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

You are not logged in. #28 20130806 02:06:07
Re: Change your subject.That's OK. Great minds think alike and all that. You cannot teach a man anything; you can only help him find it within himself..........Galileo Galilei #29 20130806 02:07:20
Re: Change your subject.I will have to concede that is probably true. 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. #30 20130806 02:24:55
Re: Change your subject.OK. Don't get me wrong. It's a useful tool but that's all. I'm a better driver than my car. Last time it tried driving on its own there was a right crunch. You cannot teach a man anything; you can only help him find it within himself..........Galileo Galilei #31 20130806 02:30:32
Re: Change your subject.
Where from the negative or positive sign in front of the root sign? #32 20130806 02:31:40
Re: Change your subject.Look at post #23, he is continuing from there. 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. #33 20130806 03:03:36
Re: Change your subject.Yep, because a negative number times a negative number is a positive number, so: Try it: Therefore, when we 'undo' the squaring, by square rooting, the answer could be positive, or negative. The square root of 4 is either 2, or 2. We can't tell. Again: Edit: this is why bobbym's original solution had two answers And: Which is the same as: Last edited by Au101 (20130806 03:06:24) #34 20130806 03:11:45
Re: Change your subject.
Still I cant grasp why there is positive and negative sign before the root. #35 20130806 03:20:53
Re: Change your subject.When you take a square root of a number there are two possible roots. (3)(3) = 9 and (3)(3)=9 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. #36 20130806 03:26:38
Re: Change your subject.eg. √9 = 3 Let's look at an actual question. Consider the graph y = x^2 Find x when y = 9 see graph below. If you said x = 3, you would loose some marks because you hadn't given all the possible values. Bob You cannot teach a man anything; you can only help him find it within himself..........Galileo Galilei #37 20130806 03:39:02
Re: Change your subject.Actually, only, but both 3 and 3 satisfy the equation .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 #38 20130806 03:53:19
Re: Change your subject.
Excellent technical observation, we should, really, say that: However, it is true to say that the square root of 9 is plus or minus 3. The problem we have is that the sign √ refers to the principal square root only. This does make the thing a little harder to understand, though Suffice it to say that when we square root both sides of an equation, we must include the ± sign, as an equation of the form: Has two solutions. Last edited by Au101 (20130806 03:54:17) #39 20130806 04:11:57
Re: Change your subject.Hi; 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. #40 20130806 04:15:40
Re: Change your subject.Interesting. You cannot teach a man anything; you can only help him find it within himself..........Galileo Galilei #41 20130806 04:19:39
Re: Change your subject.I agree, it was sloppy phrasing on my part as well. Although, bobbym, I think your post #35 was correct. 9 does have two square roots (the principal root being 3, the other being 3) the problem is that the notation √9 gives us the principal square root. This is why we have to write the ± sign before the radical. Last edited by Au101 (20130806 04:27:30) #42 20130806 04:30:23
Re: Change your subject.hi You cannot teach a man anything; you can only help him find it within himself..........Galileo Galilei #43 20130806 04:37:24
Re: Change your subject.I would imagine it dates back to early geometry. If, say, you're trying to calculate the length of a hypotenuse, you're not interested in the negative values. I imagine this general precedence of the principal square root was incorporated into the notation when it was defined. Because, of course, we define our notation to be useful to us and easy to work with. But, without realising it, you've always been using the convention whenever you've gone: If it weren't for the fact that the √ sign only referred to the principal value, you wouldn't need the ±, that would be implied by the √. Then you could just write: It's just the way we learn to think about it conceptually Last edited by Au101 (20130806 04:38:06) #45 20130806 06:12:10
Re: Change your subject.
Surely ?#46 20130806 06:24:11
Re: Change your subject.Again, the square root returns only the principal value by convention, not because it would cause contradiction otherwise. Last edited by anonimnystefy (20130806 06:25:14) 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 #47 20130806 06:24:13
Re: Change your subject.Hmmmm....on second thought, maybe? I'm not sure. My original thinking was that when the first ± is +, so is the second one and when the first ± is , so is the second one. So, for example: When the first ± is +, so is the second one and when the first ± is , so is the second one. So we have: Hence the need for a ∓ sign. In this case we would have +(+5) or (5) and only these options. But it seems reasonable to be able to say: So, yes, I think you're right. Ignore my second post. The first one still stands, though, I think But yes, anonimnystefy is right. Sorry for confusing the matter further, the important thing to note is √x is always the positive, principal root, hence the need for the ± sign before the radical sign. Last edited by Au101 (20130806 06:26:57) #48 20130806 06:32:36
Re: Change your subject.
It can become quite a complex issue (pun not intended). For example, I did this problem via contour integration: Naturally, the first step is to compute the sum of the residues of that function. Tell Mathematica to do that, and it won't give you the correct answer, thanks to the square root. #50 20130806 17:43:50
Re: Change your subject.I'd say so. 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 