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You are not logged in. #1 20060225 10:04:09
who woulda thunk it?The limit of the nth root of n as n approaches infinity equals.... 1!!! I don't know about you guys but I find this extremely remarkable! Last edited by mikau (20060225 10:06:24) A logarithm is just a misspelled algorithm. #2 20060225 10:20:38
Re: who woulda thunk it?This reminds me of e in some ways. This seems to suggest 1^∞ = ∞ but this is impossible. Therefore it must be something like the limit of (1 + 1/x )^n as n approaches infinity and x is some function of n, and n does not equal x. (otherwise this would be e). I wonder if we could figure out the relation between n and x... A logarithm is just a misspelled algorithm. #3 20060225 10:56:37
Re: who woulda thunk it?Given that 1/∞ = 0, it's not that surprising at all... El que pega primero pega dos veces. #4 20060225 11:15:39
Re: who woulda thunk it?Yes and no. I mean, if you have 1/n, when n becomes significantly large, the exponant tends to be very small, but the base tends to get very large. Just like the definition of e. limit of (1 + 1/x)^x as x approaches infinity. You're inclined to say 1/x = 0 and eliminate it, but the infinitely small difference, to the infinitieth power makes a difference. Likewise, I was inclined to believe the smallness of the exponant would be "canceled out" by the hugeness of the base. A logarithm is just a misspelled algorithm. #5 20060225 12:34:09
Re: who woulda thunk it?I haven't tried to understand your explanations, but it isn't remarkable to me. igloo myrtilles fourmis #6 20060225 16:04:44
Re: who woulda thunk it?maybe you guys are more familiar with limits then me and it doesn't come to such a suprise. Last edited by mikau (20060225 16:40:58) A logarithm is just a misspelled algorithm. #7 20060226 04:54:40
Re: who woulda thunk it?.99 ^ big number, goes down. igloo myrtilles fourmis #8 20060226 05:12:30
Re: who woulda thunk it?I'm not really suprised at 1, but I really like the way mikau took the limit. Never would have thought of doing that. "In the real world, this would be a problem. But in mathematics, we can just define a place where this problem doesn't exist. So we'll go ahead and do that now..." #9 20060226 07:22:47
Re: who woulda thunk it?you mean taking the natural log, finding the limit, and raising e to that power? Thats a pretty common technique in my mathbook. Last edited by mikau (20060226 07:29:18) A logarithm is just a misspelled algorithm. #10 20060226 08:46:56
Re: who woulda thunk it?Wait a minute... Had the solution of x = the nth root of n. Surely, what you've just said means that: Why did the vector cross the road? It wanted to be normal. #11 20060227 05:07:55
Re: who woulda thunk it?now I'm confused. A logarithm is just a misspelled algorithm. #12 20060227 07:35:50
Re: who woulda thunk it?And, as John said, anything below 1 goes to 0. "The physicists defer only to mathematicians, and the mathematicians defer only to God ..."  Leon M. Lederman 