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You are not logged in. #1 20130619 00:31:48
A horrid problemFlip a coin 2N times, where N is large. Let P(x) be the probability of obtaining I have discovered a truly marvellous signature, which this margin is too narrow to contain. Fermat Give me a lever long enough and a fulcrum on which to place it, and I shall move the world. Archimedes Young man, in mathematics you don't understand things. You just get used to them.  Neumann #2 20130619 01:11:38
Re: A horrid problemHi; to prove? In mathematics, you don't understand things. You just get used to them. I have the result, but I do not yet know how to get it. All physicists, and a good many quite respectable mathematicians are contemptuous about proof. #3 20130619 01:52:44
Re: A horrid problemI don't think that would be correct, then. The limit operator is just an excuse for doing something you know you can't. “It's the subject that nobody knows anything about that we can all talk about!” ― Richard Feynman “Taking a new step, uttering a new word, is what people fear most.” ― Fyodor Dostoyevsky, Crime and Punishment #4 20130619 02:04:07
Re: A horrid problemI do not think so either. In mathematics, you don't understand things. You just get used to them. I have the result, but I do not yet know how to get it. All physicists, and a good many quite respectable mathematicians are contemptuous about proof. #5 20130619 02:12:58
Re: A horrid problemIt does seem to work without the minus sign, though. The limit operator is just an excuse for doing something you know you can't. “It's the subject that nobody knows anything about that we can all talk about!” ― Richard Feynman “Taking a new step, uttering a new word, is what people fear most.” ― Fyodor Dostoyevsky, Crime and Punishment #6 20130619 02:18:19
Re: A horrid problemHow do you do that? 'And fun? If maths is fun, then getting a tooth extraction is fun. A viral infection is fun. Rabies shots are fun.' 'God exists because Mathematics is consistent, and the devil exists because we cannot prove it' 'Who are you to judge everything?' Alokananda #7 20130619 02:22:35
Re: A horrid problemHi; that I can prove. In mathematics, you don't understand things. You just get used to them. I have the result, but I do not yet know how to get it. All physicists, and a good many quite respectable mathematicians are contemptuous about proof. #8 20130619 08:15:17
Re: A horrid problemThat is what the original problem is asking for. But I cannot get it. I am using the limit definition and Stirling's formula. The limit operator is just an excuse for doing something you know you can't. “It's the subject that nobody knows anything about that we can all talk about!” ― Richard Feynman “Taking a new step, uttering a new word, is what people fear most.” ― Fyodor Dostoyevsky, Crime and Punishment #9 20130619 09:53:45
Re: A horrid problemPost 7 is what I need proven/ I have discovered a truly marvellous signature, which this margin is too narrow to contain. Fermat Give me a lever long enough and a fulcrum on which to place it, and I shall move the world. Archimedes Young man, in mathematics you don't understand things. You just get used to them.  Neumann #10 20130621 04:47:59
Re: A horrid problemCan you prove it then? I have discovered a truly marvellous signature, which this margin is too narrow to contain. Fermat Give me a lever long enough and a fulcrum on which to place it, and I shall move the world. Archimedes Young man, in mathematics you don't understand things. You just get used to them.  Neumann #11 20130621 10:10:35
Re: A horrid problemHi Shivamcoder3013 The limit operator is just an excuse for doing something you know you can't. “It's the subject that nobody knows anything about that we can all talk about!” ― Richard Feynman “Taking a new step, uttering a new word, is what people fear most.” ― Fyodor Dostoyevsky, Crime and Punishment #12 20130621 11:48:02
Re: A horrid problemHi; Using Stirlings: Notice the approximately equal sign that is because you are approximated a discrete distribution ( binomial ) with the Normal distribution. 1) is an approximation for 2) which the above steps prove. Even for large N it is still an approximation. When N approaches infinity 1) = 2). To prove that you might need the limit but maybe since Stirlings formula is asymptotic to the factorial it might be implied in step 3. In mathematics, you don't understand things. You just get used to them. I have the result, but I do not yet know how to get it. All physicists, and a good many quite respectable mathematicians are contemptuous about proof. #13 20130622 02:19:52
Re: A horrid problemI am not getting how you get that... I have discovered a truly marvellous signature, which this margin is too narrow to contain. Fermat Give me a lever long enough and a fulcrum on which to place it, and I shall move the world. Archimedes Young man, in mathematics you don't understand things. You just get used to them.  Neumann #14 20130622 03:44:15
Re: A horrid problemHi Shivamcoder3013; In mathematics, you don't understand things. You just get used to them. I have the result, but I do not yet know how to get it. All physicists, and a good many quite respectable mathematicians are contemptuous about proof. #15 20130622 10:00:03
Re: A horrid problemOk, I will try to think about it a bit. Thanks a lot. I have discovered a truly marvellous signature, which this margin is too narrow to contain. Fermat Give me a lever long enough and a fulcrum on which to place it, and I shall move the world. Archimedes Young man, in mathematics you don't understand things. You just get used to them.  Neumann #16 20130622 21:34:59
Re: A horrid problemHi bobbym The limit operator is just an excuse for doing something you know you can't. “It's the subject that nobody knows anything about that we can all talk about!” ― Richard Feynman “Taking a new step, uttering a new word, is what people fear most.” ― Fyodor Dostoyevsky, Crime and Punishment #17 20130622 21:43:39
Re: A horrid problemyields 0.001079819330263761 The exact answer is: yields 0.0010798643294 Seems pretty good. Try for larger n with x small in comparison to convince yourself numerically.
I think the limit is 1. According to M that is true. Why do you think the limit is not 1?
Stirlings is an asymptotic form for the factorial. The limit of the ratio of Stirlings and the factorial is 1. The fact that he use Stirlings in his proof guarantees the above limit. In mathematics, you don't understand things. You just get used to them. I have the result, but I do not yet know how to get it. All physicists, and a good many quite respectable mathematicians are contemptuous about proof. 