2024-02-07 21:21:25 somiajZ-module: am I messing up the logic now...grr
2024-02-07 21:22:10 somiajrex: If a is a free variable, then you need a universe, though I guess if you already know something about a you don't, thanks for pointing that out.
2024-02-07 21:22:37 rexno I mean things like -1 \not\in ℕ
2024-02-07 21:22:41 rexwhy do I need a universe here?
2024-02-07 21:23:19 somiajyea, that is what I was stating, if you knew something about the object, it wasn't a free variable, then you are correct, a universal set isn't needed
2024-02-07 21:23:33 rexthat's what you meant. I see
2024-02-07 21:23:44 somiajI was (maybe incorrectly) assuming that x and y were free variables here (vs already in some other set or something is known about them, like yoru example)
2024-02-07 21:24:15 somiajso yea, I guess there are contexts in which you can use not in A, but A^c may not be welldefined
2024-02-07 21:28:21 rexwith free variables you mean, that it is implicit to what universe they belong?
2024-02-07 21:43:04 mh_leZ-module: can I get you to take a look at a solution?
2024-02-07 21:57:48 mahboubineI've got a function and I calculated it's derivative to determine whether the function is increasing or decreasing at different intervals.
2024-02-07 21:59:16 mahboubinebut the exercise correction also found the points from which the curve stars descending or ascending, for instance f(x) decends from 0 to -1/4 and back up until 0 and so on
2024-02-07 21:59:26 mahboubineI am wondering how to find those points as well
2024-02-07 22:01:14 blackfieldwell you're looking for points c such that f'(c)=0, or undefined..
2024-02-07 22:04:14 blackfieldthen you can test f''(c)>0 (then the point is a local minimum), or if f''(c)<0 it's a local maximum
2024-02-07 22:08:32 mahboubineI came to that conclusion as well
2024-02-07 22:08:39 mahboubinepretty easy now that I see it.
2024-02-07 22:08:45 mahboubinethanks, blackfield
2024-02-07 22:08:51 blackfield:)
2024-02-07 23:51:00 biberaohi
2024-02-08 00:53:39 boumawould you call within a 75% CI weak evidence ? i would call it no evidence
2024-02-08 01:00:28 somiajbouma: I would just call it a 75% CI, so 1 and 4 chance you are wrong.
2024-02-08 01:00:49 somiajI don't think a p value of 0.25 is that common, most prefer 0.05 or smaller
2024-02-08 01:34:20 PlanckWalkCi width has little to do with evidence strength.
2024-02-08 02:19:35 KZ-Spectrahello
2024-02-08 02:34:19 KZ-Spectraoriginally, the indices n+m and n-m do not coincide.
2024-02-08 02:34:39 KZ-Spectraso when impose periodicity, then I want that also to be the case
2024-02-08 02:35:15 KZ-Spectraanyway, here is a fun problem
2024-02-08 02:35:43 KZ-Spectra"Find the remainder when 9 x 99 x 999 x ... x 99....9 (999 9s) is divided by 1000"
2024-02-08 02:35:49 KZ-SpectraZ-module: ^
2024-02-08 02:43:44 Z-moduleso the last factor there is 10^999 - 1 ?
2024-02-08 03:01:14 KZ-Spectrayeah
2024-02-08 03:02:30 KZ-Spectrait's the flavor of mod arithmetic since that's what we have been doing :)
2024-02-08 03:08:00 KZ-SpectraZ-module: I'll give you the end answer: 109
2024-02-08 03:09:22 KZ-SpectraZ-module: https://i.imgur.com/vTstSUO.png can we just do this?
2024-02-08 03:15:15 PlanckWalkKZ-Spectra: Are you assuming that u_{n+m} = u_{n-m} in general?
2024-02-08 03:15:30 KZ-Spectraoh no
2024-02-08 03:19:04 PlanckWalkOh, I had trouble seeing the subscripts. After I zoomed in so I could see Z^+, yeah that's fine.
2024-02-08 03:19:16 PlanckWalkErr, superscripts
2024-02-08 03:20:09 KZ-SpectraPlanckWalk: were you comparing with the mathbin link from earlier? https://mathb.in/77541 Equation 1
2024-02-08 03:20:24 PlanckWalkNo
2024-02-08 03:21:14 PlanckWalkIt looks like it stands alone
2024-02-08 03:22:22 PlanckWalkThere are possible questions of conditional convergence, though.
2024-02-08 03:23:48 KZ-Spectrathose u's are complex
2024-02-08 03:23:49 PlanckWalkDefining a sum over Z usually requires absolute convergence, but the LHS doesn't.
2024-02-08 03:23:54 PlanckWalkDoesn't matter
2024-02-08 03:24:38 PlanckWalkSo *if* the RHS is defined, it is equal to the LHS.
2024-02-08 03:25:34 KZ-Spectrado I even need to go to Z to do my mod arithmetic argument?
2024-02-08 03:25:52 PlanckWalkNo idea, I haven't read through the mathbin at all.
2024-02-08 03:26:03 PlanckWalk(and probably won't since I'm just in a tea break at work)
2024-02-08 06:12:54 HasdielDoes anyone know of a good self-hosted open source alternative to wolfram alpha?
2024-02-08 07:18:54 PellepluttHello everyone. Our boss have given us a math problem for fun. If we solve it we will get a cake apparently. None of us here are able to solve it since it seems pretty complex so i thought i just put it out here if someone wants to take a chance :)
2024-02-08 07:18:56 PellepluttIn a fictive world. Tell me how one human male and ten human females would repopulate an deserted island in the fastest way. How many years would it take for the population to reach 1 million with unlimited food supply, pre-build shelters and enough space. Take in to calculation that a human female cannot reproduce until 13 years old on average and
2024-02-08 07:18:57 Pellepluttwill only have 1.1 child per year, The maternal mortality rate will be 0,3 %. Please show the calculation for the population reaching 1 million. Take also into calculation that 3,4 % of the the island population die before 40 due to accident and diseases.
2024-02-08 07:36:27 greenbagelsPelleplutt: interesting problem for a boss to give their employees lol
2024-02-08 07:37:11 Pellepluttgreenbagels indeed :) He has been playing around with AI but i do not know why this question came from that
2024-02-08 07:43:22 isekaijinPelleplutt: Is your boss a weeb or what? What the hell is with that plot?
2024-02-08 07:43:41 greenbagelsisekaijin: lol it is a very male-centric plot
2024-02-08 07:43:50 greenbagelsPelleplutt: how old are the original people?
2024-02-08 07:44:08 PellepluttI think he is about 43 or something
2024-02-08 07:44:15 greenbagelsno i mean in the problem
2024-02-08 07:44:55 Pellepluttoh, good question. We can assume they are above 13 and below 40
2024-02-08 08:00:15 PellepluttI guess we have to assume that its 50% males and 50% females that is born aswell
2024-02-08 08:15:37 PlanckWalkLooks like something you could just plug into a spreadsheet.
2024-02-08 08:15:47 PlanckWalkWith lots of simplifying assumptions, of course.
2024-02-08 08:16:33 PlanckWalkProabbly the most annoying relevant one would be reduced fertility with age.
2024-02-08 08:18:02 PlanckWalkInbreeding would be definitely a concern, but make a lot less difference than pretty much any other assumptions.
2024-02-08 08:19:11 PlanckWalkBut basically the boss will either give you a cake or not, on his whims. There isn't a true "correct answer" to this.
2024-02-08 08:19:26 PlanckWalk(and it's not a math problem anyway)
2024-02-08 08:25:12 PlanckWalk(If only 3.4% die before 40 on this isolated island with no pre-existing civilization then it's a fucking miracle)
2024-02-08 08:25:29 PlanckWalk(Even with food and shelter)
2024-02-08 08:29:51 PlanckWalkAnyway, maybe try asking on worldbuilding.stackexchange.com or something :-p
2024-02-08 08:30:15 PlanckWalkBecause it sounds like the premise for some crappy harem litrpg.
2024-02-08 08:33:28 PellepluttPlanckWalk haha yeah i guess :)
2024-02-08 08:33:40 PellepluttAssumtion is that there is no inbreeding problem aswell :P
2024-02-08 09:30:44 PlanckWalkPelleplutt: Then eh, if you take off every sane limit like that then you could probably do it in just over a century.
2024-02-08 09:32:12 PlanckWalk(The stated mortality rates are irrelevant, and shouldn't even have been mentioned)
2024-02-08 10:03:19 mh_lemorning all
2024-02-08 10:03:46 mahboubinemornin' mh_le
2024-02-08 10:06:00 biberaohi
2024-02-08 10:29:29 sigma1is T := { {}, {{}} } transitive?
2024-02-08 10:58:45 sigma1I'm not sure whether these are transitive T: = {∅, {{∅}} and S:= {∅, {{∅}}, {∅}} I get confused with the ∅
2024-02-08 10:59:49 machinewhoreS is transitive iff each element of S is a subset of S.
2024-02-08 11:01:00 machinewhoreIs ∅ a subset of T? Is {{∅}} a subset of T?
2024-02-08 11:01:08 sigma1it'd be T: = {∅, {{∅}} btw
2024-02-08 11:01:20 machinewhoreStill missing a bracket.
2024-02-08 11:01:35 sigma1T: = {∅, {{∅}}}
2024-02-08 11:02:01 machinewhoreIf you answer those two questions I asked, then you will know if T is transitive or not.
2024-02-08 11:02:19 biberaoimmibis: mh_le going to do it in latex
2024-02-08 11:02:22 biberaosorry
2024-02-08 11:02:26 biberaoi meant mh_le
2024-02-08 11:02:28 sigma1since the elements of ∅(i.e. none) are contained in T
2024-02-08 11:03:07 mh_lebiberao: ah cool
2024-02-08 11:07:43 machinewhoresigma1: Figure it out?
2024-02-08 11:12:46 sigma1machinewhore the set {{∅}} is a subset of T, because its element is part of T
2024-02-08 11:13:05 PlanckWalkIts element is {∅}
2024-02-08 11:14:31 PlanckWalkThe elements of T are ∅ and {{∅}}
2024-02-08 11:16:32 machinewhoreYup, those are the elements of T.
2024-02-08 11:16:41 biberaomh_le: i might need help structuring :D
2024-02-08 11:23:36 mh_lebiberao: is a solution to an assignment you are typesetting?
2024-02-08 11:24:42 biberaoyes
2024-02-08 11:25:19 mh_leok, I don't know spanish so I'm not sure I will be able to help
2024-02-08 11:25:52 biberaomh_le: its not even spanish
2024-02-08 11:25:54 biberao:\
2024-02-08 11:26:05 biberaobut the issue is structuring i wanted to make it similar
2024-02-08 11:26:27 mh_lebiberao: I'm not sure what you mean by that
2024-02-08 11:27:15 biberaomh_le: i want to be able to have like exercice 1 and so on
2024-02-08 11:27:18 biberaogood alignment
2024-02-08 11:27:37 mh_lebiberao: let's go to #latex
2024-02-08 11:27:55 biberaook
2024-02-08 11:31:52 sigma1PlanckWalk so T is transitive as ∅ is a subset of T
2024-02-08 11:33:02 sigma1and the members of {{ø}} is only {ø}, and {ø} is a subset of A
2024-02-08 11:35:03 PlanckWalkThat's not the test for transitivity
2024-02-08 11:35:17 machinewhoresigma: What are the members of T?
2024-02-08 11:35:35 sigma1ø, {{ø}}
2024-02-08 11:35:48 machinewhoreCorrect.
2024-02-08 11:35:57 machinewhoreIs ø a subset of T?
2024-02-08 11:36:10 sigma1yes
2024-02-08 11:36:13 machinewhoreCorrect.
2024-02-08 11:36:16 machinewhoreIs {{ø}} a subset of T?
2024-02-08 11:36:42 sigma1yes
2024-02-08 11:37:04 machinewhoreWhat is the definition of "subset'?
2024-02-08 11:38:12 sigma1If B is a set whose elements are included in a set A we say that B is included in A or that B subset of A
2024-02-08 11:38:28 PlanckWalkLet's not use the word "included".
2024-02-08 11:38:53 PlanckWalkSometimes people use it to mean "element of", sometimes they use it to mean "subset of".
2024-02-08 11:39:15 PlanckWalkAs you did!
2024-02-08 11:39:25 machinewhore!^
2024-02-08 11:39:38 PlanckWalkAs in, you use it both ways.
2024-02-08 11:39:41 PlanckWalkused* it
2024-02-08 11:40:45 PlanckWalkSo try again without using the word "included".
2024-02-08 11:41:49 sigma1'part of a set A' instead of that
2024-02-08 11:44:04 PlanckWalkNo, let's not.
2024-02-08 11:44:17 PlanckWalkTry looking up a definition.
2024-02-08 11:45:00 PlanckWalkThe one you're using is broken.
2024-02-08 11:48:05 machinewhore42sigma1: Are you a native English speaker?
2024-02-08 11:50:42 sigma1A is a subset of B, if and only if every element of A is an element of B
2024-02-08 11:51:00 PlanckWalkThat one looks better
2024-02-08 11:51:36 PlanckWalkI severy element of {{ø}} an element of T?
2024-02-08 11:53:35 sigma1it seems so
2024-02-08 11:53:49 PlanckWalkWhat are the elements of {{ø}}?
2024-02-08 11:54:50 sigma1the set {ø}
2024-02-08 11:54:58 PlanckWalkWhat are the elements of T?
2024-02-08 11:55:32 sigma1the set {ø} and ø
2024-02-08 11:55:39 *PlanckWalk scrolls up.
2024-02-08 11:55:42 PlanckWalkAre you sure?
2024-02-08 11:57:43 sigma1err the other should be {{ø}}
2024-02-08 11:58:36 PlanckWalkWhich other?
2024-02-08 11:59:00 sigma1{{ø}} and ø
2024-02-08 11:59:19 PlanckWalkOkay. Is {ø} an element of T?
2024-02-08 11:59:35 sigma1no
2024-02-08 12:00:06 PlanckWalkRight, so now you can answer whether T is transitive.
2024-02-08 12:00:34 PlanckWalkYou've checked its elements, and found one that's not a subset.
2024-02-08 12:01:33 mh_leLet B - i -> B' - p -> B'' be an exact sequence of left R-modules, and let A be a right R-module and consider the maps id_A (X) i and id_A (X) p then (id_A (X) p) \circ (id_A (X) i) = id_A (X) 0, but why is this the zero map?
2024-02-08 12:01:47 mh_leR is a ring
2024-02-08 12:06:00 mh_lehere 0 must be the map b \mapsto i(b)\mapto p(i(b))=0 for all b in B, but the Id_A is not zero
2024-02-08 12:06:13 mh_lethe map*
2024-02-08 12:07:52 mh_lewait
2024-02-08 12:11:47 sigma1is U\T transitive?
2024-02-08 12:12:43 mh_ler( a (X) b) = (ar (x) b) = (a (x) rb). so ( a (x) 0) = 0
2024-02-08 12:13:03 mh_lethat's not right
2024-02-08 12:20:22 --Mode ##math [+o int-e] by ChanServ
2024-02-08 12:20:25 --Mode ##math [+b-o *!*@2a02:810b:4b40:2998:* int-e] by int-e
2024-02-08 12:28:39 mh_leso it was pretty obvious that a (x) 0 = 0
2024-02-08 13:56:52 sigma1the text asks me whether U \ T is transitive
2024-02-08 13:58:57 int-eCool. What are U and T?
2024-02-08 14:21:39 biberaoZ-module: ?
2024-02-08 14:22:29 brass_Can the sine function be achieved using finite combination of the basic operations?
2024-02-08 14:24:34 dTalNo, sine is transcendental
2024-02-08 15:34:27 paulowhy are solutions shown as complex when the line clearly intersects the graph in real space?
2024-02-08 16:12:14 brass_dTal Can I message you privately, I can't respond here.
2024-02-08 16:12:50 dTalYou can't?
2024-02-08 16:12:54 dTalErm, I guess...
2024-02-08 16:13:24 brass_?Yup ok, it's just that what I might say may sound too dumb on an elementary level.
2024-02-08 16:27:14 ecravenhello ;) I'm looking for a function that does the following: I know N (the number of items) and i (the index of the current pick). I'd like to go from i=0..N-1, and get back a "random" ordering (so not 0, 1, 2, ... but 5, 7, 23, 1, ...) where each number from 0 to N-1 occurs exactly once for i=0..N-1.
2024-02-08 16:27:34 ecravenI've tried i*K mod N with K being a coprime to N, but that .. doesn't seem to be correct.
2024-02-08 16:30:27 Z-modulepaulo: putting y = 3 in that and working with the resulting equation x^3 + 7x^2 - 144x - 9, I get (if I haven't made an error) the discriminant to be 13133457, which (being positive) means there are three distinct real roots. *Somehow* the particular numbers are fouling up the floating-point solvers. Notice how very minuscule all those imaginary parts are.
2024-02-08 16:32:08 mh_lehey all
2024-02-08 16:34:55 ecravenand it works fine, I just implemented it wrong ;)
2024-02-08 17:05:51 biberaoZ-module: tell me what you think https://github.com/gitmapd/gitmapd.github.io/blob/master/limites%20nova%20ficha.pdf <- finished exercise 2 and 3
2024-02-08 17:14:49 Z-moduleLooks good, biberao
2024-02-08 17:16:41 biberaoZ-module: ive added another thing to prove bounded for 3-2n
2024-02-08 17:16:49 biberaoif you do f5 should have updated
2024-02-08 17:19:43 Z-moduleI think you mean 3 - 2/n
2024-02-08 17:19:50 biberaono
2024-02-08 17:19:50 Z-module(here in irc)
2024-02-08 17:19:52 biberao3-2n
2024-02-08 17:19:58 Z-modulethe sequence 3 - 2n is not bounded
2024-02-08 17:20:09 biberaothats what i said
2024-02-08 17:20:14 biberaoi meant to say
2024-02-08 17:20:20 biberaohow do i prove its not bounded
2024-02-08 17:20:39 biberaoi did lim n (3-2n) = -inf
2024-02-08 17:20:48 biberaothats what i meant to say
2024-02-08 17:20:53 biberaomawk: thanks :D
2024-02-08 17:22:22 Z-moduleTake any real r (of any sign). Then 3 - 2n < r iff (3 - r)/2 < n , so for all n > (3 - r)/2, that holds. This is the meaning of lim (3 - 2n) = -infty
2024-02-08 17:23:46 biberaoah
2024-02-08 17:23:56 biberaomaybe i should use the delta epsilon?
2024-02-08 17:27:48 Z-moduleThat's what this is, but in the form used for sequences
2024-02-08 17:28:50 Z-moduleA sequence {b_n} goes to +infty if: Forall r exists M forall n > M b_n > r Change that last > to < and you get the form for -> -infty
2024-02-08 17:31:04 mh_lehi Z-module
2024-02-08 17:33:27 Z-moduleThis reminds me of a very neat thing. Let g_n mean (the (n+1)st prime) - (the nth prime), the nth prime gap. It turns out we don't need really heavy analytic number theory for the following: merely the pretty basic (easier-to-prove than you might think) Chebyshev bounds suffice, and I think only one side of it is even enough: Infinitely many n exist with g_n < g_(n+1) > g_(n+2), also infinitely many with g_n > g_(n+1) < g_(n+2).
2024-02-08 17:52:49 biberaoback
2024-02-08 17:52:51 biberaosorry
2024-02-08 17:53:27 biberaoZ-module: thank you
2024-02-08 17:56:29 thesebCan someone tell me how they got the "observed power" on this A/B test calculator? https://abtestguide.com/calc/
2024-02-08 18:05:45 biberaoZ-module: so for example if an = 3-2n was a monotonic increasing i could do an > M
2024-02-08 18:05:59 biberaook
2024-02-08 18:06:01 biberaoi guess that works
2024-02-08 18:06:03 biberaothank you
2024-02-08 18:06:47 Z-moduleby the way, a sequence can -> +infty without being monotonic or eventually monotonic. For example: 1, 2, 3, 2, 3, 4, 3, 4, 5, 4, 5, 6 ...
2024-02-08 18:07:09 biberaoi see
2024-02-08 18:07:20 biberaofor this case is this right to say 1 < 3-2n < -inf
2024-02-08 18:07:22 biberao?
2024-02-08 18:07:32 biberaoi dont know if its a good notation
2024-02-08 18:07:42 Z-moduleHowever, that prime gaps sequence {g_n}, while unbounded, does not -> infty, as we've only known with proof for around a decade.
2024-02-08 18:08:05 Z-modulenothing is < -infty
2024-02-08 18:08:13 Z-moduleso don't write that
2024-02-08 18:08:14 biberaook
2024-02-08 18:08:20 biberaobut you understood what i meant
2024-02-08 18:08:25 biberaook
2024-02-08 18:08:28 Z-moduleI didn't, nor would anyone else
2024-02-08 18:08:29 biberaoi meant to say
2024-02-08 18:08:32 biberaosorry
2024-02-08 18:08:34 biberaoi meant to say
2024-02-08 18:08:44 biberao-inf < 3-2n < 1
2024-02-08 18:09:14 greenbagels<= 1
2024-02-08 18:09:21 Z-moduleokay but -infty < any reals you like, so there's no point writing that. Finitely many innequalities have nothing to do with -> -infty
2024-02-08 18:09:34 biberaogreenbagels: thank you
2024-02-08 18:09:51 biberaolike now i understood what you taught me today
2024-02-08 18:18:11 biberaocheck my updated
2024-02-08 18:18:17 biberaoExercise 2 d)
2024-02-08 18:18:19 biberaoplease
2024-02-08 18:26:08 Z-moduleI don't think you need to check or mention that 1 > every a_n at all. Simply the fact that eventually all a_n are < any pre-selected number is enough to get that the sequence is not bounded. Also you shouldn't write lim a_n = -infty at the top like that: only write it after showing it to be true.
2024-02-08 18:27:06 biberaowhat if for example
2024-02-08 18:27:17 Z-modulethe 1 > all a_n would be relevant if you were dealing with "unbounded only on one side" as a separate / special case of "unbounded".
2024-02-08 18:27:21 Z-modulebut you're not
2024-02-08 18:27:40 biberaoah so with a_n >M or a_n < M
2024-02-08 18:27:42 biberaoworks for both sides?
2024-02-08 18:37:35 Z-module{b_n} is "bounded" iff some positive r exists with |b_n| < r (same as: -r < b_n < r ) for all n. Equivalent to saying some reals r < s exist with r < b_n < s for all n. The negation of this, {b_n} unbounded, is: EITHER: for every r, for infinitely many n, r < b_n (that's unbounded above), OR: for every r, for infinitely many n, r > b_n (unbounded below). Or both.
2024-02-08 18:39:07 Z-moduleBut unbounded above is weaker than {b_n} -> +infty ; unbounded below is weaker than {b_n} -> -infty. The sequence 0, 1, 0, 2, 0, 3, 0, 4, ... is unbounded above, but does not -> +infty.
2024-02-08 18:44:05 biberaoZ-module: so thats the way we did earlier then
2024-02-08 19:12:37 greenbagelsrealistically i dont know if i have the time for it tbh
2024-02-08 19:12:55 mh_leok no problem :)
2024-02-08 19:39:08 SimplarI'm having issues with elementary problem. I want to find out how to prove that even divided by odd is always even if the divisor divides dividend. I know that even number has 2 among the multiples, while odd number never does, so the two won't go anywhere.
2024-02-08 19:39:15 SimplarBut how to prove the same with subtractions?
2024-02-08 19:57:50 Z-moduleSimplar: 2m - (2n + 1) = 2(m - n) - 1 = 2(m - n - 1) + 1 and this last is odd.
2024-02-08 20:09:22 SimplarZ-module: I meant (2m) / (2n+1)
2024-02-08 20:09:39 SimplarHow can we guarantee that the quotient will always be even?
2024-02-08 20:10:06 Simplar2m = (2n+1)q + r
2024-02-08 20:13:59 Guest5398Hello, sorry, If you have 7 Characters and every 1 day Chance of Birth is 1%, how can i create a function that will Tell me the amount of Characters after n days?
2024-02-08 20:24:46 Z-moduleSimplar: The question presupposes that the numerator n = 2m is an integer multiple of the denominator d where d is odd. So 2m = kd for some k. So 2m/d = k, and k can't be odd because then d, also being odd, would mean kd is also odd, not true since kd = 2m.
2024-02-08 20:25:06 Z-modulealso, note taht "difference" referes to the - operator, not the / operator
2024-02-08 20:28:06 Z-moduleSimplar: another way to put that. 2m = kd and prime factoriation is unique (up to order), so 2 appears somewhere in the prime factorization of kd. But it's not in d, so it must be in k. So 2m/d = k is even.
2024-02-08 20:33:50 Guest5398Its Like having seven dollars and getting 1% interest? Having 7 Characters having a Baby at 1% Chance . That should be IT.
2024-02-08 20:35:17 pavoniaGuest5398: What is the relation between characters and birth here?
2024-02-08 20:36:21 pavoniaOr is it like characters in a game?
2024-02-08 20:36:40 Guest5398I mean Characters can increase by 1 at a 1% Chance per one Character per day
2024-02-08 20:36:46 Guest5398Yes. Sorry.
2024-02-08 20:42:24 mahboubinebasic question: I've calculated the derivative of some function f, then I was asked to calculate f'(x) at some point c. I did this and the result was an undetermined form (5/0) where do I move from there?
2024-02-08 20:42:49 mahboubineI am used to facing undetermined forms in limits but I don't know how to deal with them in this case
2024-02-08 20:43:36 pavoniaGuest5398: I guess it's a matter of definition if the chance after N days is 0.01*N or (1.01)^N
2024-02-08 20:43:43 pavonia...
2024-02-08 20:46:19 serveeewhy is topology so hard to understand
2024-02-08 20:46:26 serveeeset topology that is
2024-02-08 20:46:37 mh_leis it?
2024-02-08 20:46:49 serveeemaybe im just not understanding it right
2024-02-08 20:47:02 Galoisit's a lot easier if you know real analysis well
2024-02-08 20:47:26 serveeehow so
2024-02-08 20:47:47 Galoisin real analysis you (are supposed to) learn about open and closed sets arising from metric spaces
2024-02-08 20:47:52 mh_leserveee: topology is the study of continuity
2024-02-08 20:48:12 serveeei should go back some steps then
2024-02-08 20:48:23 Galoismetric spaces are already an abstraction of Euclidean space, and one which is useful in many ways, but abstracting to open and closed sets is a perfectly natural next step, and that gives you topology
2024-02-08 20:48:32 serveeefrustrating but this isnt something im not familiar with
2024-02-08 20:48:45 mh_leserveee: you are welcome to ask if there is something specific that's not clear to you
2024-02-08 21:17:11 Z-modulemahboubine: what's your f, and your c ? f might not actually be differentiable at c
2024-02-08 21:20:53 mh_leZ-module: pm?
2024-02-08 21:33:28 mahboubineZ-module: oh forgot about this, as you said f turned out not differentiable at c
2024-02-08 21:33:35 mahboubineI was overthinking the whole thing
2024-02-08 22:27:54 adderI'm trying to do IDWDS on a three table game, but I'm not sure how. Can someone help? | | Ann | Bob | Carla |
2024-02-08 22:28:28 b0nnadder: FTR a paste site would have been more appropriate than posting into the channel
2024-02-08 22:29:00 adderI know, I just mispasted the screenshot url. I meant to paste: https://imgur.com/AM8lJ0J.png
2024-02-08 22:29:36 adderSo what I don't get is how a three-table game reduced to a single table.
2024-02-08 22:29:48 adderThat is, I'm not following what the text says.
2024-02-08 22:35:18 int-eHmm. the label on the 2nd (or is that 4th) figure should be "Anna votes for A".
2024-02-08 22:36:03 adderAh, that makes sense.
2024-02-08 22:36:25 int-eadder: But that seems to be the only thing wrong with it... what are you having trouble with?
2024-02-08 22:39:10 adderNothing, it checks out now.
2024-02-08 22:39:13 adderThanks, int-e.
2024-02-08 22:39:20 int-eCool, np.
21:21somiajZ-module: am I messing up the logic now...grr
21:22somiajrex: If a is a free variable, then you need a universe, though I guess if you already know something about a you don't, thanks for pointing that out.
21:22rexno I mean things like -1 \not\in ℕ
21:22rexwhy do I need a universe here?
21:23somiajyea, that is what I was stating, if you knew something about the object, it wasn't a free variable, then you are correct, a universal set isn't needed
21:23rexthat's what you meant. I see
21:23somiajI was (maybe incorrectly) assuming that x and y were free variables here (vs already in some other set or something is known about them, like yoru example)
21:24somiajso yea, I guess there are contexts in which you can use not in A, but A^c may not be welldefined
21:28rexwith free variables you mean, that it is implicit to what universe they belong?
21:43mh_leZ-module: can I get you to take a look at a solution?
21:57mahboubineI've got a function and I calculated it's derivative to determine whether the function is increasing or decreasing at different intervals.
21:59mahboubinebut the exercise correction also found the points from which the curve stars descending or ascending, for instance f(x) decends from 0 to -1/4 and back up until 0 and so on
21:59mahboubineI am wondering how to find those points as well
22:01blackfieldwell you're looking for points c such that f'(c)=0, or undefined..
22:04blackfieldthen you can test f''(c)>0 (then the point is a local minimum), or if f''(c)<0 it's a local maximum
22:08mahboubineI came to that conclusion as well
22:08mahboubinepretty easy now that I see it.
22:08mahboubinethanks, blackfield
22:08blackfield:)
23:51biberaohi
00:53boumawould you call within a 75% CI weak evidence ? i would call it no evidence
01:00somiajbouma: I would just call it a 75% CI, so 1 and 4 chance you are wrong.
01:00somiajI don't think a p value of 0.25 is that common, most prefer 0.05 or smaller
01:34PlanckWalkCi width has little to do with evidence strength.
02:19KZ-Spectrahello
02:34KZ-Spectraoriginally, the indices n+m and n-m do not coincide.
02:34KZ-Spectraso when impose periodicity, then I want that also to be the case
02:35KZ-Spectraanyway, here is a fun problem
02:35KZ-Spectra"Find the remainder when 9 x 99 x 999 x ... x 99....9 (999 9s) is divided by 1000"
02:35KZ-SpectraZ-module: ^
02:43Z-moduleso the last factor there is 10^999 - 1 ?
03:01KZ-Spectrayeah
03:02KZ-Spectrait's the flavor of mod arithmetic since that's what we have been doing :)
03:08KZ-SpectraZ-module: I'll give you the end answer: 109
03:09KZ-SpectraZ-module: https://i.imgur.com/vTstSUO.png can we just do this?
03:15PlanckWalkKZ-Spectra: Are you assuming that u_{n+m} = u_{n-m} in general?
03:15KZ-Spectraoh no
03:19PlanckWalkOh, I had trouble seeing the subscripts. After I zoomed in so I could see Z^+, yeah that's fine.
03:19PlanckWalkErr, superscripts
03:20KZ-SpectraPlanckWalk: were you comparing with the mathbin link from earlier? https://mathb.in/77541 Equation 1
03:20PlanckWalkNo
03:21PlanckWalkIt looks like it stands alone
03:22PlanckWalkThere are possible questions of conditional convergence, though.
03:23KZ-Spectrathose u's are complex
03:23PlanckWalkDefining a sum over Z usually requires absolute convergence, but the LHS doesn't.
03:23PlanckWalkDoesn't matter
03:24PlanckWalkSo *if* the RHS is defined, it is equal to the LHS.
03:25KZ-Spectrado I even need to go to Z to do my mod arithmetic argument?
03:25PlanckWalkNo idea, I haven't read through the mathbin at all.
03:26PlanckWalk(and probably won't since I'm just in a tea break at work)
06:12HasdielDoes anyone know of a good self-hosted open source alternative to wolfram alpha?
07:18PellepluttHello everyone. Our boss have given us a math problem for fun. If we solve it we will get a cake apparently. None of us here are able to solve it since it seems pretty complex so i thought i just put it out here if someone wants to take a chance :)
07:18PellepluttIn a fictive world. Tell me how one human male and ten human females would repopulate an deserted island in the fastest way. How many years would it take for the population to reach 1 million with unlimited food supply, pre-build shelters and enough space. Take in to calculation that a human female cannot reproduce until 13 years old on average and
07:18Pellepluttwill only have 1.1 child per year, The maternal mortality rate will be 0,3 %. Please show the calculation for the population reaching 1 million. Take also into calculation that 3,4 % of the the island population die before 40 due to accident and diseases.
07:36greenbagelsPelleplutt: interesting problem for a boss to give their employees lol
07:37Pellepluttgreenbagels indeed :) He has been playing around with AI but i do not know why this question came from that
07:43isekaijinPelleplutt: Is your boss a weeb or what? What the hell is with that plot?
07:43greenbagelsisekaijin: lol it is a very male-centric plot
07:43greenbagelsPelleplutt: how old are the original people?
07:44PellepluttI think he is about 43 or something
07:44greenbagelsno i mean in the problem
07:44Pellepluttoh, good question. We can assume they are above 13 and below 40
08:00PellepluttI guess we have to assume that its 50% males and 50% females that is born aswell
08:15PlanckWalkLooks like something you could just plug into a spreadsheet.
08:15PlanckWalkWith lots of simplifying assumptions, of course.
08:16PlanckWalkProabbly the most annoying relevant one would be reduced fertility with age.
08:18PlanckWalkInbreeding would be definitely a concern, but make a lot less difference than pretty much any other assumptions.
08:19PlanckWalkBut basically the boss will either give you a cake or not, on his whims. There isn't a true "correct answer" to this.
08:19PlanckWalk(and it's not a math problem anyway)
08:25PlanckWalk(If only 3.4% die before 40 on this isolated island with no pre-existing civilization then it's a fucking miracle)
08:25PlanckWalk(Even with food and shelter)
08:29PlanckWalkAnyway, maybe try asking on worldbuilding.stackexchange.com or something :-p
08:30PlanckWalkBecause it sounds like the premise for some crappy harem litrpg.
08:33PellepluttPlanckWalk haha yeah i guess :)
08:33PellepluttAssumtion is that there is no inbreeding problem aswell :P
09:30PlanckWalkPelleplutt: Then eh, if you take off every sane limit like that then you could probably do it in just over a century.
09:32PlanckWalk(The stated mortality rates are irrelevant, and shouldn't even have been mentioned)
10:03mh_lemorning all
10:03mahboubinemornin' mh_le
10:06biberaohi
10:29sigma1is T := { {}, {{}} } transitive?
10:30Inlinevertically not, horizontally maybe
10:33mh_lesigma1: what is the definition of "transitive" in this sense?
10:34sigma1is each element of the set is a subset of the set
10:34sigma1*If
10:35mh_leif would help if you were a bit more precise
10:36sigma1A set H is transitive if every one of its elements is a subset.
10:37mh_lethen yes
10:40sigma1and T := { {}, {{}}, {{{}}} } ?
10:41lericsonwe went through this, sigma1
10:41lericsoncan you check for yourself?
10:47biberaomath time
10:48mh_lewhich kind?
10:50biberaomh_le: i did some trig and sequences yesterday night
10:50mh_legreat
10:51machinewhoreIs there a collection of urn problems/solutions somewhere that I can use for practice?
10:52mh_leurn?
10:52mh_leyou mean counting/probability problems?
10:52machinewhoreyeah
10:53machinewhoreeg, 50 red balls and 50 black balls randomly distributed between 2 urns, yada yada
10:58sigma1I'm not sure whether these are transitive T: = {∅, {{∅}} and S:= {∅, {{∅}}, {∅}} I get confused with the ∅
10:59machinewhoreS is transitive iff each element of S is a subset of S.
11:01machinewhoreIs ∅ a subset of T? Is {{∅}} a subset of T?
11:01sigma1it'd be T: = {∅, {{∅}} btw
11:01machinewhoreStill missing a bracket.
11:01sigma1T: = {∅, {{∅}}}
11:02machinewhoreIf you answer those two questions I asked, then you will know if T is transitive or not.
11:02biberaoimmibis: mh_le going to do it in latex
11:02biberaosorry
11:02biberaoi meant mh_le
11:02sigma1since the elements of ∅(i.e. none) are contained in T
11:03mh_lebiberao: ah cool
11:07machinewhoresigma1: Figure it out?
11:12sigma1machinewhore the set {{∅}} is a subset of T, because its element is part of T
11:13PlanckWalkIts element is {∅}
11:14PlanckWalkThe elements of T are ∅ and {{∅}}
11:16machinewhoreYup, those are the elements of T.
11:16biberaomh_le: i might need help structuring :D
11:23mh_lebiberao: is a solution to an assignment you are typesetting?
11:24biberaoyes
11:25mh_leok, I don't know spanish so I'm not sure I will be able to help
11:25biberaomh_le: its not even spanish
11:25biberao:\
11:26biberaobut the issue is structuring i wanted to make it similar
11:26mh_lebiberao: I'm not sure what you mean by that
11:27biberaomh_le: i want to be able to have like exercice 1 and so on
11:27biberaogood alignment
11:27mh_lebiberao: let's go to #latex
11:27biberaook
11:31sigma1PlanckWalk so T is transitive as ∅ is a subset of T
11:33sigma1and the members of {{ø}} is only {ø}, and {ø} is a subset of A
11:35PlanckWalkThat's not the test for transitivity
11:35machinewhoresigma: What are the members of T?
11:35sigma1ø, {{ø}}
11:35machinewhoreCorrect.
11:35machinewhoreIs ø a subset of T?
11:36sigma1yes
11:36machinewhoreCorrect.
11:36machinewhoreIs {{ø}} a subset of T?
11:36sigma1yes
11:37machinewhoreWhat is the definition of "subset'?
11:38sigma1If B is a set whose elements are included in a set A we say that B is included in A or that B subset of A
11:38PlanckWalkLet's not use the word "included".
11:38PlanckWalkSometimes people use it to mean "element of", sometimes they use it to mean "subset of".
11:39PlanckWalkAs you did!
11:39machinewhore!^
11:39PlanckWalkAs in, you use it both ways.
11:39PlanckWalkused* it
11:40PlanckWalkSo try again without using the word "included".
11:41sigma1'part of a set A' instead of that
11:44PlanckWalkNo, let's not.
11:44PlanckWalkTry looking up a definition.
11:45PlanckWalkThe one you're using is broken.
11:48machinewhore42sigma1: Are you a native English speaker?
11:50sigma1A is a subset of B, if and only if every element of A is an element of B
11:51PlanckWalkThat one looks better
11:51PlanckWalkI severy element of {{ø}} an element of T?
11:53sigma1it seems so
11:53PlanckWalkWhat are the elements of {{ø}}?
11:54sigma1the set {ø}
11:54PlanckWalkWhat are the elements of T?
11:55sigma1the set {ø} and ø
11:55 *PlanckWalk scrolls up.
11:55PlanckWalkAre you sure?
11:57sigma1err the other should be {{ø}}
11:58PlanckWalkWhich other?
11:59sigma1{{ø}} and ø
11:59PlanckWalkOkay. Is {ø} an element of T?
11:59sigma1no
12:00PlanckWalkRight, so now you can answer whether T is transitive.
12:00PlanckWalkYou've checked its elements, and found one that's not a subset.
12:01mh_leLet B - i -> B' - p -> B'' be an exact sequence of left R-modules, and let A be a right R-module and consider the maps id_A (X) i and id_A (X) p then (id_A (X) p) \circ (id_A (X) i) = id_A (X) 0, but why is this the zero map?
12:01mh_leR is a ring
12:06mh_lehere 0 must be the map b \mapsto i(b)\mapto p(i(b))=0 for all b in B, but the Id_A is not zero
12:06mh_lethe map*
12:07mh_lewait
12:11sigma1is U\T transitive?
12:12mh_ler( a (X) b) = (ar (x) b) = (a (x) rb). so ( a (x) 0) = 0
12:13mh_lethat's not right
12:20--Mode ##math [+o int-e] by ChanServ
12:20--Mode ##math [+b-o *!*@2a02:810b:4b40:2998:* int-e] by int-e
12:28mh_leso it was pretty obvious that a (x) 0 = 0
13:56sigma1the text asks me whether U \ T is transitive
13:58int-eCool. What are U and T?
14:21biberaoZ-module: ?
14:22brass_Can the sine function be achieved using finite combination of the basic operations?
15:34paulowhy are solutions shown as complex when the line clearly intersects the graph in real space?
16:12brass_dTal Can I message you privately, I can't respond here.
16:12dTalYou can't?
16:12dTalErm, I guess...
16:13brass_?Yup ok, it's just that what I might say may sound too dumb on an elementary level.
16:27ecravenhello ;) I'm looking for a function that does the following: I know N (the number of items) and i (the index of the current pick). I'd like to go from i=0..N-1, and get back a "random" ordering (so not 0, 1, 2, ... but 5, 7, 23, 1, ...) where each number from 0 to N-1 occurs exactly once for i=0..N-1.
16:27ecravenI've tried i*K mod N with K being a coprime to N, but that .. doesn't seem to be correct.
16:30Z-modulepaulo: putting y = 3 in that and working with the resulting equation x^3 + 7x^2 - 144x - 9, I get (if I haven't made an error) the discriminant to be 13133457, which (being positive) means there are three distinct real roots. *Somehow* the particular numbers are fouling up the floating-point solvers. Notice how very minuscule all those imaginary parts are.
16:32mh_lehey all
16:34ecravenand it works fine, I just implemented it wrong ;)
17:05biberaoZ-module: tell me what you think https://github.com/gitmapd/gitmapd.github.io/blob/master/limites%20nova%20ficha.pdf <- finished exercise 2 and 3
17:14Z-moduleLooks good, biberao
17:16biberaoZ-module: ive added another thing to prove bounded for 3-2n
17:16biberaoif you do f5 should have updated
17:19Z-moduleI think you mean 3 - 2/n
17:19biberaono
17:19Z-module(here in irc)
17:19biberao3-2n
17:19Z-modulethe sequence 3 - 2n is not bounded
17:20biberaothats what i said
17:20biberaoi meant to say
17:20biberaohow do i prove its not bounded
17:20biberaoi did lim n (3-2n) = -inf
17:20biberaothats what i meant to say
17:20biberaomawk: thanks :D
17:22Z-moduleTake any real r (of any sign). Then 3 - 2n < r iff (3 - r)/2 < n , so for all n > (3 - r)/2, that holds. This is the meaning of lim (3 - 2n) = -infty
17:23biberaoah
17:23biberaomaybe i should use the delta epsilon?
17:27Z-moduleThat's what this is, but in the form used for sequences
17:28Z-moduleA sequence {b_n} goes to +infty if: Forall r exists M forall n > M b_n > r Change that last > to < and you get the form for -> -infty
17:31mh_lehi Z-module
17:33Z-moduleThis reminds me of a very neat thing. Let g_n mean (the (n+1)st prime) - (the nth prime), the nth prime gap. It turns out we don't need really heavy analytic number theory for the following: merely the pretty basic (easier-to-prove than you might think) Chebyshev bounds suffice, and I think only one side of it is even enough: Infinitely many n exist with g_n < g_(n+1) > g_(n+2), also infinitely many with g_n > g_(n+1) < g_(n+2).
17:52biberaoback
17:52biberaosorry
17:53biberaoZ-module: thank you
17:56thesebCan someone tell me how they got the "observed power" on this A/B test calculator? https://abtestguide.com/calc/
17:57theseb"two proportions hypothesis testing"
18:05biberaoZ-module: so for example if an = 3-2n was a monotonic increasing i could do an > M
18:05biberaook
18:06biberaoi guess that works
18:06biberaothank you
18:06Z-moduleby the way, a sequence can -> +infty without being monotonic or eventually monotonic. For example: 1, 2, 3, 2, 3, 4, 3, 4, 5, 4, 5, 6 ...
18:07biberaoi see
18:07biberaofor this case is this right to say 1 < 3-2n < -inf
18:07biberao?
18:07biberaoi dont know if its a good notation
18:07Z-moduleHowever, that prime gaps sequence {g_n}, while unbounded, does not -> infty, as we've only known with proof for around a decade.
18:08Z-modulenothing is < -infty
18:08Z-moduleso don't write that
18:08biberaook
18:08biberaobut you understood what i meant
18:08biberaook
18:08Z-moduleI didn't, nor would anyone else
18:08biberaoi meant to say
18:08biberaosorry
18:08biberaoi meant to say
18:08biberao-inf < 3-2n < 1
18:09greenbagels<= 1
18:09Z-moduleokay but -infty < any reals you like, so there's no point writing that. Finitely many innequalities have nothing to do with -> -infty
18:09biberaogreenbagels: thank you
18:09biberaolike now i understood what you taught me today
18:18biberaocheck my updated
18:18biberaoExercise 2 d)
18:18biberaoplease
18:26Z-moduleI don't think you need to check or mention that 1 > every a_n at all. Simply the fact that eventually all a_n are < any pre-selected number is enough to get that the sequence is not bounded. Also you shouldn't write lim a_n = -infty at the top like that: only write it after showing it to be true.
18:27biberaowhat if for example
18:27Z-modulethe 1 > all a_n would be relevant if you were dealing with "unbounded only on one side" as a separate / special case of "unbounded".
18:27Z-modulebut you're not
18:27biberaoah so with a_n >M or a_n < M
18:27biberaoworks for both sides?
18:37Z-module{b_n} is "bounded" iff some positive r exists with |b_n| < r (same as: -r < b_n < r ) for all n. Equivalent to saying some reals r < s exist with r < b_n < s for all n. The negation of this, {b_n} unbounded, is: EITHER: for every r, for infinitely many n, r < b_n (that's unbounded above), OR: for every r, for infinitely many n, r > b_n (unbounded below). Or both.
18:39Z-moduleBut unbounded above is weaker than {b_n} -> +infty ; unbounded below is weaker than {b_n} -> -infty. The sequence 0, 1, 0, 2, 0, 3, 0, 4, ... is unbounded above, but does not -> +infty.
18:44biberaoZ-module: so thats the way we did earlier then
18:44biberaob_n < M or b_n > M
18:47biberaook gtg
18:47biberaothank you
18:48greenbagelsanother happy customer
19:11mh_lehi
19:11mh_lehey greenbagels
19:11greenbagelshi
19:12mh_leany progres on Wald?
19:12greenbagelsrealistically i dont know if i have the time for it tbh
19:12mh_leok no problem :)
19:39SimplarI'm having issues with elementary problem. I want to find out how to prove that even divided by odd is always even if the divisor divides dividend. I know that even number has 2 among the multiples, while odd number never does, so the two won't go anywhere.
19:39SimplarBut how to prove the same with subtractions?
19:57Z-moduleSimplar: 2m - (2n + 1) = 2(m - n) - 1 = 2(m - n - 1) + 1 and this last is odd.
20:09SimplarZ-module: I meant (2m) / (2n+1)
20:09SimplarHow can we guarantee that the quotient will always be even?
20:10Simplar2m = (2n+1)q + r
20:13Guest5398Hello, sorry, If you have 7 Characters and every 1 day Chance of Birth is 1%, how can i create a function that will Tell me the amount of Characters after n days?
20:24Z-moduleSimplar: The question presupposes that the numerator n = 2m is an integer multiple of the denominator d where d is odd. So 2m = kd for some k. So 2m/d = k, and k can't be odd because then d, also being odd, would mean kd is also odd, not true since kd = 2m.
20:25Z-modulealso, note taht "difference" referes to the - operator, not the / operator
20:28Z-moduleSimplar: another way to put that. 2m = kd and prime factoriation is unique (up to order), so 2 appears somewhere in the prime factorization of kd. But it's not in d, so it must be in k. So 2m/d = k is even.
20:33Guest5398Its Like having seven dollars and getting 1% interest? Having 7 Characters having a Baby at 1% Chance . That should be IT.
20:35pavoniaGuest5398: What is the relation between characters and birth here?
20:36pavoniaOr is it like characters in a game?
20:36Guest5398I mean Characters can increase by 1 at a 1% Chance per one Character per day
20:36Guest5398Yes. Sorry.
20:42mahboubinebasic question: I've calculated the derivative of some function f, then I was asked to calculate f'(x) at some point c. I did this and the result was an undetermined form (5/0) where do I move from there?
20:42mahboubineI am used to facing undetermined forms in limits but I don't know how to deal with them in this case
20:43pavoniaGuest5398: I guess it's a matter of definition if the chance after N days is 0.01*N or (1.01)^N
20:43pavonia...
20:46serveeewhy is topology so hard to understand
20:46serveeeset topology that is
20:46mh_leis it?
20:46serveeemaybe im just not understanding it right
20:47Galoisit's a lot easier if you know real analysis well
20:47serveeehow so
20:47Galoisin real analysis you (are supposed to) learn about open and closed sets arising from metric spaces
20:47mh_leserveee: topology is the study of continuity
20:48serveeei should go back some steps then
20:48Galoismetric spaces are already an abstraction of Euclidean space, and one which is useful in many ways, but abstracting to open and closed sets is a perfectly natural next step, and that gives you topology
20:48serveeefrustrating but this isnt something im not familiar with
20:48mh_leserveee: you are welcome to ask if there is something specific that's not clear to you
21:17Z-modulemahboubine: what's your f, and your c ? f might not actually be differentiable at c
21:20mh_leZ-module: pm?
21:33mahboubineZ-module: oh forgot about this, as you said f turned out not differentiable at c
21:33mahboubineI was overthinking the whole thing
22:27adderI'm trying to do IDWDS on a three table game, but I'm not sure how. Can someone help? | | Ann | Bob | Carla |
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