Discussion about math, puzzles, games and fun. Useful symbols: ÷ × ½ √ ∞ ≠ ≤ ≥ ≈ ⇒ ± ∈ Δ θ ∴ ∑ ∫ • π ƒ ¹ ² ³ °
 

You are not logged in. #1 20121003 23:36:21
Prove thisProve that for every real n > 0, n +(1/n) >= 2 '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 #2 20121004 01:16:30
Re: Prove thisHi Agnishom; Multiply both sides by n. This is okay because n is positive, we do not have to worry about reversing the <= . Which is obviously greater than 0 for all n>0. We are done. 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 20121004 03:52:21
Re: Prove thisThe other would be just using the AMGM inequality... 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 #5 20121004 05:54:46
Re: Prove thisHi Bob; 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 20121004 08:37:07
Re: Prove thisTrouble is: if you start by assuming what you are required to prove and show a true result it doesn't always follow that the proof is reversible. I have no problem with you thinking it through that way ... it's a good approach ... but you ought then to rewrite it with the known truth first then leading to the thing you have to prove. You cannot teach a man anything; you can only help him find it within himself..........Galileo Galilei #7 20121004 08:53:16
Re: Prove thisI have one. You cannot teach a man anything; you can only help him find it within himself..........Galileo Galilei #8 20121004 16:50:59
Re: Prove thisHi Bob; 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 20121004 17:17:48
Re: Prove thisHi Agnishom; Now we can say And we are done. 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. #10 20121004 17:25:10
Re: Prove this
Those are different from bobbym's proof because bobbym's steps are equivalent. Yours are not e.g. from x^2=y^2 doesn't follow x=y... 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 #11 20121004 17:30:29
Re: Prove thisHmmm... Why not use the Preview button? 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 20121004 17:31:42
Re: Prove thisOn this browser it is often off to the side and I can not easily see it. 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 20121004 17:34:01
Re: Prove thisOk. 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 #14 20121004 17:40:32
Re: Prove thisHi anonimnystefy; 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 20121004 18:00:10
Re: Prove thishi bobbym, You cannot teach a man anything; you can only help him find it within himself..........Galileo Galilei #16 20121004 18:07:24
Re: Prove thisHi Bob;
Truthfully, I did not know enough to call it trivial. I was oblivious. 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. #17 20121004 19:53:37
Re: Prove thishi bobbym and all
Metaphorically ... maybe. Literally ... not in my world. I'd be a rich man. You cannot teach a man anything; you can only help him find it within himself..........Galileo Galilei #18 20121004 19:57:01
Re: Prove thisIt's a very helpful tactic for exams  in one of my mechanics papers (M5) I worked backwards from a 'show that', then just rewrote what I did in reverse and crossed out the original. I think the exam board do not like this however. #19 20121004 20:52:59
Re: Prove thishi zetafunc You cannot teach a man anything; you can only help him find it within himself..........Galileo Galilei #20 20121004 21:01:34
Re: Prove thisWell, it makes some problems ridiculously easy... there was a problem in my M5 (June 2012) paper which gave some scenario involving angular motion and asked you to show that the braking force is equal to _____ (or something along those lines). But you could just work backwards and it became a lot easier. #21 20121004 21:04:53
Re: Prove thisBut if they want to be helpful and prove that you know what you're doing so everyone is on the same level for the next part of the question, why not cut out unintended solutions? #22 20121004 22:01:01
Re: Prove thisExam design has come on a long way in the last 50 years. You used to get questions where you had to work through all the parts with no prompts and if you couldn't do part (a) then the rest couldn't even be attempted. The trouble with that sort of question is that it doesn't necessarily pick out the strongest candidates and give them the highest marks. Let's say there are 10 things you have to know, A,B,C ..., J You cannot teach a man anything; you can only help him find it within himself..........Galileo Galilei #23 20121004 23:16:21
Re: Prove thisSorry for not being able to be online tomorrow '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 #24 20121004 23:23:09
Re: Prove thisHi Agnishom; 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. #25 20121004 23:42:04
Re: Prove thisHi bobbym; '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 