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<ccd> dbrock: thank you, it seems clear that angular velocity is a relative thing. How, in general do I see if something is relative or not? A variable is ether a "cross" (like potential) or "through" (like current)... What kind of tests can be done to tell if something is relative or not? Why does taking the 2nd deriv. of position give a non-relative quantity?
<dbrock> ccd: I don't understand what you mean by non-relative
<dbrock> ccd: acceleration is dependent upon force and m***
<dbrock> ccd: and yes, since angular velocity is the integral of angular acceleration over time, it is relative to angular acceleration
<delta> dbrock, can't you prove that UuV is a subspace <=> U subset of V or V subset of U?
<ccd> dbrock: non-relative, not relative to another measurement. Velocity would be relative cus it has to be measures with respect to something else... acceleration would be non relative... I suspect I am having this problem beacuse I am trying to understand acceleration without m***...
<dbrock> delta: hmmm, but that's not true. Let U be some line in R^2 and let V = R^2 \ U (i.e., everything in R^2 except U). Then U union V = R^2, but neither U subset V or V subset U is true
<dbrock> ccd: why does velocity have to be measured with respect to something else?
<dbrock> ccd: and what is that "something else"?
<ccd> dbrook: when you say how fast something is going... you usually take the something else to be the ground
<dbrock> delta: oh, wait, I forgot U and V have to be subspaces
<ccd> acceleration is different, it's a through var, it dosent need to be measured relative to something else to have meaning. I'm trying to understand why taking the 2nd derivative of position (a relative thing) gives a non-relative var.
<ccd> I dont mean to say the second derv of position is relative, I was just mentioning that position is relative.
<rumpl> anyone knows how to prove the Raabe's test??? http://mathworld.wolfram.com/RaabesTest.html
<Catfive> dbrock - take two subspaces U and V, suppose their union is a subspace W, and suppose U is not a subset of V. Let u be a vector in U that is not in V, let v be any vector in V, and set w = u + v. Now w can't be in v; otherwise w - v = u would be in v, which it isn't. Hence w is in U, and therefore v = w - u is too.
<dbrock> ccd: from a purely kinematical standpoint, acceleration is just as relative as velocity. Put two rocket-equipped video cameras facing each other in space and hook each to a television screen. Fire one of the rockets and try to tell which camera is accelerating by looking at the television screens
<ccd> dbrock: I see. it's only the effect that m*** experiences that makes aceleration no relative. Thank you!
<ccd> no+t
<dbrock> Catfive: thanks!
<lordnir> Anyone know how to make the points from L1 and L2 show up on the graph for a TI83+?
<dbrock> ccd: right, and you can't generally tell whether that effect is caused by acceleration or gravity
<dbrock> lordnir: I think you need to go to "stat plot" or something like that
<namish> lordnir, don't you just highlight the plots that contain l1 and l2?
<namish> or PlotsOn
<namish> once you have configured your plots for L1 and L2.
<lordnir> alright i'll give that a try
<dbrock> ccd: for example, they simulate weightlessness by accelerating a plane towards the earth at approximately 9.8 m/s^2 so as to exactly counteract gravity
<dbrock> ccd: to the people in the plane, it appears as though they're not accelerating at all. But watching from the ground, you can see that the plane is clearly accelerating. So that would be a reason to consider acceleration relative
<Geren> hi guys
<Geren> i was reading this Java in a Nutshell book by O'Reilly
<Geren> and in it, it mentioned that "Cl***" is a data type that represent all Java data types, including primitives. So I can do something like "Cl*** typeIn=int.type;"
<Geren> but then it stopped there, and never elaborated
<Geren> what exactly does "Cl*** typeInt=int.type" do?
<Geren> does it make "typeInt" an integer variable just like "int TypeInt" would?
<Catfive> Geren - it will probably not come as a complete surprise to you that this is the wrong place to ask that question.
<Geren> oh oops
<Geren> i meant to go into the java channel, sorry
<lolnoyuo> just gtfo
<delta> cya
<TheoMurpse> Anyone care to help me prove that the square of an integrable function is integrable, where I only know a few facts about integrals so far:
<TheoMurpse> A function f(x) is integrable iff there are step functions f1 and f2 such that for all x, f1(x)<f(x)<f2(x), and that int(f2(x),a..b) - int(f1(x),a..b) < epsilon for any epsilon
<TheoMurpse> and the definition of integral in this course is
<TheoMurpse> there exists an A such that forall e there is a d such that |S-A| < e for all Riemann sums S with width < d
<lolnoyuo> fact : none of the points in the empty set are interior points with any metric space and any metric
<YaroslavV> Suppose I want to approximate unknown bounded function on [0..1] with a one-term series expansion. If the series is fixed ahead of time, which series should I use to minimize worst L2 approximation error?
<stalkermitor> hi there
<stalkermitor> anyone around who could help me with complete induction?
<stalkermitor> wird hier auch deutsch gesprochen?
<stalkermitor> anyway.. is anyone ther who could help me with analysis?
<aFlag> you should try to simple ask your question
<stalkermitor> see. ty
<TheoMurpse> Well it's obvious for k=1 in that -1 = -1
<TheoMurpse> Wait hang on, what?
<TheoMurpse> are you doing a summation or what?
<TheoMurpse> what does "an amount from k=1 to n blahblah" mean?
<stalkermitor> yes. ty. then for the proof i have to fill in n+1..
<TheoMurpse> so it's a summation
<stalkermitor> i guess so. im not sure, if this is the real name for it in english
<TheoMurpse> so ***ume it's true for case Q, that sum((-1)^k * k^2,1..n) = (-1)^n * n(n+1)/2
<TheoMurpse> is it the sigma
<TheoMurpse> looks like a funny big E?
<TheoMurpse> yeah ich nicht spreche deutsch or however you say "i don't speak german" in german :)
<TheoMurpse> or rather i meant to type
<stalkermitor> lol.. but thanks anyway
<TheoMurpse> sum((-1)^Q * Q^2, 1..n) = (-1)^n * n(n+1)/2
<TheoMurpse> so now show for case Q+1
<neoking77> !help
<TheoMurpse> arg God i'm totally ****ing
<TheoMurpse> lemme write it on paper
<TheoMurpse> then type it in :)
<stalkermitor> yes and this is exactly my question..
<neoking77> can mathbot do anything?
<stalkermitor> as i can do it, it would be sum((-1)^Q*Q^2, 1.. n+1) = sum((-1)^Q*Q^2, 1..n) + (n+1)
<ccd> What's the term used to describe a N-1 dimension object in a N space? Like a line in 2D space...
<stalkermitor> so i could fill in because of the induction beginning: sum((-1)^Q*Q^2, 1.. n+1) = (-1)^n*n(n+1)/2 + (n+1). But, the next step seems difficult to me..
<stalkermitor> yes, im sorry its n element of N
<stalkermitor> only the natural numbers in a space perhaps..dunno. but its a sum anyway.
<TheoMurpse> ok i got it stalkermitor
<TheoMurpse> so first you've already proved it's true for case n=1
<TheoMurpse> Now ***ume it is true for case n=Q, namely that
<stalkermitor> wow. ty
<TheoMurpse> sum((-1)^k * k^2, n=1 to Q) = (-1)^Q * Q(Q+1) / 2
<TheoMurpse> Now you want to show that
<TheoMurpse> sum((-1)^k * k^2, n=1 to (Q+1)) = (-1)^(Q+1) * (Q+1)(Q+2) / 2
<TheoMurpse> so well notice that
<stalkermitor> yes. i hope i can get it..
<TheoMurpse> sum((-1)^k * k^2, n=1 to (Q+1)) = (-1)^(Q+1) * (Q+1)^2 + sum((-1)^k * k^2, n=1 to Q)
<TheoMurpse> so notice the sum((-1)^k * k^2, n=1 to Q) we already know is equal to (-1)^Q * Q * (Q+1)/2
<TheoMurpse> so substitute that in and we have
<TheoMurpse> sum((-1)^k * k^2, n=1 to (Q+1) = (-1)^(Q+1) * (Q+1)^2 + (-1)^Q * Q * (Q+1)/2
<TheoMurpse> now turn
<TheoMurpse> (-1)^(Q+1) * (Q+1)^2 + (-1)^Q * Q * (Q+1)/2
<TheoMurpse> into one fraction that is something like
<TheoMurpse> [(-1)^(Q+1) * 2 * (Q+1)^2 + (-1)^Q * Q * (Q+1)] / 2
<TheoMurpse> and then just factor out a (-1)^(Q+1) to have
<TheoMurpse> (-1)^(Q+1) * [2 * (Q+1)^2 -Q * (Q+1)] / 2
<TheoMurpse> and then multiply out the (Q+1)^2 to have
<TheoMurpse> (-1)^(Q+1) * [2Q^2 + 4Q + 2 - Q^2 - Q] / 2
<TheoMurpse> and then simplify within the [ ]s to have
<TheoMurpse> (-1)^(Q+1) * [Q^2 + 3Q + 2] / 2
<TheoMurpse> and then notice that
<TheoMurpse> Q^2 + 3Q + 2 = (Q+2)(Q+1)
<TheoMurpse> so now you have
<stalkermitor> now i get it..
<TheoMurpse> (-1)^(Q+1) * (Q+1)(Q+2)/2
<TheoMurpse> and you're done :)
<stalkermitor> thank you very much.
<stalkermitor> :-)
<TheoMurpse> you're welcome
<TheoMurpse> it was a nice break from crappy real analysis
<stalkermitor> hehe..
<TheoMurpse> just keep workign on induction
<TheoMurpse> it's very powerful
<stalkermitor> i have to notice it but i guess i really now get it how to work with inductions..
<TheoMurpse> and once you get the hang of it
<TheoMurpse> it's pretty easy to understand
<stalkermitor> yes. its probably the symbols which can confuse if you are not conform with them..
<TheoMurpse> yeah
<stalkermitor> okay. thank you a lot for your help theomurpse. i spent my wohle afternoon just sitting and didnt know what to do. next time i know where to go, if i got a question..:-)
<TheoMurpse> no problem. you're welcome
<TheoMurpse> what does stalkermitor mean?
<stalkermitor> its just a game within the words.. you know the expression "storker"?
<dbrock> okay, I thought that Catfive's hint would enable me to complete this proof, but I can't seem to put it together. I want to prove that the union of any finite number of subspaces U_1, ..., U_n cannot make up a vector space. I can prove this for n = 2 (in fact, Catfive gave me a complete proof for this case), but I don't see how to generalize it to an arbitrary number of subspaces
<stalkermitor> someone who terrorizes people with sms or phoning..
<TheoMurpse> nope cant say i do
<TheoMurpse> oh wow
<TheoMurpse> i know stalker in english
<dbrock> Catfive's proof for n = 2 basically takes one vector from each of the subspaces and shows that their sum is not in either of the subspaces
<stalkermitor> yes.. i knew it once.. errm.. it was just to find a name very quick for the irc..;-)
<dbrock> but when n = 3, the sum of one vector from each subspace could in fact be in one of the subspaces (if the subspaces were linearly dependent), so I don't think the proof works for this case
<dbrock> in other words, I have a bunch of subspaces, and I want to construct a vector that is in neither of the subspaces
<TheoMurpse> :)
<stalkermitor> jeez. i wrote it down again. and i really got it now! wow. thats awesome!:-)
<stalkermitor> ok. thanks again for help theomurpse and see you all. good night.:-)
<TheoMurpse> gnight
<Dacicus> Hello.
<Dacicus> I have this problem that I'm supposed to solve using Lagrange multipliers: "Find the maximum and minimum volumes of a rectangular box whose surface area is 1500 cm^2 and whose total edge length is 200 cm."
<lolnoyuo> hi
<Mulder> Dacicus, skip to it then
<Dacicus> I'm using the variables l, w, and h to represent the length, width, and height, respectively.
<Dacicus> Then I have V(l, w, h) = lwh; A(l, w, h) = lw + lh + wh = 750 cm^2; L(l, w, h) = l + w + h = 50 cm.
<Dacicus> I set up the system, but I can only get that l = w = h.
<Mulder> you have 5 equations
<Mulder> and 5 unknowns
<Dacicus> I think that would be okay, but it doesn't fit the constraints. I get different values using each constraint.
<Dacicus> Yeah.
<Mulder> are you sure lw + lh + wh = surfacearea? :P
<Dacicus> No, it's SA/2
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