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You are not logged in. #1 20060821 20:18:34
3.3333333 + 6.66666666Hello. I'm new to the boards and I'd be so grateful if someone could answer this question. #2 20060821 20:46:29
Re: 3.3333333 + 6.66666666A Big Welcome! "The physicists defer only to mathematicians, and the mathematicians defer only to God ..."  Leon M. Lederman #3 20060821 21:29:44
Re: 3.3333333 + 6.66666666yes 9.999.... = 10 The Beginning Of All Things To End. The End Of All Things To Come. #4 20060821 22:14:25
Re: 3.3333333 + 6.66666666If 9.999... is not equal 10, you should be able to find a number between the two, but you can't. Bang postponed. Not big enough. Reboot. #5 20060821 22:56:32
Re: 3.3333333 + 6.66666666
That is an excellent way for me to understand it. Thank you so much. #6 20060822 02:07:06
Re: 3.3333333 + 6.66666666Numen's view is great. You can also say that 3.333... = 3 + 1/3 = 10/3 and 6.666... = 6 + 2/3 = 20/3, and we have Last edited by Zhylliolom (20060822 02:12:54) #7 20060822 03:16:21
Re: 3.3333333 + 6.66666666Another way: Last edited by krassi_holmz (20060822 05:22:52) IPBLE: Increasing Performance By Lowering Expectations. #8 20060822 03:35:33
Re: 3.3333333 + 6.66666666
*cough* 10 The Beginning Of All Things To End. The End Of All Things To Come. #9 20060822 06:08:33
Re: 3.3333333 + 6.66666666You could also use a system other than decimal. #10 20060822 07:50:00
Re: 3.3333333 + 6.66666666Excellent! So far the survey yields 100% "Yes" votes. But the sample size is too small to draw any conclusions "The physicists defer only to mathematicians, and the mathematicians defer only to God ..."  Leon M. Lederman #11 20060822 08:27:59
Re: 3.3333333 + 6.66666666I think they are different. igloo myrtilles fourmis #12 20060822 08:54:49
Re: 3.3333333 + 6.66666666Ho boy, the conversation is sure gonna take off now. "The physicists defer only to mathematicians, and the mathematicians defer only to God ..."  Leon M. Lederman #13 20060822 09:31:56
Re: 3.3333333 + 6.66666666John, if that's the case, then tell me, what is ∞  1? Because instead of ∞ 3's after the decimal place in 3.333... × 10 there will be "only" ∞  1, in your view of the problem. Krassi's display may leave room for ambiguity, but Numen and I's posts have rather clear methods/reasons which leave little to be debated. #14 20060822 13:16:04
Re: 3.3333333 + 6.66666666The reason that I brought up the whole Base 3 representation is to show it is just a "limitation" of our decimal system. Certain numbers, like 1/3 can't be expressed 100% accurately in the decimal system. But it can be expressed exactly in base 3. .33333... (base 10) = 1/3 = .1 (base 3). So for cases like these, switching to a different base can be helpful. #15 20060822 13:22:34
Re: 3.3333333 + 6.66666666
...with a finite number of digits. "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..." #16 20060822 15:31:09
Re: 3.3333333 + 6.66666666If q is rational, then q=10 in base q IPBLE: Increasing Performance By Lowering Expectations. #17 20060822 19:06:01
Re: 3.3333333 + 6.66666666
The flaw there is that as there are infinite 3's, there is no end. Why did the vector cross the road? It wanted to be normal. #18 20060822 19:41:36
Re: 3.3333333 + 6.66666666The closest to 1/3 is 0.333... Last edited by Devanté (20060822 19:46:17) #19 20060822 20:53:59
Re: 3.3333333 + 6.66666666This is what I like about this forum ... you can express a different idea and people will discuss it nicely. "The physicists defer only to mathematicians, and the mathematicians defer only to God ..."  Leon M. Lederman #20 20060822 21:13:03
Re: 3.3333333 + 6.66666666Interesting...I've never thought about it that way before. #21 20060822 22:06:29
Re: 3.3333333 + 6.66666666And there's also the other example: Last edited by Devanté (20060822 22:06:45) #22 20110922 17:14:37
Re: 3.3333333 + 6.66666666This is my first time here and i really like the way you guys respond to questions. Am a novice and i'd like you to pls solve this equation for me. #23 20110922 19:04:30
Re: 3.3333333 + 6.66666666Hi Shina; 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. #24 20110922 22:01:26
Re: 3.3333333 + 6.66666666Hi, I'm fairly sure that that's true, however, I'm not sure if that's the best and most illustrative way of using limits, but somebody more knowledgeable might be able to help. Perhaps: Would be better? What I can point out, though, is that multiplication by ten doesn't mean that there will be a zero on the end of the number, e.g. 33.3 times 10 = 333. Since we use base ten, multiplication by ten simply means that we move everything up one place value  one ten. If, then, we are dealing with an integer, then everything gets moved along one place value and since the last digit is in the 1s column, we move it to the 10s and add a 0. If we have a decimal, however, then we move everything along, e.g. from the hundredths up, which will move our last digit into the tenths  no need for a zero. Since 3.3... is a nonterminating decimal we will never get to the end and so we will never have to worry about putting a zero there. Thanks Last edited by Au101 (20110922 22:01:49) #25 20111008 04:39:54
Re: 3.3333333 + 6.66666666I'd have to disagree with most of what people are saying here, reason being is because to me it sounds like most people are assuming 3.3 recurring = 3 1/3, however, what if 3.3 recurring were just that? I'll agree with what most people are saying if you meant that 3.3 recurring was SUPPOSED to equal 3 1/3, although I can't because it doesn't. 3 1/3 expressed as a decimal equals 3.3 recurring because you can never get to the end, because ultimately it can not be accurately defined as a decimal. So in turn, I would argue that using 3.3 recurring + 6.6 recurring = 9.9 recurring not 10, unless 3.3 recurring was meant to be 3 1/3 in the beginning. The problem I'm having is what you originally meant, because if you meant 3.3 recurring as 3 1/3, then what I'm saying here is wrong, but looking at 3.3 recurring by itself, I'd disagree with what most people are saying. Life isn’t a simple Math: there are always other variables. [unknown] But Nature flies from the infinite, for the infinite is unending or imperfect, and Nature ever seeks an end. Aristotle 