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#math
<arrenlex> Or is my logic wrong?
<TRWBW> arrenlex: it does, but that doesn't make it much easier, they key point is that if a continuos function drops below the average it must drop below it for some delta around where it drops. then you can break up the integral, like i said. read my posts.
<arrenlex> I'm trying to understand them, yeah. Thanks a lot for your help.
<TRWBW> arrenlex: np, gl
<TRWBW> arrenlex: maybe this will help you see it, maybe not. if you have a finite sum a_1+..+a_n, every a_i is less than equal to the average, can any of the a_i be less the the average?
<arrenlex> TRWBW: Thanks a lot for trying, but I think I'm getting somewhere with what's been said already; thanks lots, though.
<TRWBW> arrenlex: with the trick of subtracting the average, that becomes: if you have sum a_1+...+a_n, a_i<=0, and at least one of the a_i<0, can they sum to 0?
<seb-_> TRWBW: no
<TRWBW> seb-_: <arrenlex> *screams* this seems SO OBVIOUS but I'm completely stuck! How do you prove that a continuous function that never exceeds its average value must be constant?
<seb-_> TRWBW: heh
<seb-_> arrenlex: i hope you got it now
<arrenlex> Yep, I got it. Thank you, all.
<seb-_> arrenlex: what was the mental snag?
<arrenlex> Me not understanding that A-f(x)>0.
<arrenlex> >=0, sorry.
<arrenlex> That means that g(x)=A-f(x)>=0, but since integral(g)=0 as I said above, that means g must be 0 for the whole interval, because it's non-negative.
<arrenlex> Which means that A=f(x) for all x.
<cerealkiller219> seb: you nearby
<thermoplyae> In case you guys had any doubts, set theory is hard
<arctanx> o \in{\mathbb{R}}?
<Kasasdkad> thermoplyae: I had no doubts
<Kasasdkad> Though I doubt it's as hard as classical plane geometry
<Kasasdkad> Which is pretty much the most difficult thing ever
<thermoplyae> Pretty much
<Kampen> what, specifically, is the field that deals with topological groups called?
<Kampen> a professor said that isn't algebraic topology
<Kampen> buti don't know what else it could be
<thermoplyae> I think plane geometry and number theory are the two big towers of mathematics that I will never really venture into
<thermoplyae> I often see them in the distance, but...
<Kampen> is it more just algebra?
<Kampen> topological algebra or something of that sort?
<Kampen> like say you had some (X, T, G) a set X equipped with a topology T and a group G. That seems algebraic to me.
<Kampen> just need a few more axioms
<Kampen> e.g., likely the separation ones
<Kampen> to separeate orbits, etc.
<Kampen> separate*
<gzl> Kampen: they are used lots in analysis
<joblot> does taking the derivative of a matrix mean anything?
<Jafet> Depends on what "derivative" means.
<joblot> dM/dx
<thermoplyae> Does M vary with x?
<thermoplyae> If not, then the answer is easy -- and makes sense
<gzl> joblot: http://en.wikipedia.org/wiki/Matrix_calculus
<thermoplyae> Well, really it'll make sense no matter what
<joblot> thermoplyae: well I suppose to be interesting, it has to, maybe like a Jacobian
<joblot> gzl: thanks, checking
<thermoplyae> You'd just look at it as a function R -> R^(n*m)
<thermoplyae> I'm to show that every chain contains a well ordered cofinal subset
<thermoplyae> Ideas on where to start?
<joblot> oh dear, there is a matrix calculus with rules more horrible than scalar calculus
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