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You are not logged in. #1051 20120702 20:51:32
Re: 0.9999....(recurring) = 1?hi Stangerzv
That works for me. When I calculate (on paper) 1 divided by 3, I stop and write 'recurring' because I don't have any paper big enough. You cannot teach a man anything; you can only help him find it within himself..........Galileo Galilei #1052 20120702 21:00:25
Re: 0.9999....(recurring) = 1?Hi; We have a common ratio r = 1 / 10. Without the use of the this theorem practical mathematics would fall apart. .9999999... = 1 works for me. 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. #1053 20120719 09:44:06
Re: 0.9999....(recurring) = 1?Interesting how this thread got so long. is a mathematical fact. The reason it is so difficult for people to understand may be due to confusion over the concept of infinity. Here are some different ways to think about it:___________ 1) pointed out above ___________ 2) is equivalent to . But since the number of 0's are infinite, you never "reach" the 1; it is equivalent to 0! ___________ 3) a popular proof ___________ Last edited by MrButterman (20120719 09:44:44) #1054 20120719 09:56:52
Re: 0.9999....(recurring) = 1?Hi MrButterman;
These type threads are on every forum. Mostly they are so long because the opponents of .9999... = 1 can not be convinced by any of those proofs or any others. 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. #1055 20121027 16:14:04
Re: 0.9999....(recurring) = 1?To be fair, the proofs they offer can be argued from a logical standpoint (so long as you understand everything that is going on), but there is nothing in mathematics that can prove how they are different otherwise. I myself do not...personally believe this as a mathematical "fact," but also realize how futile it is to argue against it. So like those many, it is impossible to convince me as well, after all, there is a reason this idea is so highly controversial. Last edited by Calligar (20121027 16:16:01) 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 #1056 20121027 21:44:32
Re: 0.9999....(recurring) = 1?Hi y'all Writing "pretty" math (two dimensional) is easier to read and grasp than LaTex (one dimensional). LaTex is like painting on many strips of paper and then stacking them to see what picture they make. #1057 20121121 07:40:53
Re: 0.9999....(recurring) = 1?
The term mathematical fact might be a little vague. First, not every number is rational  not every number can be represented as the quotient of integers. For example the width of a square whose area is 2 is not a rational number. That is, we need the full blown set of real numbers. Figuring out what the real numbers (really) look like is a hard challenge, and providing a description of them in set theory was a major challenge. There are two main approaches: Dedekind's cuts and Cauchy sequences. They produce the same set. Essentially, take a bounded sequence of rational numbers, and identify a "number" L with this sequence. The real numbers are the rational numbers with all these Ls. Thus in the construction of real numbers, we see that every real number is the limit of a sequence of rationals. #1058 20121121 23:54:10
Re: 0.9999....(recurring) = 1?Well, I guess I can try to be a little bit more clear...
Firstly, when I say mathematical fact, I am really just referring to what is currently accepted and arguably "known" in mathematics. Secondly, the limit of sequence is just another way to represent it being infinitely close, but still not exactly equal to the number (unless I'm mistaken). Just like for it representing 1/3 with <0.3,0.33,0.333,etc. (I might not have put everything in proper terms, sorry if that causes any confusion, wasn't sure how to say it simply off the top of my head). Also would like to make a note, you messed up slightly when you posted; it should be 0.9, not 0,9 for the first one unless I'm mistaken (but doesn't really have any relevance to anything). In other words, it is just more rules that exist that otherwise, as I was saying, prove it's a mathematically fact. Remember when I said this...
In mathematics, there is no way to represent the difference between 0.¯9 and 1. All proofs (including false ones) either assume things (for specifically this), or simply define it as one only because of the infinitely close distance (there might be a few other reasons, but those are the 2 major I see). Even though some people will argue things like it is 0.0...1 away, or 1/10¯0 away, which might arguably seem right, one can argue about the infinite distance, therefore making it an impossible argument to win. So this argument doesn't carry on (with me) over confusion, I'll explain in more detail. Last edited by Calligar (20121121 23:57:16) 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 #1059 20121122 02:25:36
Re: 0.9999....(recurring) = 1?Unless I'm mistaken, it's more then simply for convenience. Also, 0.¯9 doesn't end, because the ¯ over any number (which I put before the repeating number because otherwise I'd have to show in a picture), means it goes on forever. If it had an end, that means we'd be able to put something after it, therefore, there'd be no reason for this controversy in the first place. 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 #1060 20121122 04:10:47
Re: 0.9999....(recurring) = 1?0.999... doesn't exist. Recurring 9's aren't allowed. 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 #1061 20121122 04:19:17
Re: 0.9999....(recurring) = 1???? 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 #1062 20121122 21:35:05
Re: 0.9999....(recurring) = 1?But if 1/3 = 0.333... Then Why does 0.333... Not become = to 0.4 Because that would then be the Same Infinite Calculation as... #1063 20121122 21:49:45
Re: 0.9999....(recurring) = 1?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. #1064 20121122 21:54:50
Re: 0.9999....(recurring) = 1?But approaching 0 and seems to be approaching Are both not Actually ever going to get there ? #1065 20121122 21:57:56
Re: 0.9999....(recurring) = 1?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. #1066 20121123 00:53:07
Re: 0.9999....(recurring) = 1?But the number 0.9999... itself doesn't exist... 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 #1067 20121123 01:02:23
Re: 0.9999....(recurring) = 1?I don't look at it that way. To me it is shorthand for a series that thank the Lord, sums to 1. 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. #1068 20121123 03:26:52
Re: 0.9999....(recurring) = 1?.9 + .1 = 1 #1069 20121123 04:09:40
Re: 0.9999....(recurring) = 1?
How many times must I say this? No numbers exist. They are all just elements in an imaginary set that mathematicians have invented. You cannot teach a man anything; you can only help him find it within himself..........Galileo Galilei #1070 20121123 04:24:04
Re: 0.9999....(recurring) = 1?Hi Bob 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 #1071 20121123 04:29:46
Re: 0.9999....(recurring) = 1?Hi! Let's reduce the .9999... down to its "roots" .1111... which is supposed to be equal to 1/9. Writing "pretty" math (two dimensional) is easier to read and grasp than LaTex (one dimensional). LaTex is like painting on many strips of paper and then stacking them to see what picture they make. #1072 20121123 05:50:37
Re: 0.9999....(recurring) = 1?
What number is that? 3 ? You cannot teach a man anything; you can only help him find it within himself..........Galileo Galilei #1073 20121123 06:12:18
Re: 0.9999....(recurring) = 1?No, 3 is allowed, 0.(9) isn't. There cannot be recurring 9's after the decimal point. 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 #1074 20121123 06:27:28
Re: 0.9999....(recurring) = 1?Why not? You cannot teach a man anything; you can only help him find it within himself..........Galileo Galilei #1075 20121123 07:51:49
Re: 0.9999....(recurring) = 1?Hi SMboy;
Is .1 the same as .00001 or .0000000001 or ... 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. 