21:21 somiaj Z-module: am I messing up the logic now...grr
21:22 somiaj rex: 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.
21:22 rex no I mean things like -1 \not\in ℕ
21:22 rex why do I need a universe here?
21:23 somiaj yea, 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
21:23 rex that's what you meant. I see
21:23 somiaj I 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)
21:24 somiaj so yea, I guess there are contexts in which you can use not in A, but A^c may not be welldefined
21:28 rex with free variables you mean, that it is implicit to what universe they belong?
21:43 mh_le Z-module: can I get you to take a look at a solution?
21:57 mahboubine I've got a function and I calculated it's derivative to determine whether the function is increasing or decreasing at different intervals.
21:59 mahboubine but 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
21:59 mahboubine I am wondering how to find those points as well
22:01 blackfield well you're looking for points c such that f'(c)=0, or undefined..
22:04 blackfield then you can test f''(c)>0 (then the point is a local minimum), or if f''(c)<0 it's a local maximum
22:08 mahboubine I came to that conclusion as well
22:08 mahboubine pretty easy now that I see it.
22:08 mahboubine thanks, blackfield
22:08 blackfield :)
23:51 biberao hi
00:53 bouma would you call within a 75% CI weak evidence ? i would call it no evidence
01:00 somiaj bouma: I would just call it a 75% CI, so 1 and 4 chance you are wrong.
01:00 somiaj I don't think a p value of 0.25 is that common, most prefer 0.05 or smaller
01:34 PlanckWalk Ci width has little to do with evidence strength.
02:19 KZ-Spectra hello
02:34 KZ-Spectra originally, the indices n+m and n-m do not coincide.
02:34 KZ-Spectra so when impose periodicity, then I want that also to be the case
02:35 KZ-Spectra anyway, here is a fun problem
02:35 KZ-Spectra "Find the remainder when 9 x 99 x 999  x ... x 99....9 (999 9s) is divided by 1000"
02:35 KZ-Spectra Z-module: ^
02:43 Z-module so the last factor there is 10^999 - 1 ?
03:01 KZ-Spectra yeah
03:02 KZ-Spectra it's the flavor of mod arithmetic since that's what we have been doing :)
03:08 KZ-Spectra Z-module:  I'll give you the end answer: 109
03:09 KZ-Spectra Z-module: https://i.imgur.com/vTstSUO.png can we just do this?
03:13 PlanckWalk yeah, 9*99*999^997 = 891*(-1) = 109 (mod 1000)
03:15 PlanckWalk KZ-Spectra: Are you assuming that u_{n+m} = u_{n-m} in general?
03:15 KZ-Spectra oh no
03:19 PlanckWalk Oh, I had trouble seeing the subscripts.  After I zoomed in so I could see Z^+, yeah that's fine.
03:19 PlanckWalk Err, superscripts
03:20 KZ-Spectra PlanckWalk:  were you comparing with the mathbin link from earlier? https://mathb.in/77541 Equation 1
03:20 PlanckWalk No
03:21 PlanckWalk It looks like it stands alone
03:22 PlanckWalk There are possible questions of conditional convergence, though.
03:23 KZ-Spectra those u's are complex
03:23 PlanckWalk Defining a sum over Z usually requires absolute convergence, but the LHS doesn't.
03:23 PlanckWalk Doesn't matter
03:24 PlanckWalk So *if* the RHS is defined, it is equal to the LHS.
03:25 KZ-Spectra do I even need to go to Z to do my mod arithmetic argument?
03:25 PlanckWalk No idea, I haven't read through the mathbin at all.
03:26 PlanckWalk (and probably won't since I'm just in a tea break at work)
06:12 Hasdiel Does anyone know of a good self-hosted open source alternative to wolfram alpha?
07:18 Pelleplutt Hello 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 :)
07:18 Pelleplutt In 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
07:18 Pelleplutt will 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.
07:36 greenbagels Pelleplutt: interesting problem for a boss to give their employees lol
07:37 Pelleplutt greenbagels indeed :) He has been playing around with AI but i do not know why this question came from that
07:43 isekaijin Pelleplutt: Is your boss a weeb or what? What the hell is with that plot?
07:43 greenbagels isekaijin: lol it is a very male-centric plot
07:43 greenbagels Pelleplutt: how old are the original people?
07:44 Pelleplutt I think he is about 43 or something
07:44 greenbagels no i mean in the problem
07:44 Pelleplutt oh, good question. We can assume they are above 13 and below 40
08:00 Pelleplutt I guess we have to assume that its 50% males and 50% females that is born aswell
08:15 PlanckWalk Looks like something you could just plug into a spreadsheet.
08:15 PlanckWalk With lots of simplifying assumptions, of course.
08:16 PlanckWalk Proabbly the most annoying relevant one would be reduced fertility with age.
08:18 PlanckWalk Inbreeding would be definitely a concern, but make a lot less difference than pretty much any other assumptions.
08:19 PlanckWalk But basically the boss will either give you a cake or not, on his whims.  There isn't a true "correct answer" to this.
08:19 PlanckWalk (and it's not a math problem anyway)
08:25 PlanckWalk (If only 3.4% die before 40 on this isolated island with no pre-existing civilization then it's a fucking miracle)
08:25 PlanckWalk (Even with food and shelter)
08:29 PlanckWalk Anyway, maybe try asking on worldbuilding.stackexchange.com or something :-p
08:30 PlanckWalk Because it sounds like the premise for some crappy harem litrpg.
08:33 Pelleplutt PlanckWalk haha yeah i guess :)
08:33 Pelleplutt Assumtion is that there is no inbreeding problem aswell :P
09:30 PlanckWalk Pelleplutt: Then eh, if you take off every sane limit like that then you could probably do it in just over a century.
09:32 PlanckWalk (The stated mortality rates are irrelevant, and shouldn't even have been mentioned)
10:03 mh_le morning all
10:03 mahboubine mornin' mh_le
10:06 biberao hi
10:29 sigma1 is T := { {}, {{}} } transitive?
10:30 Inline vertically not, horizontally maybe
10:33 mh_le sigma1: what is the definition of "transitive" in this sense?
10:34 sigma1 is each element of the set is a subset of the set
10:34 sigma1 *If
10:35 mh_le if would help if you were a bit more precise
10:36 sigma1 A set H is transitive if every one of its elements is a subset.
10:37 mh_le then yes
10:40 sigma1 and T := { {}, {{}}, {{{}}} } ?
10:41 lericson we went through this, sigma1
10:41 lericson can you check for yourself?
10:47 biberao math time
10:48 mh_le which kind?
10:50 biberao mh_le: i did some trig and sequences yesterday night
10:50 mh_le great
10:51 machinewhore Is there a collection of urn problems/solutions somewhere that I can use for practice?
10:52 mh_le urn?
10:52 mh_le you mean counting/probability problems?
10:52 machinewhore yeah
10:53 machinewhore eg, 50 red balls and 50 black balls randomly distributed between 2 urns, yada yada
10:53 mh_le https://www.google.com/search?q=counting+and+probability+problems&oq=counting+and+probability&gs_lcrp=EgZjaHJvbWUqCAgCEAAYFhgeMgYIABBFGDkyBwgBEAAYgAQyCAgCEAAYFhgeMggIAxAAGBYYHjIICAQQABgWGB4yCAgFEAAYFhgeMggIBhAAGBYYHjIICAcQABgWGB4yCAgIEAAYFhgeMggICRAAGBYYHtIBCDcwNTJqMGo3qAIAsAIA&sourceid=chrome&ie=UTF-8
10:58 sigma1 I'm not sure whether these are transitive T: = {∅, {{∅}} and S:= {∅, {{∅}}, {∅}} I get confused with the ∅
10:59 machinewhore S is transitive iff each element of S is a subset of S.
11:01 machinewhore Is ∅ a subset of T? Is {{∅}} a subset of T?
11:01 sigma1 it'd be T: = {∅, {{∅}} btw
11:01 machinewhore Still missing a bracket.
11:01 sigma1 T: = {∅, {{∅}}}
11:02 machinewhore If you answer those two questions I asked, then you will know if T is transitive or not.
11:02 biberao immibis: mh_le going to do it in latex
11:02 biberao sorry
11:02 biberao i meant mh_le
11:02 sigma1 since the elements of ∅(i.e. none) are contained in T
11:03 mh_le biberao: ah cool
11:07 machinewhore sigma1: Figure it out?
11:12 sigma1 machinewhore the set {{∅}} is a subset of T, because its element is part of T
11:13 PlanckWalk Its element is {∅}
11:14 PlanckWalk The elements of T are ∅ and {{∅}}
11:16 machinewhore Yup, those are the elements of T.
11:16 biberao mh_le: i might need help  structuring :D
11:23 mh_le biberao: is a solution to an assignment you are typesetting?
11:24 biberao yes
11:25 mh_le ok, I don't know spanish so I'm not sure I will be able to help
11:25 biberao mh_le: its not even spanish
11:25 biberao :\
11:26 biberao but the issue is structuring i wanted to make it similar
11:26 mh_le biberao: I'm not sure what you mean by that
11:27 biberao mh_le: i want to be able to have like exercice 1 and so on
11:27 biberao good alignment
11:27 mh_le biberao: let's go to #latex
11:27 biberao ok
11:31 sigma1 PlanckWalk so T is transitive as ∅ is a subset of T
11:33 sigma1 and the members of {{ø}} is only {ø}, and {ø} is a subset of A
11:35 PlanckWalk That's not the test for transitivity
11:35 machinewhore sigma: What are the members of T?
11:35 sigma1 ø, {{ø}}
11:35 machinewhore Correct.
11:35 machinewhore Is ø a subset of T?
11:36 sigma1 yes
11:36 machinewhore Correct.
11:36 machinewhore Is {{ø}} a subset of T?
11:36 sigma1 yes
11:37 machinewhore What is the definition of "subset'?
11:38 sigma1 If 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
11:38 PlanckWalk Let's not use the word "included".
11:38 PlanckWalk Sometimes people use it to mean "element of", sometimes they use it to mean "subset of".
11:39 PlanckWalk As you did!
11:39 machinewhore !^
11:39 PlanckWalk As in, you use it both ways.
11:39 PlanckWalk used* it
11:40 PlanckWalk So try again without using the word "included".
11:41 sigma1 'part of a set A' instead of that
11:44 PlanckWalk No, let's not.
11:44 PlanckWalk Try looking up a definition.
11:45 PlanckWalk The one you're using is broken.
11:48 machinewhore42 sigma1: Are you a native English speaker?
11:50 sigma1 A is a subset of B, if and only if every element of A is an element of B
11:51 PlanckWalk That one looks better
11:51 PlanckWalk I severy element of {{ø}} an element of T?
11:53 sigma1 it seems so
11:53 PlanckWalk What are the elements of {{ø}}?
11:54 sigma1 the set {ø}
11:54 PlanckWalk What are the elements of T?
11:55 sigma1 the set {ø}  and ø
11:55  * PlanckWalk scrolls up.
11:55 PlanckWalk Are you sure?
11:57 sigma1 err the other should be {{ø}}
11:58 PlanckWalk Which other?
11:59 sigma1 {{ø}} and ø
11:59 PlanckWalk Okay.  Is {ø} an element of T?
11:59 sigma1 no
12:00 PlanckWalk Right, so now you can answer whether T is transitive.
12:00 PlanckWalk You've checked its elements, and found one that's not a subset.
12:01 mh_le Let 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?
12:01 mh_le R is a ring
12:06 mh_le here 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
12:06 mh_le the map*
12:07 mh_le wait
12:11 sigma1 is U\T transitive?
12:12 mh_le r( a (X) b) = (ar (x) b) = (a (x) rb). so ( a (x) 0) = 0
12:13 mh_le that'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
12:28 mh_le so it was pretty obvious that a (x) 0 = 0
13:56 sigma1 the text asks me whether U \ T is transitive
13:58 int-e Cool. What are U and T?
14:21 biberao Z-module: ?
14:22 brass_ Can the sine function be achieved using finite combination of the basic operations?
14:24 dTal No, sine is transcendental
14:25 dTal Why do you ask?
15:33 paulo https://www.wolframalpha.com/input?i=y%5E2%3D%28x%28x-9%29%28x%2B16%29%29%2C+y+%3D+3
15:34 paulo why are solutions shown as complex when the line clearly intersects the graph in real space?
16:12 brass_ dTal Can I message you privately, I can't respond here.
16:12 dTal You can't?
16:12 dTal Erm, I guess...
16:13 brass_ ?Yup ok, it's just that what I might say may sound too dumb on an elementary level.
16:27 ecraven hello ;) 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.
16:27 ecraven I've tried i*K mod N with K being a coprime to N, but that .. doesn't seem to be correct.
16:30 Z-module paulo: 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.
16:32 mh_le hey all
16:34 ecraven and it works fine, I just implemented it wrong ;)
17:05 biberao Z-module: tell me what you think https://github.com/gitmapd/gitmapd.github.io/blob/master/limites%20nova%20ficha.pdf <- finished exercise 2 and 3
17:14 Z-module Looks good, biberao
17:16 biberao Z-module: ive added another thing to prove bounded for 3-2n
17:16 biberao if you do f5 should have updated
17:19 Z-module I think you mean 3 - 2/n
17:19 biberao no
17:19 Z-module (here in irc)
17:19 biberao 3-2n
17:19 Z-module the sequence  3 - 2n   is not bounded
17:20 biberao thats what i said
17:20 biberao i meant to say
17:20 biberao how do i prove its not bounded
17:20 biberao i did lim n (3-2n) = -inf
17:20 biberao thats what i meant to say
17:20 biberao mawk: thanks :D
17:22 Z-module Take 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
17:23 biberao ah
17:23 biberao maybe i should use the delta epsilon?
17:27 Z-module That's what this is, but in the form used for sequences
17:28 Z-module A 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
17:31 mh_le hi Z-module
17:33 Z-module This 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).
17:52 biberao back
17:52 biberao sorry
17:53 biberao Z-module: thank you
17:56 theseb Can someone tell me how they got the "observed power" on this A/B test calculator? https://abtestguide.com/calc/
17:57 theseb "two proportions hypothesis testing"
18:05 biberao Z-module: so for example if an = 3-2n was a monotonic increasing i could do  an > M
18:05 biberao ok
18:06 biberao i guess that works
18:06 biberao thank you
18:06 Z-module by 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 ...
18:07 biberao i see
18:07 biberao for this case is this right to say 1 < 3-2n < -inf
18:07 biberao ?
18:07 biberao i dont know if its a good notation
18:07 Z-module However, that prime gaps sequence {g_n}, while unbounded, does not -> infty, as we've only known with proof for around a decade.
18:08 Z-module nothing is < -infty
18:08 Z-module so don't write that
18:08 biberao ok
18:08 biberao but you understood what i meant
18:08 biberao ok
18:08 Z-module I didn't, nor would anyone else
18:08 biberao i meant to say
18:08 biberao sorry
18:08 biberao i meant to say
18:08 biberao -inf < 3-2n < 1
18:09 greenbagels <= 1
18:09 Z-module okay but  -infty < any reals you like,  so there's no point writing that. Finitely many innequalities have nothing to do with -> -infty
18:09 biberao greenbagels: thank you
18:09 biberao like now i understood what you taught me today
18:18 biberao check my updated
18:18 biberao Exercise 2 d)
18:18 biberao please
18:26 Z-module I 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.
18:27 biberao what if for example
18:27 Z-module the  1 > all a_n   would be relevant if you were dealing with "unbounded only on one side" as a separate / special case of "unbounded".
18:27 Z-module but you're not
18:27 biberao ah so with a_n >M or a_n < M
18:27 biberao works for both sides?
18:37 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.
18:39 Z-module But 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.
18:44 biberao Z-module: so thats the way we did earlier then
18:44 biberao b_n < M or b_n > M
18:47 biberao ok gtg
18:47 biberao thank you
18:48 greenbagels another happy customer
19:11 mh_le hi
19:11 mh_le hey greenbagels
19:11 greenbagels hi
19:12 mh_le any progres on Wald?
19:12 greenbagels realistically i dont know if i have the time for it tbh
19:12 mh_le ok no problem :)
19:39 Simplar I'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.
19:39 Simplar But how to prove the same with subtractions?
19:57 Z-module Simplar:  2m - (2n + 1) = 2(m - n) - 1 = 2(m - n - 1) + 1   and this last is odd.
20:09 Simplar Z-module: I meant (2m) / (2n+1)
20:09 Simplar How can we guarantee that the quotient will always be even?
20:10 Simplar 2m = (2n+1)q + r
20:13 Guest5398 Hello, 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?
20:24 Z-module Simplar: 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.
20:25 Z-module also, note taht "difference" referes to the - operator, not the / operator
20:28 Z-module Simplar: 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.
20:33 Guest5398 Its Like having seven dollars and getting 1% interest? Having 7 Characters having a Baby at 1% Chance . That should be IT.
20:35 pavonia Guest5398: What is the relation between characters and birth here?
20:36 pavonia Or is it like characters in a game?
20:36 Guest5398 I mean Characters can increase by 1 at a 1% Chance per one Character per day
20:36 Guest5398 Yes. Sorry.
20:42 mahboubine basic 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?
20:42 mahboubine I am used to facing undetermined forms in limits but I don't know how to deal with them in this case
20:43 pavonia Guest5398: I guess it's a matter of definition if the chance after N days is 0.01*N or (1.01)^N
20:43 pavonia ...
20:46 serveee why is topology so hard to understand
20:46 serveee set topology that is
20:46 mh_le is it?
20:46 serveee maybe im just not understanding it right
20:47 Galois it's a lot easier if you know real analysis well
20:47 serveee how so
20:47 Galois in real analysis you (are supposed to) learn about open and closed sets arising from metric spaces
20:47 mh_le serveee: topology is the study of continuity
20:48 serveee i should go back some steps then
20:48 Galois metric 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
20:48 serveee frustrating but this isnt something im not familiar with
20:48 mh_le serveee: you are welcome to ask if there is something specific that's not clear to you
21:17 Z-module mahboubine: what's your f, and your c ?  f might not actually be differentiable at c
21:20 mh_le Z-module: pm?
21:33 mahboubine Z-module: oh forgot about this, as you said f turned out not differentiable at c
21:33 mahboubine I was overthinking the whole thing
22:27 adder I'm trying to do IDWDS on a three table game, but I'm not sure how. Can someone help? |  | Ann | Bob | Carla |
22:27 adder | ---- | ---- | ---- | ---- |
22:27 adder | Ann | (2, 0, 1) | (2, 0, 1) | (2, 0, 1) |
22:27 adder | Bob | (2, 0, 1) | (0, 1, 2) | (0, 1, 2) |
22:27 adder | Carla | (2, 0, 1) | (1, 2, 0) | (1, 2, 0) |
22:27 adder 
22:27 adder Carla votes Ann
22:27 adder 
22:27 adder |  | Ann | Bob | Carla |
22:27 adder | ---- | ---- | ---- | ---- |
22:27 adder | Ann | (2, 0, 1) | (0, 1, 2) | (2, 0, 1) |
22:27 adder | Bob | (0, 1, 2) | (0, 1, 2) | (0, 1, 2) |
22:28 adder Sorry.
22:28 b0nn adder: FTR a paste site would have been more appropriate than posting into the channel
22:29 adder I know, I just mispasted the screenshot url. I meant to paste: https://imgur.com/AM8lJ0J.png
22:29 adder So what I don't get is how a three-table game reduced to a single table.
22:29 adder That is, I'm not following what the text says.
22:35 int-e Hmm. the label on the 2nd (or is that 4th) figure should be "Anna votes for A".
22:36 adder Ah, that makes sense.
22:36 int-e adder: But that seems to be the only thing wrong with it... what are you having trouble with?
22:39 adder Nothing, it checks out now.
22:39 adder Thanks, int-e.
22:39 int-e Cool, np.