## #math - Thu 22 Feb 2007 between 00:57 and 01:59

### NY Lost Funds

 arrenlex TRWBW: Yeah, A=(1/(b-a))integral(f,a,b). But I can't figure out how to use that. me22 Abs[min value of function] <= (integral over width) / width <= Abs[max value of function] TRWBW arrenlex: if f(x)<=c then integral is <= (b-a)*c. if f(x0) *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: heharrenlex: 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.>=0, sorry.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.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 doubtsThough I doubt it's as hard as classical plane geometryWhich is pretty much the most difficult thing ever thermoplyae Pretty much Kampen what, specifically, is the field that deals with topological groups called?a professor said that isn't algebraic topologybuti 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 intoI often see them in the distance, but... Kampen is it more just algebra?