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

You are not logged in. #26 20130131 01:39:49
Re: 0.999... = 1? Or not?Hi john_gabriel; 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. #27 20130201 02:29:43
Re: 0.999... = 1? Or not?.9999999 repeating equals 1 depending on your tolerance, and if we are talking applied or theoretical math. If we divide 1 by 3 we get .333333 repeating. This is not a perfect representation of 1/3, as each repeating 3 gets you ever closer to 1/3. The question is when do mathematicians say "after this 3 let us just say it just equals 1 third." So yes .9999999 repeating can equal 1, but at some point you are rounding up, the amount you round up gets ever smaller as you reach more nines, but eventually you round up (i.e. with .999 you round up by .001, and with .99999 it is .00001) Spooooon!!! #28 20130205 05:11:57
Re: 0.999... = 1? Or not?Muxdemux: Didn't you only prove (1) for the natural numbers? #29 20130205 06:10:13
Re: 0.999... = 1? Or not?This argument keeps surfacing on the forum and I keep trying to explain. To save you having to find my earlier posts I'll say it again. They define it to mean the same thing and it's easy to see why. When the builders were assigning positive integers to the houses in my street they decided to leave out the number between 12 and 14. They thought it might be harder to sell a house with that label because some people think it is an unlucky number. So that number doesn't exist in that context. The lady who delivers the mail still manages to put the right letters in the right boxes so it doesn't seem to cause much of a problem. Some people have never heard of complex numbers, or quaternions but they still get used by those who have. It is occasionally useful to define an expression as having a certain value because the formulas work better that way. That's where the following definitions come from: There are lots more like this. Now it happens to suit some mathematicians to define: You may not like it. You may not want to use it. That's Ok. You don't have to. But it has been defined so it has as much existence as any other number. It's a waste of time debating that. You might as well start arguing about whether the two symbols below are the same. They don't look the same but ........ Bob You cannot teach a man anything; you can only help him find it within himself..........Galileo Galilei #30 20130205 11:32:16
Re: 0.999... = 1? Or not?Bob bundy: "To say that numbers have no existence at all except as mathematical concepts" is false. #31 20130205 18:05:27
Re: 0.999... = 1? Or not?
I agree if we are talking theoretical math, however ask a manufacturer, engineer, architect, etc. if they measure one third to an infinite accuracy. As this can not be done realistically we "say" .999999... at some point equals 1, even though theoretically it does not. That is one I meant by .9999999... can equal 1. Spooooon!!! #32 20130205 19:01:48
Re: 0.999... = 1? Or not?Thanks John Gabriel
Apart from the word 'false' what you have said is exactly what I have said. Define a number properly and that's what it means to say it exists. I'm completely happy with that. That's why I took the trouble to define 0.9999....... You cannot teach a man anything; you can only help him find it within himself..........Galileo Galilei #33 20130209 02:38:59
Re: 0.999... = 1? Or not?Muxdemux: Of course I only proved (1) for natural numbers  this is all one can do with induction. The problem arises when you take the limit and the inequality results in an absurdity. Last edited by john_gabriel (20130209 02:40:57) #34 20130209 02:48:15
Re: 0.999... = 1? Or not?
It is not designed as a put down or insult. It is a phase that every member went through. When you get to 10 posts you will achieve a new status. 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. #35 20130209 02:56:53
Re: 0.999... = 1? Or not?Well, alright then. But I don't know how much longer I will be around. Sigh,... #36 20130209 03:44:17
Re: 0.999... = 1? Or not?Not so long probably '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 #38 20130211 01:13:22
Re: 0.999... = 1? Or not?You are at 7, now. '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 #39 20130211 03:45:18
Re: 0.999... = 1? Or not?hi Agnishom, You cannot teach a man anything; you can only help him find it within himself..........Galileo Galilei #40 20130211 04:46:19
Re: 0.999... = 1? Or not?Actually, the empty set is a subset of every set, but it is not in every set. 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 #41 20130211 06:20:18
Re: 0.999... = 1? Or not?Expert or Master... I have discovered a truly marvellous signature, which this margin is too narrow to contain. Fermat Give me a lever long enough and a fulcrum on which to place it, and I shall move the world. Archimedes Young man, in mathematics you don't understand things. You just get used to them.  Neumann #42 20130216 23:46:10
Re: 0.999... = 1? Or not?
How? Is it any different? '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 #43 20130217 00:04:55
Re: 0.999... = 1? Or not?When a set is a subset of another set, it means that all elements of the first set are elements of the second set. 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 #44 20130217 03:31:03
Re: 0.999... = 1? Or not?
bobbym is correct.Ii went throught this process a lot.It is not a "insult".It is a correct title. Hey. 