trytolite | how 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. |

TRWBW | trytolite: 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? |

TRWBW | noway-: 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? |

TRWBW | noway-: base case would be bijection from [1] to [n] implies n=1 |

noway- | ok |

doofy2 | if 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? |

TRWBW | doofy2: build it up one point at a time |

doofy2 | i got it TRWBW thank you :) |

kmh_afk | doofy2 : multinetworking ? |

trytolite | trwbw: ahhh.. so i should find the antiderative as usual, but for the endpoint b, and then calculate the limit as b goes to inf. ? |

EdBoy | yes |

trytolite | cool, thanks |

EdBoy | what? 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 |

kilimanjaro | trytolite, if the limit diverges, the indefinite integral does not exist |

trytolite | heh kilimanjaro: gotcha :) |

noway- | TRWBW: Do I need any more explanation for the base case? |

kilimanjaro | noway-, 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? |

kilimanjaro | I'm not sure that induction is truly sufficient anyways |

noway- | its a problem in our book... it gives a hint to use induction... |

r00723r0 | is 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 |

kilimanjaro | I 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 |

structured | r00723r0: could take log of both sides and separate x/y terms on either side qeuation |

r00723r0 | structured, but how would that find the non-trivial solutions? |

structured | r00723r0: 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 |

Daggie | if 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? |