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You are not logged in. #1 20090916 11:39:13
Some nasty inequalitiesHI; Prove: 2) With Prove: Last edited by bobbym (20090916 11:43:27) 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. #2 20090916 11:47:25
Re: Some nasty inequalitiesWow, they sure look nasty! (At first sight, at any rate.) #3 20090916 12:00:28
Re: Some nasty inequalitiesHi Jane; 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. #4 20090916 16:12:08
Re: Some nasty inequalities
Well, I can at least start by proving that .
Quite easy, as it turns out. In fact, as you can see, the inequality is strict. So far so good. #5 20090916 21:54:14
Re: Some nasty inequalitiesHi Jane; Did sub c = 1  a  b Hold b constant So a is at maximum when a = (1  b) / 2. If we now substitue the maximum value for a and the inequality still holds then it holds for lesser values of a. Substituting into yields with simplification Do the switch cause of multiplication by  27 The above is obviously true, so Hope yours is shorter! Last edited by bobbym (20090917 00:15:07) 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. #6 20090917 03:41:32
Re: Some nasty inequalitiesI always thought using calculus to tackle these kinds of inequalities is a bit of a bruteforce tactic. Much like using the Jordan–Hölder theorem in group theory to prove the fundamental theorem of arithmetic, if you know what I mean. #7 20090917 06:26:54
Re: Some nasty inequalitiesHi Jane; Last edited by bobbym (20090918 06:06:02) 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 20091017 17:22:36
Re: Some nasty inequalitiesHi; Last edited by bobbym (20091017 17:23:15) 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. #9 20091017 22:00:51#10 20091017 22:19:51
Re: Some nasty inequalitiesHi Jane;
Using a lot of that bruteforce myself I am forced to disagree with their comments. I like it a lot! Last edited by bobbym (20091018 11:50:00) 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. #11 20091017 22:47:04
Re: Some nasty inequalitiesWow, Muirhead's inequality looks quite powerful, thanks for introducing me to it #12 20091017 22:52:49
Re: Some nasty inequalitiesHi identity; Last edited by bobbym (20091017 22:53:07) 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 20091017 23:41:30
Re: Some nasty inequalitiesHaha, unwise to use Muirhead in an IMO solution, because it is not elegant enough? #14 20091018 10:39:49
Re: Some nasty inequalitiesHi identity; Last edited by bobbym (20091018 11:47:21) 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 20091023 09:29:21
Re: Some nasty inequalitiesHi; Last edited by bobbym (20091023 10:25:08) 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. #16 20091023 10:27:33
Re: Some nasty inequalitiesI think you have the inequality sign the wrong way round. #17 20091023 11:08:36
Re: Some nasty inequalitiesHi Jane; 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. 