[ 3 / biz / cgl / ck / diy / fa / g / ic / jp / lit / sci / tg / vr / vt ] [ index / top / reports / report a bug ] [ 4plebs / archived.moe / rbt ]

/vt/ is now archived.Become a Patron!

# /sci/ - Science & Math

[ Toggle deleted replies ]
File: 157 KB, 689x659, 1487564367062.jpg [View same] [iqdb] [saucenao] [google] [report]

Is 0.9999999...=1?

 >> Anonymous Mon Feb 20 03:22:49 2017 No.8688742 yes
 >> Anonymous Mon Feb 20 03:23:34 2017 No.8688743 No
 >> Anonymous Mon Feb 20 03:25:00 2017 No.8688744 maybe
 >> Anonymous Mon Feb 20 03:26:44 2017 No.8688745 i dont know
 >> Anonymous Mon Feb 20 03:27:17 2017 No.8688746 If you want
 >> Anonymous Mon Feb 20 03:48:47 2017 No.8688766 Sometimes
 >> Anonymous Mon Feb 20 04:03:21 2017 No.8688785 It's plausible
 >> Anonymous Mon Feb 20 04:35:35 2017 No.8688825 >>8688734Define how much smaller than 1 it is.
 >> Anonymous Mon Feb 20 04:53:58 2017 No.8688851 >>8688825an infinitesimal
 >> Anonymous Mon Feb 20 05:00:00 2017 No.8688858 >>8688734Yes.
 >> Anonymous Mon Feb 20 05:02:48 2017 No.8688863 >>8688734Yes it is
 >> Anonymous Mon Feb 20 05:04:38 2017 No.8688865 >>8688734suck my dick you retarded troll, nobump btw
 >> Anonymous Mon Feb 20 05:08:40 2017 No.8688870 >>8688734Depends. Is 0.9999999... = 0.999...999 ?
 >> Anonymous Mon Feb 20 05:13:49 2017 No.8688873 >>8688742>>8688743>>8688744>>8688745>not followed by "can you repeat the question"0/10
 >> Anonymous Mon Feb 20 05:26:08 2017 No.8688879 >>86887340.99999999...=x9.99999999...=10x9=9x1=xThus, 1=0.99999...You could also define the sum of 9/(10^n) for n=1 to infinity, and then prove that that sum converges towards 1
 >> Anonymous Mon Feb 20 06:04:31 2017 No.8688904 Is 0.999.... + 0.000...1 = 1 or = 1.000...1
 >> Anonymous Mon Feb 20 06:06:56 2017 No.8688907 Is a banana an apple? No, it's a banana
 >> Anonymous Mon Feb 20 06:24:58 2017 No.8688917 >>8688879Is is a shipost? How do you get from 9.9999... = 10x to 9 = 9x.Looks like youre preupposing.0.9999... = 1.
 >> Anonymous Mon Feb 20 06:31:19 2017 No.8688922 >>8688917subtract x from both sides dipshit
 >> Anonymous Mon Feb 20 06:32:55 2017 No.8688925 >>86889170.9999999999..... = x9.9999999999..... = 10x9.9999999999..... - 0.99999999... = 10x - x9 = 9x
 >> Anonymous Mon Feb 20 06:45:28 2017 No.8688938 >>8688734Whoever made this picture is a fucking retard. Making a Nazi themed pic and cba to even look up how the fuck to write Sieg Heil properly? sad af senpai
 >> Anonymous Mon Feb 20 06:47:58 2017 No.8688939 Of course not you stupid asshole. Its just so close that |1 - .99999...| < e for any e > 0.
 >> Anonymous Mon Feb 20 06:50:14 2017 No.8688945 >>86889229.9999... ( - 0.9999...) != 10.9999.... ( - 0.9999...)9 != 10 Are you usually this autistic or is it just this once?
 >> Anonymous Mon Feb 20 06:52:30 2017 No.8688946 >>86889259.9999... - 0.9999... = 910.9999... - 0.9999... = 109 != 10
 >> Anonymous Mon Feb 20 06:53:09 2017 No.8688949 >>8688945Why are you posting on /sci/ if you don't know how to do arithmetic?
 >> Anonymous Mon Feb 20 06:59:40 2017 No.8688962 >>86889251.1 = x11 = 10x11 - 0.1 = 10x - x11 = 11x1.1 = 1Am I shitposting yet?
 >> Anonymous Mon Feb 20 07:02:23 2017 No.8688969 >>8688962yup
 >> Anonymous Mon Feb 20 07:06:42 2017 No.8688978 >>86889499 == 10?
 >> Anonymous Mon Feb 20 07:09:25 2017 No.8688982 >>8688978At one point you replaced 10x with 10.9999...See the problem?
 >> Anonymous Mon Feb 20 07:15:10 2017 No.8688991 >>8688982But 10x - x != 9, 10x - x = 10
 >> Anonymous Mon Feb 20 07:23:56 2017 No.8689003 >>8688991dude.10x does not mean "ten plus x" it means "ten times x".So if you got 10 x and take one x away, you are left with 9 x.>>>/b/sqt
 >> Anonymous Mon Feb 20 07:29:07 2017 No.8689013 $\displaystyle1 = \frac {3}{3} = 3 \cdot \frac {1}{3} = 3 \cdot 0.333... = 0.999...$
 >> Anonymous Mon Feb 20 07:56:15 2017 No.8689045 >>8688907But what if you have an infinitely long banana. It could turn into an apple after awhile
 >> Anonymous Mon Feb 20 08:51:02 2017 No.8689101 The fact that these threads still get responses from people believing that so many posters here would actually be that stupid amuses me.Just stop responding to obvious shitposting and read some better threads.
 >> Anonymous Mon Feb 20 12:54:07 2017 No.8689477 >>8688734If by 0.999999... you mean 3*1/3 yesIf you mean the summation to infinity of 9*10^-k starting from k = 1 no>It's equivalent!No, limit doesn't mean it's equal, means it get closer and closer
 >> Anonymous Mon Feb 20 12:58:27 2017 No.8689487 >>8689013But 1/3 != 0.333...It's only an approximation.
 >> Anonymous Mon Feb 20 13:01:59 2017 No.8689494 >>8688991>10x - x = 10kek is this bait?or are you an engineer?
 >> Anonymous Mon Feb 20 13:04:06 2017 No.8689498 >>8688734No, think about it.If 0.99999... = 1 then lets try to go deeper down the rabbit hole.Think about it. What is the number0.89999999999999...Wouldn't it just be0.999....so it is also 1?Now lets go even deeper1 = 0.9... = 0.89... = 0.889... = 0.8889... But then we can repeat this process forever so =0.888888...So now 1 = 0.888888... ????????Really makes me think why retards think 1 = 0.99... when it is so obviously fallacious.
 >> Anonymous Mon Feb 20 13:07:01 2017 No.8689501 >>8689498$0.8999... = 0.999... - 0.1 \\= 1 - 0.1 \\= 0.9$
 >> Anonymous Mon Feb 20 13:11:56 2017 No.8689511 >>8689501No, you stupid. lets follow your amazing logic again.0.9999... - 0.1.... = 0.99999... - 0.9..... (because 1 = 0.999... SUPPOSEDLY) = 0Amazing. Tell me, at which state university did you get your degree in mathematics?
 >> Anonymous Mon Feb 20 13:14:14 2017 No.8689513 >>8689511$0.999... - 0.1 = 0.999... - 0.0999... = 1 - 0.1$Stop embarrassing yourself
 >> Anonymous Mon Feb 20 13:16:46 2017 No.8689516 >>8689513The reason you are getting that error is because you are unknowingly doing an infinite number of computations when in reality you can never do that.Uh... have you taken analysis!
 >> Anonymous Mon Feb 20 13:18:40 2017 No.8689519 >>8688734This has to just be a criticism of the number system. 0.99999... is 0.0000...;...0001 smaller than 1. Should every time x is solved for, you write eg. x = 6, 5.9999...? No, of course not. Those are two separate values. Unless if theres some magic nth number hidden at the end of base 10 between 9 and 0 that forces infinitly repeating decimals to always round up we have a problem here. There is something fundementally flawed here and it should be dealt with.
 >> Anonymous Mon Feb 20 13:23:03 2017 No.8689526 $\frac{1}{9} = 0.111... \\\frac{3}{9} = 0.333... \\\frac{7}{9} = 0.777... \\\frac{9}{9} = 0.999...$What else does $\frac{9}{9}$ equal to? That's right, 1 (one).Actual proof by another anon here: >>8688879
 >> Anonymous Mon Feb 20 13:24:14 2017 No.8689531 >>8689516(Not that guy)>Uh... have you taken analysis!You, clearly, have not, for >>8689513 is exactly right.
 >> Anonymous Mon Feb 20 13:33:30 2017 No.8689549 >>8689531Yeah yeah. Crazy people always think they are right.I think you should go back to introductory analysis to see where your mistake is.
 >> Anonymous Mon Feb 20 13:40:55 2017 No.8689560 >>8689549>Yeah yeah. Crazy people always think they are right.Evidently.
 >> Anonymous Mon Feb 20 13:43:22 2017 No.8689563 >>8689560>Evidently.Indeed.
 >> Anonymous Mon Feb 20 13:48:24 2017 No.8689569 >>8688879this is an extremely dumb proof desu. You can't multiply an infinite number by 10 and expect the maths to work out. By multiplying you're implicitly removing a digit somewhere down the line so 9.99999... isn't the same number of 9's as .99999... according to someone who believes .999... =/= 1.The only proof that makes sense without begging the question is by proving there is no number between the two values and thus that they are essentially the same value. Everything else can be explained away as simply math tricks.
 >> Anonymous Mon Feb 20 13:51:51 2017 No.8689573 File: 1.52 MB, 723x904, 1486677392831.png [View same] [iqdb] [saucenao] [google] [report] >>8689519>Should every time x is solved for, you write eg. x = 6, 5.9999...?Well, you CAN write it that way and it would still be true, but why would you do that?
 >> Anonymous Mon Feb 20 13:54:02 2017 No.8689576 >>8689569>Everything else can be explained away as simply math tricks.All of mathematics can be explained away as simply math tricks if you are looking for an excuse to disregard an argument you don't understand. That doesn't make it wrong.
 >> Anonymous Mon Feb 20 13:54:16 2017 No.8689578 >>8689569>9.99999... isn't the same number of 9's as .99999...Yes it is. Infinity + 1 = Infinity.Infinity + Infinity = InfinityIt's always the same quantity of 9's.
 >> Anonymous Mon Feb 20 13:55:52 2017 No.8689580 >>8689569Yep, this all breaks down to believing that infinitely large hotels are good analogies.https://en.wikipedia.org/wiki/Hilbert's_paradox_of_the_Grand_Hotel
 >> Anonymous Mon Feb 20 13:56:10 2017 No.8689581 File: 527 KB, 1000x666, 1486671397754.jpg [View same] [iqdb] [saucenao] [google] [report] >>8689569>By multiplying you're implicitly removing a digit somewhere down the lineHAHAHAHAHAHAHAHAHHAHAHAHHAHAHAHAHHAHAHAHAHAHHAHAHAHHAHAHAHAHAHHAHAHAAHHAAHAHAHAHHAHAHA desu
 >> Anonymous Mon Feb 20 13:59:01 2017 No.8689585 >>8688734sure you can manipulate the math to get .999...=1 but it doesn't make it true.Nothing is perfect, including math
 >> Anonymous Mon Feb 20 14:01:41 2017 No.8689589 File: 69 KB, 604x453, 1484272177281.jpg [View same] [iqdb] [saucenao] [google] [report] >>8689585>sure you can prove it>but that doesn't make it true
 >> Anonymous Mon Feb 20 14:02:17 2017 No.8689591 >>8689578I'm not saying 1 doesn't equal .9999... I'm saying if you already believe that it doesn't then this isn't a sufficient proof to change someone's mind. (1 - some infinitesimal) = x10 - 10(infinitesimal) = 10x10 - 10(infinitesimal) - (1 - infinitesimal) = 10x - x9x = 9 - 9(infinitesimal)x = 1 - infinitesimal, back to where you startedwhat you should be proving is that an infinitesimal value of .00000000...1 doesn't exist not using algebra tricks to sidestep the question
 >> Anonymous Mon Feb 20 14:04:07 2017 No.8689596 >>86889622nd line to 3rd line is wrongYou subtract .1 from left side and x from the right. And x = 1.1 not .1
 >> Anonymous Mon Feb 20 14:05:48 2017 No.8689601 >>8689591>what you should be proving is that an infinitesimal value of .00000000...1 doesn't existWell, it's pretty obvious that it doesn't exist. You are putting an end to an infinite series, making it finite.
 >> Anonymous Mon Feb 20 14:08:44 2017 No.8689604 >>8688734AHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHH AHHHHHHHHHHHHHHHHHHH AHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHAHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHH
 >> Anonymous Mon Feb 20 14:08:45 2017 No.8689605
 >> Anonymous Mon Feb 20 14:11:43 2017 No.8689615 File: 194 KB, 600x550, 1460295987964.png [View same] [iqdb] [saucenao] [google] [report] $\frac{1}{3} = 0.333... \\\frac{1}{3} + \frac{1}{3} + \frac{1}{3} = 0.333... + 0.333... + 0.333... = 0.999... \\\frac{1}{3} + \frac{1}{3} \frac{1}{3} = 1 \\0.999... = 1$
 >> Anonymous Mon Feb 20 15:20:37 2017 No.8689742 >>8688734.999... = Reality1 (reaching 1 from zero) = Fantasy, imagination, simulation, virtual environment.Seriously sci, if a 0x0x0 singularity blew up by expanding by the smallest unit of distance ("infinitely" small), it would take "infinity" to get to one unit (we're not there yet). Are all of you anti-Zeno? Did you hear of paradoxes, and specifically Zeno's paradox?I'd say it's "effectively" (as if) equal but it'd be better to calculate it, if possible, as 1. The inequality--exactly--is the difference presented above.
 >> Anonymous Mon Feb 20 15:39:46 2017 No.8689771 You retards give me one """"proof"""" of this bullshit that doesn't rely on fallacious decimal approximations of fractions and I'll stop laughing at you.
 >> Anonymous Mon Feb 20 15:50:37 2017 No.8689802 >>8689771>fallacious decimal approximations of fractionsexplain why that is true.
 >> Anonymous Mon Feb 20 15:58:33 2017 No.8689824 >>8689771What is the actual decimal form of 1/9 then?
 >> Anonymous Mon Feb 20 15:58:52 2017 No.8689826 0.999... is not even a numberliterally kill yourself
 >> Anonymous Mon Feb 20 16:00:31 2017 No.8689834 >>8689802>>8689824'converges to' is not the same as 'equal to'
 >> Anonymous Mon Feb 20 16:07:02 2017 No.8689855 >>8689826>pi isn't a number>1/3 isn't a number>you are not a faggot
 >> Anonymous Mon Feb 20 16:08:46 2017 No.8689862 >>8689834Then, can you mathematically prove that .999... isn't equal to 1?
 >> Anonymous Mon Feb 20 16:12:54 2017 No.8689879 >>8689855you're basically too stupid to deserve a (You) but really thanks for the laugh
 >> Anonymous Mon Feb 20 16:15:54 2017 No.8689888 File: 236 KB, 200x200, 1484164721947.gif [View same] [iqdb] [saucenao] [google] [report] >>8689879Thank you for proving my point anon.
 >> Anonymous Mon Feb 20 16:16:51 2017 No.8689895 How can .9999... equal both .99999... and 1 at the same time? It's one or the other, you can't have both
 >> Anonymous Mon Feb 20 16:19:25 2017 No.8689904 >>8689834But "converges to in the limit" is.
 >> Anonymous Mon Feb 20 16:19:28 2017 No.8689906 >>8689895>How can 0 equal both 0 and -0 at the same time? It's one or the other, you can't have both
 >> Anonymous Mon Feb 20 16:19:30 2017 No.8689908 >>8689895$how can \frac{2}{4} equal both \frac{1}{2} and 0.5 at the same time?$
 >> Anonymous Mon Feb 20 16:20:28 2017 No.8689911 >>8688745can you repeat the question
 >> Anonymous Mon Feb 20 19:13:53 2017 No.8690399 >>8689895Welp guess you can't be both a man and straight then, pick one faggot, are you a girl or a homo?
 >> Anonymous Mon Feb 20 19:16:51 2017 No.8690403 >>8688925but that would equal 9=9.111111111xREFUTED
 >> Pepe Mon Feb 20 19:49:32 2017 No.8690463 >>86887341= 0.9 +0.11 (1/1) = 1 (1/3)- 0 (2/3)
 >> Anonymous Tue Feb 21 07:32:28 2017 No.8691411 Real numbers x and y are the same iff there are no rational numbers between them, as per the Dedekind construction of the reals.
 >> Anonymous Tue Feb 21 11:09:37 2017 No.8691709 File: 288 KB, 1399x953, d850a31588a50ca1552ff691213af673.jpg [View same] [iqdb] [saucenao] [google] [report]
 >> Anonymous Tue Feb 21 11:11:29 2017 No.8691714 File: 1.57 MB, 2688x1520, IMAG0864.jpg [View same] [iqdb] [saucenao] [google] [report] How to finish?
 >> Anonymous Tue Feb 21 11:14:04 2017 No.8691720 >>8688734YesT. Engineer
 >> Anonymous Tue Feb 21 11:52:03 2017 No.8691798 >>8689895what are you doing on /sci/ TJ """""Henry""""" Yoshi
 >> Anonymous Tue Feb 21 11:58:00 2017 No.8691810 >>8690403how is 0.999... - 0.999... = 0.111... ?
 >> Anonymous Tue Feb 21 12:08:31 2017 No.8691823 File: 112 KB, 953x613, 0.999equals1.jpg [View same] [iqdb] [saucenao] [google] [report]
 >> Anonymous Tue Feb 21 14:00:05 2017 No.8692058 >>8691823>non of these mentions the definition of real numbers which make it obvious beyond a sliver of a doubt that 0.99999...=1.
 >> Anonymous Tue Feb 21 14:11:39 2017 No.8692082 >>8688734depends for what you need it.
 >> Anonymous Tue Feb 21 14:54:11 2017 No.8692166 >>8688734No. There is an infinitely small number's difference between N and 1.There are two infinities to think about here and they logically progress alongside eachother if we think about it where N's number of digits = RN's number of digits then we have thisAt any definable set of digits within theinfinite set we see that N and RN's value is equal to 1. 0.999 + 0.001 = 1This is the case at every single number of digits, as we are dealing with two infinite numbers which share the same sum. So the infinite number, N and the infinite number RN sum to 1.N - RN != N
 >> Anonymous Tue Feb 21 14:55:51 2017 No.8692171   >>8692166N - RN would have to be true in order for N = 1
 >> Anonymous Tue Feb 21 14:59:50 2017 No.8692180 >>8692166N - RN = N would have to be true for N to be 1. But RN is not 0.
 >> Anonymous Tue Feb 21 21:24:28 2017 No.8692986 >>8688734>Is 0.9999999...=1?No, the left side is equivalent to 1 - εYour task (should you choose to accept it) is to find the value of ε
 >> Anonymous Tue Feb 21 22:13:09 2017 No.8693085 File: 68 KB, 1280x665, 2015-03-29_21.14.38.jpg [View same] [iqdb] [saucenao] [google] [report] >>86887340.99... = 0.33... X 0.33...0.33... = 1/31/3 X 3 = 1Simple conversion
 >> Anonymous Tue Feb 21 22:17:23 2017 No.8693090 >>8689585>sure you can use math correctly to get unfalsifiable numbers>that doesn't make it true
 >> Anonymous Wed Feb 22 00:11:17 2017 No.8693255 >>8688734Almost
 >> Anonymous Wed Feb 22 01:24:28 2017 No.8693335 >>8688734replace = with ≈ and it is true, however in terms of a floating point 1 > 0.9999999....
 >> Anonymous Wed Feb 22 01:38:39 2017 No.8693346 >>86887340.9999999... = 1.1111111...
 >> Anonymous Wed Feb 22 01:40:56 2017 No.8693347 >>86894980.8999...=0.9>>8689477What does "closer and closer" mean to you. You think infinite iterations means it can't be done? If you start with 0.9, "add" another 9 in the next second and keep adding 9s, each iteration halving the time it takes you to add a 9, you'll have infinite iterations within 2 seconds.>>8689596And 3rd to 4th. As he said, he's shitposting
 >> Anonymous Wed Feb 22 01:44:46 2017 No.8693353 >>8689578>Infinity + 1 = Infinity.>Infinity + Infinity = Infinityboth of these statements are false. you cannot perform arithmetic with infinity as doing so implies it is a bounded number. same with the repeating decimals.
 >> Anonymous Wed Feb 22 02:47:03 2017 No.8693392 >>8688870The 9's at the end are arbitrary because there is an infinite amount of 9's before you get to the last three. So yes, they are the same thing.
 >> Anonymous Wed Feb 22 03:10:40 2017 No.8693407 >>8692166Please read through a definition of real numbers.1=0.9999.... is true by definition, as the differnece between the cauchy series $x_n=1$ and $y_n=\sum_{i=1}^n{9*\frac{1}{10^i}}$ tends (obviously) to zero, which is the definition for 2 real numbers equalling eachother.
 >> Anonymous Wed Feb 22 05:29:08 2017 No.8693472 >>8693407>inb4 some retard saying "hurrr TENDS to 0, but is never actually 0">>8693392They are not the sane thing because the first form is a valid form of a number, the other is not. There is no "end", it's infinitely long
 >> Anonymous Wed Feb 22 05:44:54 2017 No.8693487 You'd think it would be enough to just explain that zero is by definition an infinitely small number, but nooo.
 >> Anonymous Wed Feb 22 19:38:51 2017 No.8695426 >>8693085What did I just read.> 0.33... • 0.33... = 0.99...You're joking, right?Right?
 >> Anonymous Wed Feb 22 19:42:21 2017 No.8695447 >>8688734YOU HAVE TO SAY THAT THE 0.00...1 DOES NOT EXIST.Stop.Please.
 >> Anonymous Wed Feb 22 19:46:25 2017 No.8695469 Haven't read the thread, so someone might have already given this example> 1/3 = 0.333..> 1/3 + 1/3 + 1/3 = 1> 0.333.. + 0.333... + 0.333.. = 0.999..> 0.999.. = 1This is my favourite and comfiest proof
 >> Anonymous Wed Feb 22 19:53:48 2017 No.8695497 >>8692986this is the best explanation for methat number ε is 0.000...so 1-0=1
 >> Anonymous Wed Feb 22 20:01:37 2017 No.8695520 File: 2 KB, 153x77, Untitled.png [View same] [iqdb] [saucenao] [google] [report] You niggers should be able to solve this.
>>