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# /sci/ - Science & Math

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0.999~ ≠ 1

And it never will....

infinitely.

 >> Anonymous Sat Apr 1 20:43:17 2017 No.8797348 True, but I don't know what that tilde is supposed to mean. 0.999..., however, does = 1.
 >> Anonymous Sat Apr 1 20:43:42 2017 No.8797350 >>8797338its all about the last 1
 >> Anonymous Sat Apr 1 21:07:48 2017 No.8797391 File: 132 KB, 960x732, 1446645658580.jpg [View same] [iqdb] [saucenao] [google] [report] >>8797348It's one way to display an unending repeating string. Also no. You will never reach your dream. It is mathematically impossible. Don't try using a glitch in our current system to justify it.
 >> Anonymous Sat Apr 1 21:20:59 2017 No.8797419 >>8797391not a glitch lol
 >> Anonymous Sat Apr 1 21:31:20 2017 No.8797435 >>8797419Is glitch.
 >> Anonymous Sat Apr 1 22:35:47 2017 No.8797534 File: 114 KB, 596x600, 1330032919880.jpg [View same] [iqdb] [saucenao] [google] [report] >Can't grasp interresting mathematical concepts>Get stuck for years debating whether $.\bar{9} = 1$Sad is the life of a brainlet.
 >> Anonymous Sat Apr 1 22:38:29 2017 No.8797540 >>8797338Do you even math, bro?$0.999... = 0.333... \cdot 3 = \frac{1}{3} \cdot 3 = \frac{3}{3} = 1$
 >> Anonymous Sat Apr 1 23:11:29 2017 No.8797594 >>8797540>$0.333... \cdot 3 = \frac{1}{3} \cdot 3$nice circular reasoning
 >> Anonymous Sat Apr 1 23:26:45 2017 No.8797620 >>8797338IntegerWhole numberAlmost only counts with explosions and bowling...
 >> Anonymous Sat Apr 1 23:33:47 2017 No.8797629 >>8797594So you really don't understand math, do you? You apparently don't understand what circular reasoning is.
 >> Anonymous Sat Apr 1 23:51:26 2017 No.8797662 File: 157 KB, 449x624, Picard_with_hair.jpg [View same] [iqdb] [saucenao] [google] [report] So think of 0.999... as a distance and 1 as the destination. No matter what you do, you can never reach that destination. Saying 0.999... = 1 means you cheated and reached out to smack your destination because its utterly right there forever. That doesn't mean you actually reached it if you stuck to the original distance.Think another way, it is literally the exact opposite of the speed of light in that you are virtually frozen in place...moving but never reaching.
 >> Anonymous Sat Apr 1 23:55:59 2017 No.8797665 >>8797662What the fuck are you blathering about? Your metaphor is both terrible and wrong.
 >> Anonymous Sun Apr 2 00:10:07 2017 No.8797682 >>8797665Or just beyond your comprehensionPS: It is.
 >> Anonymous Sun Apr 2 00:13:11 2017 No.8797686 >>8797338Aww shitAll math since Newton BTFO How will limitfucks ever recover?
 >> Anonymous Sun Apr 2 00:13:13 2017 No.8797687 >>8797682No, it's just bad. 0.999... is just a notational variant of 1. Both are completely equal. This can both be shown arithmetically.
 >> Anonymous Sun Apr 2 00:17:48 2017 No.8797691 File: 106 KB, 953x613, 0.999 = 1.jpg [View same] [iqdb] [saucenao] [google] [report]
 >> Anonymous Sun Apr 2 00:18:08 2017 No.8797693 >>8797338Approaches 1 is good enough for me.My emphasis is combinatorics and related shit though, couldn't care less
 >> Anonymous Sun Apr 2 00:38:42 2017 No.8797723 So what's 1 - 0.999... ?
 >> Anonymous Sun Apr 2 00:44:23 2017 No.8797738 >>8797723obviously 0.000...
 >> Anonymous Sun Apr 2 00:59:29 2017 No.8797758 Ok so I have a question. 0.333... equals 0.34, right? And 0.34 * 3 is 1.02. How is this possible?
 >> Anonymous Sun Apr 2 01:00:46 2017 No.8797760 >>8797738That's what I thought. That would make them equal I guess
 >> Anonymous Sun Apr 2 01:17:57 2017 No.8797775 >>8797758>0.333... equals 0.34, right?No it doesn't. That is an approximation.
 >> Anonymous Sun Apr 2 01:26:20 2017 No.8797788 >>8797662>Zeno's paradox.Oh wow.
 >> Anonymous Sun Apr 2 01:27:08 2017 No.8797789 >>8797391>mathematically impossibleThere is no contradiction in 0.999... = 1 but there is in 0.999... + 0.000...1 = 1 for the Real setTry to actually put some effort into learning real maths and stop being a fucking disgusting sensing-type brainlet
 >> Anonymous Sun Apr 2 01:36:50 2017 No.8797811 >>8797789also for two different real numbers to not be equal, there must exist another real number in between those two numbers, but since numbers of the form 0.000...n do not exist in the real number set, there are no real numbers greater than 0.999... AND less than 1
 >> Anonymous Sun Apr 2 07:12:14 2017 No.8798143 >>8797811There are. $\rm 0.aaa..._{11}$ is greater than $0.999..._{10}$.
 >> Anonymous Sun Apr 2 08:01:18 2017 No.8798184 >>8798143they are actually equal
 >> Anonymous Sun Apr 2 19:36:12 2017 No.8799321 >>8797662Ok, so if it's a distance and 1's the destination, what's the error from your distance to destination?ie|0.9999....-1|=?
 >> Anonymous Sun Apr 2 19:40:50 2017 No.8799326 >>8797391"glitches" are real. If our current axioms and definitions imply that 0.999...=1 (which they do), then it is what it is. If you prefer a different set of axioms and definitions where 0.999... =\= 1 then I would be curious to know what they are.
 >> Anonymous Sun Apr 2 19:42:44 2017 No.8799327 >>87977890.000...1 is nonsensical. It implies an infinite chain of zeroes but it has an end? Thats a contradiction. Thiw number cannot exist
 >> Anonymous Sun Apr 2 20:16:44 2017 No.8799391 >>8797338let me explain to all the brainlet why 0.999 =/= 11/3 =/= 0.333why? because you cannot divide 10 by 3 therefore even if you have indefinite amount of 3 following it will not be equal to 1/3. You cannot express 1/3 in base 10.
 >> Anonymous Sun Apr 2 20:18:53 2017 No.8799398 >>8799391You are a mongoloid. Good to see mathematical illiteracy is still widespread today.
 >> Anonymous Sun Apr 2 20:24:03 2017 No.8799410 >>8797338First of all, 0.999... is a rational number since it only consist of a repeating decimal. Thus, it must have a quotient to represent it. Since it can't be directly represented by a quotien, it must be equal to something that can be represented as a quotient.It can be represented as the infinite sum below.>9*(1/10)+9*(1/10)^2+9*(1/10)^3...¨This is the geometric series seen below with a=9 and r=1/10.>ar+ar^2+ar^3+ar^4+ar^5...The solution to this geometric series is seen below, when the summation is done to infinity and |r|<1>ar/(1-r)We insert the given numbers for the representation of 0.999... and get that it is equal to one.>(9*(1/10))/(1-(1/10))=(9/10)/(9/10)=1Even though limits have been used, it can be argued that 0.999...=1 because it has to be equal to something that can be represented as a quotient, because it is by definition a rational number and can't be represented as a quotient in and of itself.
 >> Anonymous Sun Apr 2 20:24:08 2017 No.8799411 >>8799327then how can you have an infinite string of 9's?In ordinal arithmetic there is the concept of "infinity plus one".why can't we imagine infinitely many 0's followed by a 1?
 >> Anonymous Sun Apr 2 20:27:23 2017 No.8799416 >>8799411Because this implies that the series is not infinite, since it has an end after which you place a 1. It makes no sense to talk about an infinite series of 9's with a 1 at the end, since there is precisely no end to the series. A concept like 'infinity plus one' may make sense when for example you are speaking of the cardinality of a set, but it makes none in this context.
 >> Anonymous Sun Apr 2 20:31:54 2017 No.8799426 OP is right. Also, the set of all rationals is greater than the set of all integers.
 >> Anonymous Sun Apr 2 20:32:17 2017 No.8799429 >>8799398>kid who says infinity is a number
 >> Anonymous Sun Apr 2 20:39:00 2017 No.8799440 >>8799429Infinity can be treated as a value. In fact, some infinities are greater than other, for instance $\aleph_0 < \aleph_1$. It baffles my mind that you would discuss the concept of infinity on a message board dedicated to math and science when you don't even seem to know what is taught in a first year math course.
 >> Anonymous Sun Apr 2 20:41:01 2017 No.8799446 >>8799426>the set of all rationals is greater than the set of all integersSometimes b8 is far too obvious.
 >> Anonymous Sun Apr 2 20:54:11 2017 No.8799473 >>8799426And of course, there are only finitely many primes."0.9.. /= 1"ers: Learn about equivalence classes of limits of rational series or about Dedekind cuts. If this is too hard, you might enjoy:https://www.youtube.com/watch?v=PvceKeHl0Sg
 >> Anonymous Sun Apr 2 21:00:27 2017 No.8799484 File: 66 KB, 554x400, 1489000646449.png [View same] [iqdb] [saucenao] [google] [report] easy proof:suppose .99999... and 1 are distinct real numbersnow b/c real numbers are dense you should be able to find some x s.t. .999999... < x < 1no such x exists.99999... and 1 are not distinctthey are equal
 >> Anonymous Sun Apr 2 21:02:26 2017 No.8799488 >>8799484what about 0.999.................10
 >> Anonymous Sun Apr 2 21:07:35 2017 No.8799502 >>8799488Previous comments have addressed this already.>>8799327>>8799416Note that I've advised your caretaker that you are on the internet without supervision again.
 >> Anonymous Sun Apr 2 21:13:21 2017 No.8799521 >>8799440>ye bruh i bright infinity is number>mathematical illiteracyit's like you are saying infinity is a natural or real number, which it is not0.33... is only but an approximation of 1/3
 >> Anonymous Sun Apr 2 21:16:31 2017 No.8799525 >>8799521No. Go back to school.
 >> Anonymous Sun Apr 2 21:17:26 2017 No.8799528 >>8797338Finally! SOMEONE who knows what they're talking about!
 >> Anonymous Sun Apr 2 21:26:29 2017 No.8799554 Suppose you tell me that .9999 is not equal to 1 because it is different by .0001. I will agree, and say that the number actually has another 9, and so is .99999. Then you will say "Aha! It's still off by .00001!" It is clear that this process will continue forever. I think there are arguments for either side:---You could say that no matter how many 9s I add it will never be 1. This is true.---I could say that the difference between .999... and 1 can not be a number greater than 0. This would also be true.I think it comes down to physical interpretation, which is why mathematics was created in the first place. From a physical standpoint, there's no denying that .999....is equal to 1 in every sense of the word equal (and if you have some threshold for how close two numbers must be for you to allow them the adjective "basically equal," that threshold will surely be surpassed).
 >> Anonymous Sun Apr 2 22:20:07 2017 No.8799629 File: 185 KB, 415x578, 1417994822219.png [View same] [iqdb] [saucenao] [google] [report] >>8797691Have you stopped to think that the problem isn't that the original statement is wrong, but that the math used to prove it is wrong is flawed because we don't yet fully understand math? Hence our current understanding tells us something that is in reality impossible?
 >> Anonymous Sun Apr 2 22:33:12 2017 No.8799649 >>8799629>the math used to prove it is wrongMath as such is not something that can be wrong, at least not in the sense you are implying. You can make mathematical errors, but there is no true math as opposed to false math. Mathematics is simply finding conclusions that necessarily follow from a set of axioms. Whichever axioms you choose is entirely up to you. From the axioms we traditionally accept, $0.999... = 1$. You could develop a mathematical system in which this is not the case.
 >> Anonymous Sun Apr 2 22:52:26 2017 No.8799685 File: 477 KB, 500x280, 1336955935818.gif [View same] [iqdb] [saucenao] [google] [report] >>8799649I question that. You may be perfectly correct, but you also may not be. I feel like we are still stuck in the dark ages of our understanding and that math is not as universal as we like to assume.
 >> Anonymous Sun Apr 2 22:58:41 2017 No.8799697 >>8799685I feel like we are still stuck in the dark ages of our understandingwhat makes you think that?
 >> Anonymous Sun Apr 2 23:04:11 2017 No.8799716 >>8799697This simple equation and the fact that people think it is wrong because of our current evolution of math that can claim otherwise...>0.999... ≠ 1
 >> Anonymous Mon Apr 3 00:14:09 2017 No.8799861 let x = .999...therefore 10x = 9.999...10x - x = 9.999... - .999...9x=9x=1therefore .999...=1where did i make a mistake?
 >> Anonymous Mon Apr 3 00:30:47 2017 No.8799889 >>8799327that's what I'm saying
 >> Anonymous Mon Apr 3 00:49:05 2017 No.8799906 >>8799889The real question is$0.000... = 0$
 >> Anonymous Mon Apr 3 00:52:28 2017 No.8799910 >>8797338ITT OP is a brainlet and can't accept a fact with countless proofssaved you guys some time
 >> Anonymous Mon Apr 3 04:44:31 2017 No.8800198 >>8797540>>8797691>An open set is the same thing as a closed set!
 >> Anonymous Mon Apr 3 04:57:40 2017 No.8800215 >>8797338>computers using floating points to approximate decimals: .999~ = 1>EEs modelling electrical wave forms in real life: pi = 1>Astrophysicist measuring the energy of a blackhole jet: 100=1heh, I laugh at your analysis and pure math. (as a math grad I understand your pain but do not share it cuz physics>math imo)
 >> Anonymous Mon Apr 3 04:58:28 2017 No.8800216 If .999 = 1 why don't they just write 1?check and mate
 >> Anonymous Mon Apr 3 05:21:29 2017 No.8800243 >>8797338The problem is that the so called "Reals" aren't real, which means any arithmetic or math done with them is pointless and retarded.
 >> Anonymous Mon Apr 3 09:16:44 2017 No.8800456 File: 6 KB, 225x225, kek.jpg [View same] [iqdb] [saucenao] [google] [report] >>8800198$0.333...$ and $\frac{1}{3}$ are not sets dummy.
 >> Anonymous Mon Apr 3 09:24:51 2017 No.8800466 >>8797338Assume 0.9999... != 1OP is a faggotContradiction, therefore 0.9999...=1QED
 >> Anonymous Mon Apr 3 09:56:12 2017 No.8800496 >>8800456>he doesn't understand limit theory
 >> Anonymous Mon Apr 3 10:20:15 2017 No.8800534 >>8797338Weird how that works
 >> Anonymous Mon Apr 3 11:05:10 2017 No.8800601 >>8800496>he misapplies limit theory.
 >> Anonymous Mon Apr 3 11:17:21 2017 No.8800623 No further proof for existence of infinity needs to be made other than existence of one.
 >> Anonymous Mon Apr 3 11:34:34 2017 No.8800647 >>8797338The limit as the number of digits approaches infinity is equal to one. By definition. That's what limits are for.
 >> Anonymous Mon Apr 3 13:43:28 2017 No.8800900 >>8797338.333... equals 1/3.666... equals 2/3.999... equals 3/3
 >> Anonymous Mon Apr 3 13:47:42 2017 No.8800906 >>8799697If the sum of all positive integers equals -1/12 then math must be somehow broken
 >> Anonymous Mon Apr 3 14:08:39 2017 No.8800951 But dude they're different numbers
 >> Anonymous Mon Apr 3 14:18:48 2017 No.8800976 >>8800906Or you don't understand mathematics.
 >> Anonymous Mon Apr 3 14:26:30 2017 No.8800997 >>8797691Thank you.
 >> Anonymous Mon Apr 3 14:27:33 2017 No.8801002 >>8799484This.
 >> Anonymous Mon Apr 3 14:50:25 2017 No.8801040 >>8797338irreverent
 >> Anonymous Mon Apr 3 16:25:31 2017 No.8801260 Just saying: Hyperreals work, and 0.999... can be seen as shorthand for 1 - ε, which isn't 1.
 >> Anonymous Mon Apr 3 16:33:37 2017 No.8801285 >>8799554>physical interpretation>why mathematics was created in the first placeThis is why schools should have history of mathematics as a required class.
 >> Anonymous Mon Apr 3 19:45:43 2017 No.8801683 >>8801260>working with hyperreals>ever
 >> Anonymous Mon Apr 3 22:22:24 2017 No.8801937 >>8800601>he doesn't understand .99999.... =/= 1 isn't an integral part of limit theory for open sets
 >> Anonymous Tue Apr 4 02:25:44 2017 No.8802363 Why does rounding infinitely long numbers blow everyones mindsWe do the same thing with pi and i never see people bitching about it
 >> Anonymous Tue Apr 4 02:38:46 2017 No.8802395 >>8802363Because this one is not about rounding, it is _literally_ the same.>>8801260There are several non-standard analysis concepts, but come on, Hyperreals, Surreals, etc. are barely ever used.
 >> Anonymous Tue Apr 4 02:45:19 2017 No.8802412 >>8802395its close enough to 1 that nobody gives a shit about the infinitesimally small bit at the end so we just call them the same
 >> Anonymous Tue Apr 4 02:46:22 2017 No.8802415 >>8802395lier
 >> Anonymous Tue Apr 4 02:49:03 2017 No.8802422 >>8800906But this isn't actually true in the sense of the word sum that you knowAll of these misunderstandings, whether it's the -1/12 meme or the 0.999 =/= 1 meme or a billion other things is just people applying their grade school level of understanding to concepts that are addressed by real math.
 >> Anonymous Tue Apr 4 09:44:05 2017 No.8802952 >>8802412>its close enough to 1 that nobody gives a shit about the infinitesimally small bit at the end so we just call them the sameNo, it is just one. That's how the real numbers work.
 >> Anonymous Tue Apr 4 15:05:08 2017 No.8803624 >>87973911/3 = 0.3 recurring2/3 = 0.6 recurring3/3 = 0.9 recurring = 1sorry
 >> Anonymous Tue Apr 4 15:06:34 2017 No.8803626 >>8799629sounds like you don't "fully understand" basic fractions and decimals mate
 >> Anonymous Tue Apr 4 15:29:57 2017 No.8803677 >>8797338for what purpose? 0.9~ is equal to 1.0 for 98% of practical uses.
 >> Anonymous Tue Apr 4 16:45:37 2017 No.8803879 >>87973380.999... + 0.0...1 = 10.0...1 = 00.999... + 0 = 10.999... = 1
 >> Anonymous Tue Apr 4 17:22:48 2017 No.8803969 >>8797338A simple proof:$X = 0.\bar{9}10X = 9.\bar{9}10X - X = 9.\{bar} - 0.\bar{9} = 9\10X - X = 9XX = 1$
 >> Anonymous Tue Apr 4 17:30:24 2017 No.8803995 >>8797338$$X = 0.\bar{9}$$$$10X = 9.\bar{9}$$$$10X - X = 9.\{bar} - 0.\bar{9} = 9$$$$10X - X = 9X$$$$X = 1$$
 >> Anonymous Tue Apr 4 17:32:21 2017 No.8804001 >>8797338Easy: not formating apparentlyX = 0.99910X = 9.99910X - X = 9.999 - 0.999 = 910X - X = 9XX = 1
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