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# /sci/ - Science & Math

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Okay so this is bugging me
1 ÷ 3 = .333- (one third)
But
.333- × 3 = .999

3/3rds is less than one according to our math?

 >> Anonymous Wed Sep 18 00:32:58 2019 No.10982191 >>10982184.999(infinite 9) = 1
 >> Anonymous Wed Sep 18 00:45:56 2019 No.10982219 >>10982184Lmao, you should work on your bait quality
 >> Anonymous Wed Sep 18 00:47:29 2019 No.10982222 >>10982184Metric bullcrap
 >> Anonymous Wed Sep 18 00:49:43 2019 No.10982227 >>10982184Here you go senpai:$\sum_{k=1}^{\infty} 9(1/10)^k = \frac{0.9}{1-0.1}\\\sum_{k=1}^{\infty} 9(1/10)^k = \frac{0.9}{0.9}\\\sum_{k=1}^{\infty} 9(1/10)^k = 1\\0.9+0.09+0.009+... = 1\\\therefore 0.999... = 1$
 >> Anonymous Wed Sep 18 02:35:33 2019 No.10982393 >>10982184".99999..." and "1" are two notational representations of the same number under the standard construction of the reals
 >> Anonymous Wed Sep 18 03:29:38 2019 No.10982430 >>10982393So you believe that If a number has nothing between it and another number then it's the same number? Seems like special pleading.
 >> Anonymous Wed Sep 18 03:48:27 2019 No.10982453   No. .999... is not one. If it were, line AZ and BZ would have the same slope, (paralel) yet somehow converge at Z.
 >> Anonymous Wed Sep 18 03:49:04 2019 No.10982455 File: 6 KB, 618x175, SlopeProof 999.png [View same] [iqdb] [saucenao] [google] [report] >>10982184No. .999... is not one. If it were, line AZ and BZ would have the same slope, (paralel) yet somehow converge at Z.
 >> Anonymous Wed Sep 18 03:54:12 2019 No.10982466   >>10982455I reject your hypothesis
 >> Anonymous Wed Sep 18 04:12:57 2019 No.10982481 >>10982430He's just telling it like it is.
 >> Anonymous Wed Sep 18 04:16:06 2019 No.10982486 File: 2 KB, 203x191, hypotenuse length.png [View same] [iqdb] [saucenao] [google] [report] >>10982455geometric proofs are notoriously weak when dealing with infinity:distance =/= lengthhypotenuse length, $n \rightarrow \infty$a+b or $\sqrt{a^{2}+b^{2}}$ ?
 >> Anonymous Wed Sep 18 06:05:32 2019 No.10982618 File: 48 KB, 350x494, Pi = 4 proof.png [View same] [iqdb] [saucenao] [google] [report] >>10982486That is kind of the same as this. They are good examples of why you can't assume that a process taken to infinity equals it's limit. A staircase with infinitely many steps of infinitely small size is not a line. A polygon with infinitely many right angles is not a circle. A number with infinitely many trailing nines is not the next digit up.
 >> Anonymous Wed Sep 18 06:39:38 2019 No.10982658 >>10982455is this a wildburger thing? never saw someone try so hard at being wrong
 >> Anonymous Wed Sep 18 07:04:11 2019 No.10982695 >>10982658Insults = I can't find anything wrong with your logic.
 >> Anonymous Wed Sep 18 07:08:14 2019 No.10982697 >>10982695no i'm not trying to use an insult, "wildburger" is a reference to N J Wildberger, not an amerifat thing
 >> Anonymous Wed Sep 18 07:43:30 2019 No.10982725 >>10982184As the decimal place approaches infinity the difference between .999999999 and 1 becomes so infinitesimally small that .9999999 = 1
 >> Anonymous Wed Sep 18 08:05:32 2019 No.10982754 >>10982184.999... = 1brainlet
 >> Anonymous Wed Sep 18 08:17:16 2019 No.10982769 >>10982618>They are good examples of why you can't assume that a process taken to infinity equals it's limit.It is, you don't understand what a limit is.
 >> Anonymous Wed Sep 18 11:57:12 2019 No.10983056 >>10982769>It is, you don't understand what a limit is.> Doesn't bother to try to explain anything.These discussions turn into religion really quickly. If a number with infinite digits is a valid construct, then why isn't a staircase with infinite steps?
 >> Anonymous Wed Sep 18 12:38:26 2019 No.10983123 >>10983056>turn into religion really quickly. Ifgoogle it, wikipedia it - no-one here is your mommy
 >> Anonymous Wed Sep 18 12:43:37 2019 No.10983136 >>10982430That's literally true, calling it "special pleading" doesn't mean anything.
 >> Anonymous Wed Sep 18 12:47:18 2019 No.10983141 >>10982430You're just saying that if x-y=0 then x=y, which is trivially true.
 >> Anonymous Wed Sep 18 12:47:23 2019 No.10983142 >>10983136So if there is nothing between A and B, then A and B are the same letter?
 >> Anonymous Wed Sep 18 12:48:50 2019 No.10983149 >>10983142in R they are
 >> Anonymous Wed Sep 18 12:53:47 2019 No.10983161 >>10983123>I'm right, you're wrong. Google it, because I'm too lazy to defend myself.
 >> Anonymous Wed Sep 18 13:17:49 2019 No.10983218 1/3 = 1/31/3 X 3 = 3/3 = 1Decimals are fractions to the tenth power.Everything I just typed is made up scribbles. This is why maths cant prove anything and is a great example. Could give a shit less about your "model" unless it provides more insights into a persuasive argument for a theory. But if the persuasive argument is squigglie math proofs fuck right off.
 >> Anonymous Wed Sep 18 13:23:59 2019 No.10983239 >>10983056>then why isn't a staircase with infinite steps?It does not converge to a line. All you have to do is look at the definition a limit.
 >> Anonymous Wed Sep 18 13:27:20 2019 No.10983246 > but muh .9's X infinity = 1This is also retarded. 1 X infinity = Infinity.9 X infinity means it can continue to be divided infinitely. Its a shitty system and maths is fucken gay
 >> Anonymous Wed Sep 18 13:59:21 2019 No.10983325 >>10983161ur not worth it
 >> Anonymous Wed Sep 18 14:01:14 2019 No.10983329 >>10983246x*inf=inf
 >> Anonymous Wed Sep 18 14:02:23 2019 No.10983338 >>10983325This dude has been checking this thread for over an hour just to say, "google it" and "you're not worth it"kewl
 >> Anonymous Wed Sep 18 16:05:47 2019 No.10983628 >>10983142>what is a discrete spacebrainlet.jpeg
 >> Anonymous Wed Sep 18 16:06:49 2019 No.10983630 >>10983246Nah you're just dumb
 >> Anonymous Thu Sep 19 03:05:19 2019 No.10985149 >>10982430I don't "believe" anything about the statement I made. It's a definite, provable fact about the standard construction of the reals and how that relates to our symbolic language for notating elements of the reals.
 >> Anonymous Thu Sep 19 03:26:30 2019 No.10985176 1/3 isn't equal to 0.333, 0.333 with the repeater symbol is an approximation of one third.This is because you are in a reality where infinity is not defined, it's outside the dimension we inhabit.So for example I can type 0.333..., or 0.333333333..., or with a million 3s, but I can't type infinite threes, so we use the symbol 1/3, or an approximation 0.333,3 X 1/3 =1. 3 X 0.3333.. does not equal 1.
 >> Anonymous Thu Sep 19 03:42:06 2019 No.10985190 >>10985176>infinity is not definedwew ladDefinition:An unbounded quantity that is greater than every real number.
 >> Anonymous Thu Sep 19 03:43:46 2019 No.10985191 >>109851761/3 = 3/10 + 1/30= 0.3 + 1/30= 0.33 + 1/300= 0.333 + 1/3000:= 0.3... + 1/inf = 0.3... + 0 = 0.3...
 >> Anonymous Thu Sep 19 03:54:37 2019 No.10985202 :) I don't mean it lacks a definition in the English language, I mean that you can't actually write an infinite number, you can only approximate, if you know what I mean, This is confusing because we are taking approximations, running them through an equation, getting an answer that is intuitively incorrect.It's just mixing up real world and vectored maths.
 >> Anonymous Thu Sep 19 04:09:32 2019 No.10985210 >>10985202>if you know what I mean,not even a clue
 >> Anonymous Thu Sep 19 15:38:01 2019 No.10986319 >>10982184tell me when you reach that last digit
 >> Yuji Sakai Thu Sep 19 15:42:16 2019 No.10986335 >>109851911/∞ ≠ 0infinity is not a number, is a concept
 >> Anonymous Thu Sep 19 16:26:39 2019 No.10986453 >>10982618how is this invalid?
 >> Anonymous Thu Sep 19 16:28:58 2019 No.10986459 >>10982184>>10982191>>10982219>>10982222>>10982227>>10982393>>10982430>>10982455>>10982481>>10982486>>10982618>>10982658>>10982695>>10982697>>10982725>>10982754>>10982769>>10983056>>10983123>>10983136>>10983141>>10983142>>10983149>>10983161>>10983218>>10983239>>10983246>>10983325>>10983329>>10983338>>10983628>>10985149>>10985176>>10985190>>10985191>>10985202>>10985210>>10986319>>10986335>>109864531/3 is not .333 that is just an approximation, you can't represent 1/3 as a decimal but .333 repeating forever is the closest value because .334 is too big and .333 is slightly too small so when they show a repeating bar it is because .333 is not actually one-third but it is the closest you can get with decimal in base 10.
 >> Anonymous Thu Sep 19 16:30:17 2019 No.10986462 >>10986453because the infinite block has infinitely many deviations from the circular form.
 >> Anonymous Thu Sep 19 16:30:19 2019 No.10986463 >>10985190>quantity>unbounded
 >> Anonymous Thu Sep 19 16:34:06 2019 No.10986484 >>10986459read a book
 >> Anonymous Thu Sep 19 16:35:04 2019 No.10986489 >>10986484>hurr infinite exists exist, just accept itvery enlightening
 >> Anonymous Thu Sep 19 16:35:45 2019 No.10986495
 >> Anonymous Thu Sep 19 16:36:51 2019 No.10986502 >>10986489>exists existthe best kind of exist
 >> Anonymous Thu Sep 19 16:37:16 2019 No.10986506 >>10986495>appeal to authority with no reasoning
 >> Anonymous Thu Sep 19 16:38:37 2019 No.10986516 >>10986506shitposter vs W|A, easy choice
 >> Anonymous Thu Sep 19 16:40:56 2019 No.10986524 >>10986516>I believe it but I can’t tell you why
 >> Anonymous Thu Sep 19 16:42:32 2019 No.10986529 >>10986524shitposter vs W|A, easy choice
 >> Anonymous Thu Sep 19 16:43:35 2019 No.10986532 File: 22 KB, 400x421, 59AA83F7-D7B5-4689-A92B-FF8D0DEA2130.jpg [View same] [iqdb] [saucenao] [google] [report]
 >> Anonymous Thu Sep 19 16:50:19 2019 No.10986549 >>10986462>>10986463>>10986484>>10986489>>10986495>>10986502>>10986506>>10986516>>10986524>>10986529>>10986532.333 infinite times would have no value because infinity is not a number so an infinite number of 3s is also not a number
 >> Anonymous Thu Sep 19 16:52:12 2019 No.10986554 >>10986549>infinity is not a numberso what
 >> Anonymous Thu Sep 19 16:56:49 2019 No.10986564 >>10986554so .333 (infinite) cannot be a number either.
 >> Anonymous Thu Sep 19 16:58:24 2019 No.10986567 >infinity is totally not a number you guys!>”but what is it?”>a quantity...
 >> Anonymous Thu Sep 19 17:00:29 2019 No.10986572 >>10986564yes, but the limit of the sequence .3, .33, .333, .3333,... surely can be defined as a number and that number is equivalent to 1/3
 >> Anonymous Thu Sep 19 17:06:35 2019 No.10986586 >>10986572in other words, 0.333... is limited by 1/3, and will never actually equal 1/3
 >> Anonymous Thu Sep 19 17:07:53 2019 No.10986592 >>10986572>>10986586So .333... does not equal 1/3 and thus is not equivalent ?
 >> Anonymous Thu Sep 19 17:10:29 2019 No.10986595 >>10986564how exactly?
 >> Anonymous Thu Sep 19 17:12:16 2019 No.10986598 >>109865920.333... is a meaningless expression. You’re assuming that something infinite exists. 0.333... should not be viewed as a number but it shows that as you repeat the process, 0.333... approaches 1/3. There’s no justification for treating it as a number though. Even if you did, it still can’t equal 1/3, because there is always a remainder. 0.33 is just as unequal as 0.333...There is always a gap between them
 >> Anonymous Thu Sep 19 17:24:24 2019 No.10986622 >>10986592.3333.... IS grade school shorthand for "the limit of the sequence .3, .33, .333, .3333, ...". idk what the expression would mean otherwise. so, yes, .333.... is equivalent to 1/3
 >> Anonymous Thu Sep 19 17:28:55 2019 No.10986633 >>10986598this is not a good way to think about decimal representations. if you are going to think about decimals-as-real-numbers, you should think about all real numbers as equivalence classes of sequences.the sequence implicitly represented by .3333.... is no less different from 1/3 as .999.... is in the equivalence class representing 1, or 1.99... is in the equivalence class representing 2.
 >> Anonymous Thu Sep 19 17:36:55 2019 No.10986652 >>10982184Anon it’s simple.S=0.999...10S=9.999...10S =9.999... -S =0.999... 9S= 9 S=10.999...=1
 >> Anonymous Thu Sep 19 17:41:11 2019 No.10986662 >>10986652>0.999... is a number>you can multiply and add itYeah I’m gonna need a justification for your extension of arithmetical operations to infinite sums
 >> Anonymous Thu Sep 19 17:49:37 2019 No.10986681 >>10986662http://www-users.math.umn.edu/~kling202/hamline/calculus/Chapter2/Limits.pdfliterally done in any calc 1 class. changing the above argument from functions to sequences is trivial.
 >> Anonymous Thu Sep 19 17:52:13 2019 No.10986686 >>10986681>10S = 9.999...Where is the ending 0?
 >> Anonymous Thu Sep 19 17:53:05 2019 No.10986689 >>10986662Finally someone who isn’t an idiot on this sub. Technically all numbers in decimal notation are infinitely long; 4 is really 4.0000...You can also take the algebra a step further:Since 1=0.999... 1=1-0.999= -1——————0.000...1=0Therefore all infinitesimals are equal to 0, since:0.000...1*X = 0*X0.000...X=0except at x= infinity
 >> Anonymous Thu Sep 19 17:59:37 2019 No.10986705 >>10986686Are you fucking stupid.It’s non terminating
 >> Anonymous Thu Sep 19 18:07:19 2019 No.10986727 >>10986705Then how do you justify multiplying it? Where is the rule that says we can multiply an infinite sum? I certainly cannot prove such a thing empirically or even intuitively. You’re pulling these rules out of nowhere. That’s not how mathematics works
 >> Anonymous Thu Sep 19 18:16:49 2019 No.10986747 >>10986727Anon, every mathematician in the world disagrees with you. Why do we allow people who haven't even done Calc to make math threads.
 >> Anonymous Thu Sep 19 18:20:53 2019 No.10986752 >>10986747And yet you yourself cannot give a justification. You’re blindly believing “every mathematician in the world” and it’s embarrassing. If you judged mathematics by majority and authority, then at one point, you would have detested infinity and infinitesimals
 >> Anonymous Thu Sep 19 18:24:41 2019 No.10986758 >>10986727 >You’re pulling these rules out of nowhere. That’s not how mathematics worksExcept that's exactly how mathematics works. It's the study of games we play on abstract structures.
 >> Anonymous Thu Sep 19 18:29:36 2019 No.10986769 >>10986752Yes anon, you, who clearly have no mathematical training whatsoever, are in the right here. A breakthrough thinker, no one has ever questioned this before and you are going to change the field of mathematics with this.
 >> Anonymous Thu Sep 19 18:34:44 2019 No.10986787 >>10986662Do you also reject multiplying pi by 2?
 >> Anonymous Thu Sep 19 18:35:28 2019 No.10986790 >>10986622oh ok
 >> Anonymous Thu Sep 19 21:13:02 2019 No.10987133 >>10986727>Where is the rule that says we canWhere is the rule that says we can't
 >> Anonymous Fri Sep 20 11:19:55 2019 No.10988357 bump
 >> Anonymous Fri Sep 20 11:37:46 2019 No.10988381 >>10983142Yes, that's literally how you prove uniqueness
 >> Anonymous Fri Sep 20 12:34:17 2019 No.10988448 1/3 is not strictly equal to 0.333... instead, it cannot be strictly equal in decimal notation. We're taught that anything can be rendered in decimal, but for some things it's not really accurate and is simply more of a cheat. unfortunately the cheat also works towards convincing some people that 0.999... = 1, even though this is not essentially the case. This has to do with seemingly-infinite repetition. In the case of rendering 1/3 as 0.333... using the cheat, it makes enough sense that this specific rendering of 0.333... approximating 1/3 specifically, times 3, would produce 0.999..., and that 1/3 *3 = 1.however, this does not hold true for something like$\sum_{n}^{\infty}\frac{1}{2^n}$ which intends to strictly produce a 0.999... result. This calculus however "uses" "infinity", which rationally isn't actual infinity but is instead seemingly infinite.to quickly define the difference between infinite and seemingly-infinite, both are technically shortened from their results and there is an unimaginable degree of accuracy should one continue with calculation, so "seemingly-infinite" is more like a realnumber (infinity-1). There is no countable proof for either infinity or seemingly-infinite, so in the same regard there is no strong evidence an (infinity-1) cannot exist as a real number too long to intelligently do any math with, which would give it the same relevant property as straight-up "infinity" does. In all, anything that is described as infinite is more likely than not simply seemingly-infinite.
 >> Anonymous Fri Sep 20 12:39:51 2019 No.10988458 >>10988448This seemingly-infinite term is necessary for describing the 0.999... number produced by the above sum algorithm, because it is strictly provable to not be the same 0.999... number rendered from 0.333...*3 where we got the 0.333... from 1/3 specifically. Any partial sum step of $n$ within the sum will produce a string of 9's followed by a string of various digits. The infinity-hopefuls contest that those trailing digits would simply vanish under the condition that actual infinity had been reached from numerating $n\rightarrow\infty$, but since there is no way to actually do this, this vanishing cheat isn't real either. The true result of this sum is a seemingly-infinite string of 9's, followed by a seemingly-infinite string of various digits, which is different from the 0.333...*3 = 0.999... number which is solely just a seemingly-infinite string of 9's. a lot of mental cheating occurs when rendering repeating numbers in higher maths, and for this example we end up shortening what seems to be infinitely repeating patterns down to just 3 digits followed by an ellipses rendered as $0.999...$
 >> Anonymous Fri Sep 20 13:06:37 2019 No.10988513 >>10988458$1 = \dfrac{3}{3} = 3 \cdot \dfrac{1}{3} = 3 \cdot 0.\bar{3} = 0.\bar{9}$
 >> Anonymous Fri Sep 20 13:11:47 2019 No.10988535 File: 1 KB, 35x31, clap.gif [View same] [iqdb] [saucenao] [google] [report]
 >> Anonymous Fri Sep 20 13:39:44 2019 No.10988601 >>10988448$\displaystyle\boxed{0 < p < 1} \\p^n-1 = (p-1)(p^{n-1}+p^{n-2}+ \dots +p+1) \\\dfrac{p^n-1}{p-1} = \sum \limits_{j=0}^{n-1}p^j \\\displaystyle\lim_{n \to \infty} \dfrac{p^n-1}{p-1} = \lim_{n \to \infty} \sum \limits_{j=0}^{n-1}p^j \\\displaystyle\dfrac{0-1}{p-1} = \sum \limits_{j=0}^{\infty}p^j \implies \dfrac{1}{1-p} = \sum \limits_{j=0}^{\infty}p^j$
 >> Anonymous Fri Sep 20 14:22:22 2019 No.10988705 >>10986453A simple explanation is that infinity does not exist so you'll never have an actual circle.
 >> Anonymous Fri Sep 20 14:25:45 2019 No.10988714 >>10988705Perfect troll explanation.
 >> Anonymous Fri Sep 20 14:39:32 2019 No.10988737 File: 68 KB, 657x527, c9d.png [View same] [iqdb] [saucenao] [google] [report] >>10986459Thanks for quoting everyone in the thread. That was very helpful and not annoying at all.
 >> Anonymous Fri Sep 20 14:42:16 2019 No.10988748 >>10988601i hope there was a point to this post
 >> Anonymous Sat Sep 21 06:00:01 2019 No.10990466 >>10988748there is
 >> Anonymous Sat Sep 21 10:11:51 2019 No.10990727 >>10982184This is just a quirk of notation. 0.999... = 1. This is because what we mean by 0.999... is just the limit of 0.9 + 0.09 + 0.009 +...; and this limit is 1. This is trivial to see if you actually think of the definition of a limit for a series: The limit of a series a_i is c if for every epsilon > 0, there exists an N > 0, such that for all natural n >= N, the distance between a_n and c is smaller than epsilon. Or in short: The limit of a series is c if the series gets within any arbitrary distance of c eventually, which is obviously true for 0.999... and 1.The reason it seems so illogical is that there seems to be some kind of room between 0.999... and 1; for any amount of nines there's still space between it and 1, so if you add nines forever, it will just get closer and never really there right? But there is no such thing as 'adding nines' as if it is some kind of temporal process. Thinking about it in these terms is already based on a misinterpretation of what 0.999... means.
 >> Anonymous Sat Sep 21 10:15:59 2019 No.10990738 >>10988601>p^n = 0prove it
 >> Anonymous Sat Sep 21 10:28:45 2019 No.10990777 >>10982219Are you stupid?0.999...=\=1 threads have been going strong for years...
 >> Anonymous Sat Sep 21 10:31:16 2019 No.10990785 >>10986727>You’re pulling these rules out of nowhere. That’s not how mathematics worksIt LITERALLY is as any book on the foundations on mathematics will tell you.
 >> Anonymous Sat Sep 21 10:49:35 2019 No.10990823 >>10990738n=infdone
 >> Anonymous Sat Sep 21 11:09:21 2019 No.10990847 >>10986564>>10986554Wonder what the theological\metaphysical implication of the perfectly equal division of the one by the three not adding back to the one perfectly over an infinite series is. It's almost as if IsRaEl is somehow more than the sum of its parts somehow... Likely this is more due to the imprecise nature of finite math, but still an interesting thought.
 >> Anonymous Sat Sep 21 11:11:14 2019 No.10990850
 >> Anonymous Sat Sep 21 11:15:13 2019 No.10990855 x = 0.999...10x = 9.999...10x - x = 9.999... - 0.999...9x = 9x = 10.999... = 1
 >> Anonymous Sat Sep 21 11:19:43 2019 No.10990862 1/9 = 0.111...+8/9 = 0.888...=9/9 = 0.999...
 >> Anonymous Sat Sep 21 15:00:40 2019 No.10991492 File: 402 KB, 211x199, what the fuck.gif [View same] [iqdb] [saucenao] [google] [report] >>10990855>>10990862>>10988601>>10988513>>10986652>>10982754>>10982227>>10982191oh please continue, don't pay any attention to the fact that there are other people in the room.
 >> Anonymous Sat Sep 21 15:03:56 2019 No.10991504 >>10990855>10x = 9.999...Where is the ending 0?>>10990823>n = infStill haven’t proven that n^inf is possible, let alone equal to 0
 >> Anonymous Sat Sep 21 15:15:17 2019 No.10991539 File: 112 KB, 953x613, 0.999 = 1.jpg [View same] [iqdb] [saucenao] [google] [report]
 >> Anonymous Sat Sep 21 16:16:42 2019 No.10991680 >>10982184Why not live a carefree life in base 3?$1_3\div10_3=0.1_3=\left({1\over{3^1}}\right)_{10}$
 >> Anonymous Sat Sep 21 19:55:09 2019 No.10992148 The thought just occured to me, Why would someone accept that 1/3 = 0.333... but not accept that 0.999... = 1.0 ?
 >> Anonymous Sat Sep 21 19:57:34 2019 No.10992151 >>10992148Because 1/3 isn’t equal to 0.333...
 >> Anonymous Sat Sep 21 20:11:15 2019 No.10992172 >>10991680>Why not live a carefree life in base 3?I heard there's niggers in it
 >> Anonymous Sat Sep 21 20:24:18 2019 No.10992195 Perhaps I sould be more specific. In the first post of this thread, Anon said he was "bugged" by the apparent paradox he posted. In that post, he accepted that 1/3=0.333... but did not acceept that 0.999...=1. That seems like cognitive dissonance, and something that should be pointed out, whether you believe in infintiy or not.
 >> Anonymous Sat Sep 21 20:29:50 2019 No.10992207 >>10992195With 0.999... we don’t see the “1” out front, so we might think they’re unequal. With 0.333... there doesn’t have to be a 1 there. We just assume it’s equal to 1/3. However, if we look at the fraction representations: 3/10, 33/100, 333/1000/ 3333/10000 etc. we see how there’s always a remainder of 1. No matter how long the fraction is, there will always be a remainder. And just saying “go to infinity” doesn’t really justify how the remainder goes away.
 >> Anonymous Sat Sep 21 20:32:52 2019 No.10992214 >>10992207333...——100...This is clearly not equal to 1/3
 >> Anonymous Sat Sep 21 20:34:00 2019 No.10992217 >>109922140333...———1000...fixed
 >> Anonymous Sat Sep 21 20:46:18 2019 No.10992249   File: 988 KB, 599x600, 3D pepe.png [View same] [iqdb] [saucenao] [google] [report] $\frac{1}{3} > \sum_{n=1}^{\infty}\frac{1}{3^n}$
 >> Anonymous Sat Sep 21 20:47:22 2019 No.10992253   File: 7 KB, 250x241, 1406248015414s.jpg [View same] [iqdb] [saucenao] [google] [report] [eqn]\frac{1}{3} > \sum_{n=1}^{\infty} \frac{1}{3^n}[/eqn]
 >> Anonymous Sat Sep 21 22:39:51 2019 No.10992586 >>10991492$\boxed{0 < p < 1} \\1 = p + (1-p) ~~~~~~ \overset{1}{ \overbrace{[=====p=====|==(1-p)==]}} \\ \text{divide p using x} ~~~~~~ \overset{1}{ \overbrace{ \underset{p}{[ \underbrace{=====x=====|==(p-x)==}]} ~~ + ~~ (1-p)}} \\\\\text{solve x and (p-x), when length ratios must be the same} \\\dfrac{x}{p-x}= \dfrac{p}{1-p} \Rightarrow x- xp = p^2 - xp \Rightarrow \underline{x=p^2} \Rightarrow \underline{(p-x)=p(1-p)} \\\overset{1}{ \overbrace{ \underset{p}{[ \underbrace{=====p^2=====|==p(1-p)==}]} ~~ + ~~ (1-p)}} \\\\\overset{1}{ \overbrace{ \underset{p^2}{[ \underbrace{=====p^3=====|==p^2(1-p)==}]} ~~+ p(1-p)+(1-p)}} \\\overset{1}{ \overbrace{ \underset{p^3}{[ \underbrace{=====p^4=====|==p^3(1-p)==}]} ~~+ p^2(1-p)+p(1-p)+(1-p)}} \\(1-p)+p(1-p)+p^2(1-p)+p^3(1-p)+ \cdots =1 ~~~~ \left | ~ \times \frac{1}{1-p} \right . \\1+p+p^2+p^3+ \cdots = \dfrac{1}{1-p}$
 >> Anonymous Sat Sep 21 22:43:17 2019 No.10992594
 >> Anonymous Sat Sep 21 22:47:07 2019 No.10992604 >>10992586You can’t justify the disappearance of the p^n term. Bullshit bullshit bullshit
 >> Anonymous Sat Sep 21 22:49:32 2019 No.10992616   >>109926040
 >> Anonymous Sat Sep 21 22:51:20 2019 No.10992623 >>10992604disappearance?
 >> Anonymous Sat Sep 21 22:55:27 2019 No.10992632 >>10992623In the second to last line, the last term should be p^n, but instead there is (...). The last term gets smaller, but you haven’t proven that it becomes 0. The sum becomes arbitrarily close to 1, but it never equals 1.
 >> Anonymous Sat Sep 21 23:12:41 2019 No.10992664
 >> Anonymous Sat Sep 21 23:16:26 2019 No.10992671 >>10991539Wait a minute with that brown example,Like for real time out.If you had 1 litre of water, so 1000 grams of water, and you pour it into 3 containers, you don't have 333.333... grams in each container, you have a precise weight in each container.This analogy is rediculous, it's the same as saying 9=10,You can't round up physical values.If you buy a gram of coke, and the dealer taps it onto the scale until it's 0.9999999 grams, that isn't 1 gram.This whole debate rages because of a misunderstanding between vectored maths and real world maths, These symbols you are looking at are approximations done by humans in order to measure our world better, you cannot have an infinitely repeating number measured in the real world anymore than you can give a value in kilometres for how far away infinity is.
 >> Anonymous Sat Sep 21 23:16:32 2019 No.10992672 >>10992664Any non-zero number p multiplied by itself will not be equal to zero. So no matter what n value, p^n will never equal zero. It’s pure bullshit and you eat it up
 >> Anonymous Sat Sep 21 23:19:32 2019 No.10992682 Theme of the thread:https://youtu.be/MM62wjLrgmA
 >> Anonymous Sat Sep 21 23:23:32 2019 No.10992693 what if i told you>1/3 is NOT .333 ad infinitum
 >> Anonymous Sat Sep 21 23:28:41 2019 No.10992712 >>10992693heresy
 >> Anonymous Sat Sep 21 23:51:06 2019 No.10992752
 >> Anonymous Sat Sep 21 23:55:46 2019 No.10992760 >>10992752and with that, you concede a lack of understanding. This discussion can go no further as you fail to defend your methods and have no chance of providing any reasons whatsoever for your sleight of hand trucks you call mathematics.
 >> Anonymous Sat Sep 21 23:57:47 2019 No.10992764 >>10992760the bus stop masturbator has spoken
 >> Anonymous Sun Sep 22 01:12:33 2019 No.10992876 just convert your bases to something other than decimal. "0.333..." in decimal can be represented as 0.4 in duodecimal, which fits into 12 three times quite nicely.
 >> Anonymous Sun Sep 22 01:16:47 2019 No.10992880 *which fits into 1(base 12), my bad
 >> Anonymous Sun Sep 22 12:48:44 2019 No.10993904 bump
 >> Anonymous Sun Sep 22 13:41:26 2019 No.10994024 some numbers shouldn't be rendered in decimal and should just be left as fractions, simple enough.$1 \div 3 = \frac{1}{3}$
 >> Anonymous Sun Sep 22 13:48:11 2019 No.10994045 File: 33 KB, 801x626, computer smarts.png [View same] [iqdb] [saucenao] [google] [report] NO WOLFRAM WHAT ARE YOU DOING AAAAAAAAAAAAA
 >> Anonymous Sun Sep 22 14:05:36 2019 No.10994098
 >> Anonymous Sun Sep 22 14:07:55 2019 No.10994107 >>10994045let's pretend finite is infinite
 >> Anonymous Sun Sep 22 14:09:05 2019 No.10994112 >>109940241/3 = 0.1_3
 >> Anonymous Sun Sep 22 14:11:01 2019 No.10994119 >>10986459>mass quotinguse an approximation next time
 >> Anonymous Sun Sep 22 14:11:09 2019 No.10994120 >>10986495this should be undefined given inf/inf is undefined.
 >> Anonymous Sun Sep 22 14:23:00 2019 No.10994162 >>10994120sure bud
 >> Anonymous Sun Sep 22 14:25:55 2019 No.10994177 >>10994162glad you two agree now
 >> Anonymous Sun Sep 22 14:33:43 2019 No.10994199 File: 36 KB, 797x638, computer smarts.png [View same] [iqdb] [saucenao] [google] [report] >>10994162idk if you're being stupid or not but wolfram thinks 0.1 followed by 56 more 1's is the literal 1/9. wolfram is incredibly retarded.
 >> Anonymous Sun Sep 22 15:33:20 2019 No.10994393 >>10994199ok bubba
 >> Anonymous Sun Sep 22 16:36:01 2019 No.10994560 File: 30 KB, 842x527, WOLFRAM NO.png [View same] [iqdb] [saucenao] [google] [report]
 >> Anonymous Sun Sep 22 16:41:29 2019 No.10994581 >>10982184The limit of 9 times 1/10^n+1 as n approaches infinity is 1.
 >> Anonymous Sun Sep 22 16:43:05 2019 No.10994589 >>10982455You're taking a limit. 0.333... is an accident of notation.
 >> Anonymous Sun Sep 22 16:44:19 2019 No.10994595 >>10994581https://www.wolframalpha.com/input/?i=sum%5B1%2F10%5E%28n%2B1%29%2C%7Bn%2C1%2Cinfinity%7D%5Dinfinity isn't a number btw.
 >> Anonymous Sun Sep 22 16:44:50 2019 No.10994598 >>10983056You need Jesus and to learn what a limit is.
 >> Anonymous Sun Sep 22 16:45:37 2019 No.10994600 >>10982191/thread
 >> Anonymous Sun Sep 22 16:46:14 2019 No.10994604 File: 218 KB, 500x340, 1564681657669.png [View same] [iqdb] [saucenao] [google] [report] >>10994598limit is only a viable concept when using it with a number and not a retarded object like infinity, which by very definition is limitLESS. >the limit is unlimitedplease use your thinker.
 >> Anonymous Sun Sep 22 16:46:21 2019 No.10994605 >>10983056Staircases don't have an infinite number of infinitely small steps in a finite distance. Any staircase that did would be a ramp.
 >> Anonymous Sun Sep 22 16:47:58 2019 No.10994608 >>109821841/3 is 1/3. Once and forever, periodic nums are bullshit use fractional otherwise we'll get noticable unwanted effects on varius calculations.
 >> Anonymous Sun Sep 22 16:50:29 2019 No.10994614 >>10986335Writing infinity as a number is shorthand for taking a limit, just like 0.999... Really not sure why anyone who doesn't at least understand the concept of a limit is on this board. You know this is a math and science board right?
 >> Anonymous Sun Sep 22 16:55:06 2019 No.10994625 >>10988714It's basically true in real life. Macroscopic objects aren't made of infinitesimal parts. There are no perfect circles, just arbitrarily approximate ones up to a point.
 >> Anonymous Sun Sep 22 17:03:50 2019 No.10994651 heres some hot new math i just came up with$\frac{1}{3} = 0.\overline{333}:A$what does ":A" mean? It's a hexidecimal numeric identifier, used to determine how the number should be read.>:A= this number is repeating without significant deviation. Direction: Hold 1 more digit than is displayed, and round. $0.333:A \rightarrow 0.333[3]$ 0.333[3] = 0.333; 0.333[3]*2 = 0.666[6] = 0.667; 0.333[3]*3 = 0.999[9] = 1.0>:B = this number is seemingly repeating but contains significant deviation [eqn]\sum_{n=1}^{\infty} \frac{1}{2^n} = 0.\overline{999}:B [/eqn]. >:C = >:D =>:E =>:F =>>$0.\overline{999}:A \neq 0.\overline{999}:B$FEEL free to fill these in.
 >> Anonymous Sun Sep 22 17:28:34 2019 No.10994699 >>10994604The entire concept of limits is that some infinities are limited. Like a curve on a plane, which, regardless of length, is made of infinite points. If you can't understand this, you will never be able to do any math or science.
 >> Anonymous Sun Sep 22 17:37:24 2019 No.10994729 >>10994699nothing is made of infinite anything and you're a daydreaming mong living in fantasy land.
 >> Anonymous Sun Sep 22 17:39:36 2019 No.10994735 I fucking hate decimals
 >> Anonymous Sun Sep 22 17:45:50 2019 No.10994751 >>10994729Maybe the true math was the infinite friends we made along the integral.
 >> Anonymous Sun Sep 22 19:09:55 2019 No.10994941 >>10994729Math can only approximate physical reality and vice versa, you absolutely retard. The point is that you can approximate at any arbitrary scale. This is shit someone with an IQ of 90 should be able to understand.
 >> Anonymous Sun Sep 22 23:29:24 2019 No.10995499 $\displaystyle \sum_{n=1}^{\infty}\frac{9}{10^n} = \frac{9}{10} + \frac{9}{100} +\frac{9}{1000} + ... = b = \frac{1}{10}(9 + \frac{9}{10} + \frac{9}{100} +...) = \frac{1}{10}(9+b) = b \\ \frac{1}{10}(9+b) = b \\ \frac{9}{10} = \frac{9}{10}b \\ 1 = b$
 >> Anonymous Sun Sep 22 23:42:07 2019 No.10995528 >>10994941it only takes 62 digits to accommodate the scale of the UNIVERSE in meters with planck length accuracy. How's that for arbitrary you dumb nigger.
 >> Anonymous Mon Sep 23 00:29:02 2019 No.10995655 >>10995528>62 digitspeanuts compared to the amount of ways you can arrange 6.022x10^23 molecules
 >> Anonymous Mon Sep 23 02:05:48 2019 No.10995774 >>10995655meme number.
 >> Anonymous Mon Sep 23 03:01:55 2019 No.10995858 >>10995774less than 20g of water
 >> Anonymous Mon Sep 23 15:38:12 2019 No.10997184 bump
 >> Anonymous Mon Sep 23 17:07:33 2019 No.10997380 >>10995499>b = 1/10bquackematics
 >> Anonymous Mon Sep 23 19:28:16 2019 No.10997680 >>10997380>i have no argument
 >> Anonymous Mon Sep 23 19:43:01 2019 No.10997701 >>10997680>9/10 + 9/100 + 9/1000... = b>b = 1/10(9 + 9/10 + 9/1000...)>b = 1/10(b)>b = 0
 >> Anonymous Mon Sep 23 19:43:09 2019 No.10997703
 >> Anonymous Tue Sep 24 00:40:19 2019 No.10998493 File: 122 KB, 900x900, prophet.jpg [View same] [iqdb] [saucenao] [google] [report]
 >> Anonymous Tue Sep 24 07:36:08 2019 No.10999140 >>10992876>>10992880based basebro
 >> Anonymous Tue Sep 24 07:40:03 2019 No.10999142 >>10986459.333 repeating is exactly 1/3 you dumb nigger
 >> Anonymous Tue Sep 24 07:52:46 2019 No.10999160 >>10986727>Where is the rule that says we can multiply an infinite sum? If you want to multiply an infinite sum by a single number, it's easy, you just multiply every summand by that number. It's called the distributive law.
 >> Anonymous Tue Sep 24 08:31:37 2019 No.10999193 1=1Q.E.D.
 >> Anonymous Tue Sep 24 10:31:24 2019 No.10999388 >>10997701>>b = 1/10(b)hurr durrit's b = 1/10(9+b)lrn2read
 >> Anonymous Tue Sep 24 13:40:56 2019 No.10999904 >>10999142No, it is not. It is conceptual approximation.
 >> Anonymous Tue Sep 24 13:43:45 2019 No.10999915 >>10982184.333...=1/3 is an approximation retard!
 >> Anonymous Tue Sep 24 13:44:47 2019 No.10999918 >>10982393Wrong. .999... is not a real. It is a hyperreal. And it is sure as hell not equal to 1.
 >> Anonymous Tue Sep 24 13:46:02 2019 No.10999920 >>10982769So let me guess, a parabola touches its asymptotes?
 >> Anonymous Tue Sep 24 16:19:28 2019 No.11000310 The absolute state of /sci/
 >> Anonymous Tue Sep 24 20:54:42 2019 No.11001098 WELCOMETOTHE MACHINE
 >> Anonymous Tue Sep 24 21:00:55 2019 No.11001107 File: 28 KB, 488x463, retardClap.png [View same] [iqdb] [saucenao] [google] [report]
 >> Anonymous Wed Sep 25 03:23:14 2019 No.11001932 >>10982184Thanks for this shit post. Kinda new to this board, this post made it very clear that everyone here is retarded. This place is an incredibly inefficient way to learn or discuss anything
 >> Anonymous Wed Sep 25 03:41:34 2019 No.11001950 >>10999915>>10994608This is the answer.1 div by 3 =! .3331 div 3 = 1/3, a ratio.1/3*3=1.Nothing breaks Limits and aproctchomations are not needed
 >> Anonymous Wed Sep 25 14:45:45 2019 No.11003165 File: 161 KB, 432x432, 1569267671600.png [View same] [iqdb] [saucenao] [google] [report] >>11001932>This place is an incredibly inefficient way to learn or discuss anythingThat's here. That's home. That's us.
 >> Anonymous Thu Sep 26 01:01:03 2019 No.11004962 bump
 >> Anonymous Thu Sep 26 17:42:47 2019 No.11006945 bump lmao
 >> Anonymous Fri Sep 27 01:09:38 2019 No.11007941 >>11001932True for the most part, there are a couple smart people that post here though.
 >> Anonymous Fri Sep 27 14:58:15 2019 No.11009451 File: 4 KB, 150x150, 1621709_10203787937878020_248716194_n.jpg [View same] [iqdb] [saucenao] [google] [report] resurrected from page 10
 >> Anonymous Fri Sep 27 15:10:27 2019 No.11009488 Bridging fractions and decimals was never meant to happen. Dont do this. They arent compatible
 >> Anonymous Fri Sep 27 15:13:06 2019 No.11009497 >>11001932Depends what you're trying to learn. Two days ago I learned how to defend my property using a neural net and through botany.
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