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Comments:
<0> i have a math question ! can some one help me with calculating?
<1> 1 + 1 = 2
<0> yeah it's 4 ;)
<1> batz: only if u ask the question
<2> we cant read your mind
<0> ok
<0> i have a 60 squares panel
<0> how meny times i can fill 5 squares in this panel?
<3> What do you mean exactly?
<3> How many ways are there to choose 5 squares from the 60?
<0> yes
<4> % Binomial[60,5]
<3> = 5461512
<4> No mbot, apparently.
<5> Suppose I wanted to show that lim sup(a_n+b_n) <= lim sup(a_n) + lim sup(b_n).
<5> So if I let E,F, and G be the set of all subsequential limits of a_n+b_n, a_n, and b_n respectively. Then E \subset (F+G), right?
<5> Is that a good way to go about this problem?
<5> Then manipulate the sup..
<0> so is it 5461512?
<4> Safrole: You just asked that 30 seconds ago.
<5> Not 30 seconds ago.
<2> batz, yes I suggest looking at http://mathworld.wolfram.com/Combination.html
<3> batz: Yes
<5> Last night maybe
<0> thanx man
<6> different network, steve
<4> Oh.
<7> Guys, how do I do standing addition in latex?
<4> Well, whatever.
<2> in your case n=60 and k =5
<7> like.. not x/y
<7> but
<7> x
<7> y
<7> like that
<7> x
<7> +y
<7> :P
<5> I'm just trying to see if I'm heading in the right direction towards proving that statement.
<4> Trixsey: Eww. You could try array.
<7> well, its a good way for adding binaries for instance :p
<3> Safrole: Yeah, it follows from sup(f + g) <= sup(f) + sup(g)
<4> \begin{array}{rr}&x\\+y\\\hline&x+y\end{array}
<3> Regarding sequences as functions from N to R
<5> where f and g are sets, K***akad
<5> ?
<8> Trixsey: try align
<5> So if I've shown that for E,F, and G as I have defined them. I have the original lim sup statement.
<3> Safrole: They're functions, I was just using sup(f) to mean the supremum of the image of f on whatever domain
<4> maskd: Does \hline work in align?
<5> It's an interesting distinction... I'm told to think of them as sets
<3> I'm not sure what your E, F, and G are though
<5> In any event.. I say like E,F, and G be the sets of subsequential limits of a_n+b_n, a_n, and b_n respectively.
<5> like/let
<3> Safrole: The image of a function is a set, that's what the supremum is being taken on
<5> and then I wanted to determine a relation between E,F, and G
<9> 1+1 FTW
<3> You mean like E = {a_i + b_i | 1 <= i <= n}, or what?
<5> all of the subsequential limits of a_n+b_n
<5> is E
<3> Well ok
<5> and then the sup E is the lim sup a_n+b_n
<5> So it seems to me that E \subset (F+G)
<8> Steve|Office: afaik no
<5> does that seem legitimate to you?
<3> Sure
<4> That's why I suggested array. But the spacing will be funny.
<5> {the set of all subsequential limits of a_n+b_n} \subset {the set of all subsequential limits of a_n} U {the set of all subsequential limits of b_n}
<3> Wait
<3> Union?
<6> I think I would show that <= and >= hold
<3> I don't think it's true with a union
<6> Since that's the easy way to do this and doesn't deal with subsequences :)
<5> you think it's easier that way?
<6> I do
<5> directly or by contradiction?
<3> But >= doesn't hold
<5> It's an inequality
<5> I just want <=
<3> lim sup (a_n + b_n) <= lim sup(a_n) + lim sup(b_n)
<5> Which is what I'm trying to establish
<6> Oh, my mistake; I misread the original problem
<6> Then you're right; subsequences are probably the best
<5> I say union kasadkad because what sense does it make to add two sets
<5> how can I write {... } + {... }
<3> I thought you meant it in the sense of F + G = {f + g | f in F, g in G}
<5> Yeah that's what I meant.
<3> Oh
<3> Ok
<3> Coz it's definitely not true for unions
<5> I guess I should explicitly write that out.
<3> Take a_n = 1 and b_n = -1 for all n
<1> calculate sum( (k+1)/k!, k=0..inf) by differentiateing the mac laurin serie of x*exp(x)
<3> Do you really need to consider subsequences though?
<10> Howdy! Please refresh my memory; sech^2(x) is thesame thing as (sech(x))^2 , correct?
<11> yes
<10> thanks !
<1> i don't really get the realtion between the mac laurin serie of x*exp(x) and the sum above
<1> maclaurin is just taylor at a=0, correct?
<12> Kasadkad, you got logs on the chan ?
<5> How else would show that Kasadkad?
<12> Catfive, _llll_ Safrole, you got logs on the chan ? if you do please give them to me
<3> Well
<3> It's definitely the case that sup {a_i + b_i | 1 <= i <= n} <= sup {a_i | 1 <= i <= n} + sup {b_i | 1 <= i <= n}
<3> And taking limits gives your result
<5> Okay... so any subsequential limit can be described by the sets you mentioned
<3> lim sup a_n = lim[n->inf] S_n, where S_n = sup {a_i | 1 <= i <= n}
<5> okay
<5> I see..
<5> There's nothing really to this
<3> That's the definition I usually think of, I wasn't thinking of the supremum of all the subsequential limits (they're the same of course)
<5> I mean there's no reason to consider subsequences
<5> at the end of the day.. they're just sets
<3> Yeah
<5> So why complicate things
<13> Hello. I want to learn math! I love logic, and I'm good at it: but I screwed up in school, on other grounds. Realizing it will sound stupid, I still need to ask: where do i start?
<14> rixxon: take a standardized test of some sort...hopefully you can attend a community college which will help you out with finding such a test and even registering for affordable cl***es
<14> self-teaching math is hard... self-teaching math if you are a lazy procrastinating bastard like me is impossible... although, I suppose it is possible to *like* math
<13> Alconquian, I'm still in school though, and I **** at learning in school. I can learn anything when I do it myself, out of interest...
<14> the only reason I really care about trigonometry and learning future linear algebra is because of programming... hopefully you can find something similar in that case
<14> I am pretty cool, I make As because I am deathly afraid of not making an A O_O
<13> Myep, I love programming and do it alot: an example of something I learned myself at home.
<14> game programming would be a good thing to screw with during your run-of-the-mill planar-ish math... beyond that, if you aren't interested in it, you should probably not take it up
<14> I...like...to...talk...like...this...
<13> And since I got interested in politics, I've learned alot about different ideologies and the society in modern and ancient times... Even though I learned nothing on those lessons in school. :P
<15> Me... too...
<16> rixxon: how do you NOT learn something in school?
<13> Alconquian, well, my plan was to learn math at home, partially because I do find it interesting (just can't learn in school) and love logic, and partially because I can take tests later and get grades.
<13> kadams: that's another story...
<14> math for me isn't particularly fun, it is just a challenge that requires studying, and a fair amount does prove to be useful in the real world
<14> school tis a game where you collect these thingies called points... :D
<13> I'm a true geek though (aspergers...) so I can actually find math "fun".
<14> if you like logic, you'll like stuff like discrete math/cobinatorics
<17> after 3 years of university, im starting to become a believer in self learning. i used to think it would not be effective, but honestly, if you are disciples and inelligent enough to learn from texts, formal cl***rooms are just extra costs
<14> comb* :X
<16> i believe in self-teaching, too, but
<17> this is why i never go to cl***es
<13> Alconquian, I'm going to have discrete math in school next year.
<17> :x
<14> you must pay the bribery fee to be granted entry-level intellectual status to get a job
<17> discrete math is very fun, especially if you like computer science topics.. discrete math is very important for CS
<17> yeah thats what im beginning to think Alconquain
<16> you won't get a degree by teaching yourself =/
<17> its a toll charge
<14> rixxon: I actually thought I hated it at first, and I literally spent all weekend studying for test (wake up...study..eat..study...go to bed), but I somehow really liked working some of the problems
<18> Hi, how would I go about integrating Integrate[te^(t / 2)] by hand?
<14> it is definitely a way of thinking different from stuff I've done in - gasp - precalculus :D
<3> I'm better at learning from cl***es than on my own
<17> its not like cl***es are BAD per se, they just really arent absolutely neccessary, at least for me. much more important is just having a mentor or someone i can ask when i really get stuck
<14> we creative people with beautiful minds are lazy farks
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