theta$ is a random variable whose distribution you already know. This should prompt you to write out the functional form of$M_X(t) = M_\theta(u(t)) = M_\theta(e^t-1)$which has already been given.
 >> Anonymous Fri Oct 30 14:36:50 2020 No.12290285 >>12290239Is he? Is that one of the problems he's trying to solve?
 >> Anonymous Fri Oct 30 14:43:41 2020 No.12290306 Do you guys use any made up symbols as you work? I made a symbol thats like a V with an | through it, like a trident. I use it to compare two objects before making a statement about them, it seems helpful. I call it comparator>>12289948The reason I asked the question is because I was counting an octagon, and I said 22 22 in my head and it instantly went to 8. But something felt off, as though it was disallowed to add 4 things at once or even recognize 4-ness as a distinct rationale without counting up by units. But then I wondered why going 2 4 6 8 is any better. Is recognizing 4 in the brain possible, or does the brain and reality split it into units at the lowest level? I believe n-ary is possible.
 >> Anonymous Fri Oct 30 14:45:48 2020 No.12290314 >>12290285Yes.
 >> Anonymous Fri Oct 30 14:47:51 2020 No.12290318 Bros. I just discovered one fundamental difference between how normal life thinking differs from mathematical thinking >almost all "if statements" irl, are in fact "iff statements", at least partiallyThis is especially true in biological, natural, and social things
 >> Anonymous Fri Oct 30 14:48:53 2020 No.12290321 >>12290226Get us started then. Post your progress.
 >> Anonymous Fri Oct 30 14:55:46 2020 No.12290347 What are some practical applications of pure magmas?
 >> Anonymous Fri Oct 30 15:16:55 2020 No.12290403 Cons cells in Lisp, I guess.It seems like anything you'd want from a pure magma $M:\Omega \to \Omega^\Omega$ can also be done by the more general action $S:\Sigma \to \Omega^\Omega$, which has both theoretical and practical uses.
 >> Anonymous Fri Oct 30 15:17:57 2020 No.12290408 >>12290347Smelting iron.
 >> Anonymous Fri Oct 30 15:19:36 2020 No.12290416 >>12290403Consing is not a binary operation.
 >> Anonymous Fri Oct 30 15:25:42 2020 No.12290425 >>12290347protecting your virginity.
 >> Anonymous Fri Oct 30 16:20:15 2020 No.12290537 https://www.youtube.com/watch?v=8OkpRK2_gVsCan someone post more songs like this?
 >> Anonymous Fri Oct 30 17:11:26 2020 No.12290662
 >> Anonymous Fri Oct 30 17:12:07 2020 No.12290663 >>12283965Any good resources for learning about series? I'm taking calc II and have an A so far but my professor really isn't very good and it's catching up. Am I supposed to be able to always be able to find what they converge to? Are partial sums always obvious? The convergence/divergence tests are fairly straight forward, we've learned up until the limit comparison test.
 >> Anonymous Fri Oct 30 17:51:30 2020 No.12290724 >>12290662Anon you're gay.
 >> Anonymous Fri Oct 30 17:58:23 2020 No.12290734 File: 22 KB, 680x375, ElMCKAGXIAM1fJQ.jpg [View same] [iqdb] [saucenao] [google] [report] Asked this in /sqt/ to no avail.This being the case, what is the difference between the "p-adics" and "base p" ?
 >> Anonymous Fri Oct 30 18:04:42 2020 No.12290748 >>12290734p-adics can have infinitely many digits left of the decimal point, but not right of it.
 >> Anonymous Fri Oct 30 18:06:00 2020 No.12290750 >>12290734They're completely different things. One is an algebraic structure and the other is just a notation for natural numbers.
 >> Anonymous Fri Oct 30 18:59:52 2020 No.12290902 >let this axis represent n-1 dimensions
 >> Anonymous Fri Oct 30 19:58:11 2020 No.12291070 What's the consensus on the best measure theory book, cu/mg/uzzlers?
 >> Anonymous Fri Oct 30 20:06:45 2020 No.12291092 File: 33 KB, 334x334, alexandre-grothendieck.jpg [View same] [iqdb] [saucenao] [google] [report] >>12291070You're supposed to rederive it yourself using your intuition anon.
 >> Anonymous Fri Oct 30 20:20:40 2020 No.12291122 >>12291092p-please anon, spare me a crumb of reference to the written assistance...
 >> Anonymous Fri Oct 30 20:33:42 2020 No.12291147 >>12290663Sort of on the same boat. Is this your first time taking this subject?What book are recommended by your professors? Meme books like Apostol, Spivak should be fine if you are proving stuff (I know this is /mg/ but sometimes non math majors come here to ask stuff).>Am I supposed to be able to always be able to find what they converge to? Kind of a tricky question but no, mostly just if they do. Also, if you're at power series, for what values of x they converge.>Are partial sums always obvious? No, not really. They require some work, there are techniques though.
 >> Anonymous Fri Oct 30 20:38:00 2020 No.12291157 >>12291147Also Professor Leonard's videos are really good. No shame in watching them, particularly if your prof sucks
 >> Anonymous Fri Oct 30 20:57:15 2020 No.12291192 File: 18 KB, 333x499, 41bnIUsE2uL._SX331_BO1,204,203,200_.jpg [View same] [iqdb] [saucenao] [google] [report] kino has arrived.
 >> Anonymous Fri Oct 30 22:36:23 2020 No.12291396 >>12285487You misunderstood the implication, it's context-dependant.If you don't understand common induction applications, then you don't really understand the concept. You barely have to think on how to apply on common examples, if you already understand the principle.
 >> Anonymous Fri Oct 30 22:52:54 2020 No.12291431 Do you guys set a benchmark of pages/problems to be finish for each block of time (hour/day/week/month/whatever) spent studying a book or paper? Why? Does it work?
 >> Anonymous Fri Oct 30 23:02:14 2020 No.12291458 >>12291431-No-I'm not THAT autistic-yes
 >> Anonymous Fri Oct 30 23:17:39 2020 No.12291478 File: 18 KB, 416x133, asasas.png [View same] [iqdb] [saucenao] [google] [report] Brainlet here.Pls explain what this means and how to solve it. I know how to solve a separable diff equation (the chapter this is from) and I know what the initial value problem isBut I'm not being able to connect the dots.Thanks.
 >> Anonymous Fri Oct 30 23:18:39 2020 No.12291480 >>12291396>commonSo you admit that understanding the induction principle need not imply the ability to solve induction problems, unless they are "common"?I can buy that, but only if you make it clear what distinguishes a "common" application from an "uncommon" one.
 >> Anonymous Fri Oct 30 23:35:07 2020 No.12291500 >>12291478Not my thing so take it with a grain of salt, but it'll probably be obvious if you differentiate both sides
 >> Anonymous Fri Oct 30 23:36:13 2020 No.12291502 >>12291478Differentiate both sides and figure out a differential equation. This is why nobody talks about integral equations, because they can be transformed into differential equations
 >> Anonymous Fri Oct 30 23:41:06 2020 No.12291507 >>12291502>>12291500That is what I did but I thought I was missing something.What do I do with the y(2) that shows up? Just treat it like a constant?
 >> Anonymous Fri Oct 30 23:44:28 2020 No.12291512
 >> Anonymous Fri Oct 30 23:54:48 2020 No.12291532 >>12291512Now I have a family of differential equations. What does that "hint" part mean?
 >> Anonymous Fri Oct 30 23:59:57 2020 No.12291542 File: 37 KB, 361x500, think with full brain.jpg [View same] [iqdb] [saucenao] [google] [report] >>12291532bruh, use your brain$y'(x)=\frac{d}{dx}\int_2^x f(t)dt=f(x)$
 >> Anonymous Sat Oct 31 00:03:20 2020 No.12291549 >>12291157Thank you anon, I'm doing alright so far, no missed marks on my homework, but I don't want to fall behind. I think I'll just diversify my resources.
 >> Anonymous Sat Oct 31 00:07:46 2020 No.12291556 What's a good book for finding the closedform of the summations?
 >> Anonymous Sat Oct 31 00:16:59 2020 No.12291577 >>12291542But that is not the equation on the picture:$y(x) = 2 + \int_2^x [t - ty(t)]dt$$y'(x) = x - xy(x) + C$What does it mean to "use an initial condition obtained from the integral equation"?If I had the value of y(a) = b then I could use it to find C and thus one equation from the family. Do I use a = 2? If so why?Thanks for the help.
 >> Anonymous Sat Oct 31 00:21:20 2020 No.12291589 >>12291577Let t-ty(t)=f(x). Use >>12291542. Notice how there is no +C there, since $\int_2^x f(t)=F(x)-F(2)$ and F(2) is a constant, so when you differentiate, it goes away
 >> Anonymous Sat Oct 31 00:33:12 2020 No.12291615 File: 1.45 MB, 900x972, 1558264300732.png [View same] [iqdb] [saucenao] [google] [report] >>12291589Thanks femanon.>>12291542Thanks femanon.
 >> Anonymous Sat Oct 31 00:40:42 2020 No.12291636 File: 39 KB, 564x640, 1591541389150.jpg [View same] [iqdb] [saucenao] [google] [report] >>12291615>>>12291589 (You)>Thanks femanon.>>>12291542 (You)>Thanks femanon.Yeah np
 >> Anonymous Sat Oct 31 00:43:45 2020 No.12291642 >>12291577a=2 is a good choice because the integral of anything from 2 to 2 is 0
 >> Anonymous Sat Oct 31 00:50:01 2020 No.12291654 File: 89 KB, 700x827, sppjoztm7vu51.jpg [View same] [iqdb] [saucenao] [google] [report] >>12286209>>12283965Looking at buying this book. Reviews are saying there are errors throughout the book. Is it still worth it? On Amazon you can open it to random pages to look through the book, and on a random page I saw a problem where the value -(-2) randomly got converted into 4... This book sounds great but random errors sounds like bullshit. Can anyone please let me know? Thanks!
 >> Anonymous Sat Oct 31 00:57:12 2020 No.12291671 >>12291654Lang is a meme.
 >> Anonymous Sat Oct 31 01:00:12 2020 No.12291678 >>12291654Download the pdf fag.
 >> Anonymous Sat Oct 31 01:00:40 2020 No.12291679 >>12291671Yeah I think I'm gonna cancel the order. I saw grammatical errors and more math errors. Really lame.
 >> Anonymous Sat Oct 31 01:01:42 2020 No.12291680 >>12291678will do ma'am.
 >> Anonymous Sat Oct 31 01:48:01 2020 No.12291745 >>12290236*Emil Post
 >> Anonymous Sat Oct 31 02:15:43 2020 No.12291778 Successor >>12291777
 >> Anonymous Sat Oct 31 02:16:00 2020 No.12291779 >>12284305Try drawing this on a number line.
 >> Anonymous Sat Oct 31 11:53:43 2020 No.12292654 >>12284305Imagine someone removing (subtracting) your debt (negative money). That increases your net worth.
>>