#math - Wed 11 Apr 2007 between 00:05 and 00:46

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trytolitehow do you usually solve an integral where one of your endpoints is infinity? i'm doing a substitution where i get tan pi/2 for one of the points.
noway-Let f be a bijection from [m] to [n]. I have to prove that m = n. It seems kinda of trivial, but we are told to use induction.
TRWBWtrytolite: that's actually a question of how do you *define* such an integral
noway-should I assume P(n) = there is a bijection from [m] to [n] implies m = n? and then do induction on m?
TRWBWnoway-: induct on m or on n, your choice, same difference
trytolite: one typical way is to define integrals over [a,b], then define integral [a,inf] as lim b->inf integral [a,b]
noway-: so yes, that works fine
noway-Why do I need induction? If f is a bijection its both an injection and surjection. Meaning there is atleast one and at most one element b such that f(a) = b, or that there is 1!
Do I use this fact for the base case?
TRWBWnoway-: base case would be bijection from [1] to [n] implies n=1
noway-ok
doofy2if you make all 48 connections from 6 dots on one side of a rectangle to 8 dots on the opposite side of the rectangle, what is the maximum number of intersections that are possible?
TRWBWdoofy2: build it up one point at a time
doofy2i got it TRWBW thank you :)
kmh_afkdoofy2 : multinetworking ?
trytolitetrwbw: ahhh.. so i should find the antiderative as usual, but for the endpoint b, and then calculate the limit as b goes to inf.
?
EdBoyyes
trytolitecool, thanks
EdBoywhat?
I don't even know what you're doing, I just know you're doing calculus
:P
but it sounds like you have the right idea
kilimanjarotrytolite, if the limit diverges, the indefinite integral does not exist
trytoliteheh
kilimanjaro: gotcha :)
noway-TRWBW: Do I need any more explanation for the base case?
kilimanjaronoway-, what more is there to explain? A bijection is surjective, hence there can only be one element in the range
noway-right, should I explain that in the proof?
I am not seeing why this problem needs induction at all?
kilimanjaroI'm not sure that induction is truly sufficient anyways
noway-its a problem in our book... it gives a hint to use induction...
r00723r0is there any way to find the non-trivial solutions (x != y) in x^y = y^x?
i made an implicit graph: http://img179.imageshack.us/img179/538/xyyxbd9.png
kilimanjaroI don't know why it does. But think about a bijection whose domain is the set of real numbers. Induction on the size of the domain is not sufficient unless you also deal with cardinals
But since induction is merely a recommendation, ignore it
structuredr00723r0: could take log of both sides and separate x/y terms on either side qeuation
r00723r0structured, but how would that find the non-trivial solutions?
structuredr00723r0: not entirely sure honestly, you mighte want to try let y = k*x in x/log(x) = y/log(y), and then solve for x
Daggieif on average one fatality per 100 collisions between cars and deer. In 300 collisions between a car and a deer, what is the expected number of fatalities and the standard deviation?

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