| [ QuizWit ] in KIDS 글 쓴 이(By): iLUSiON (띠띠빤쮸) 날 짜 (Date): 2006년 8월 3일 목요일 오후 08시 41분 00초 제 목(Title): Re: [Q] 조밀성의 증명 there was a very interesting putnam compeition problem regarding the cardinality (density) of Q and R\Q. where Q is rational numbers and R real numbers. the problem statement was like this. at the origin, you shoot a lazer beam. find the probability the lazer beam will pass thru any of the grid points (a,b) where a and b are intergers. it was a homework problem and that was before i learned about cardinality. so i claimed the probability was 1 because you can always find 1 rational number beetween any two irrational numbers and vice versa. well obviously incorrect solution. but still my math professor (at UBC) give me something like 80% hehe.... and later he showed me diagonal argument in his office. well it is a cute memory..... anyway i thought my IQ has been deleted. apprently it was not. I actually selected X in admin a month ago but i can't understand why my ID has been reappread. guess SYSOP loves me? haha..... iLUSiON - le plus grand de tous http://cyworld.nate.com/ilusion |