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# /sci/ - Science & Math

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There we go, all sorted out.

 >> Anonymous Sat Oct 12 05:03:01 2019 No.11052112 >>11052098Bravo
 >> Anonymous Sat Oct 12 05:05:21 2019 No.11052118 >>11052098>iq~0
 >> Anonymous Sat Oct 12 05:37:27 2019 No.11052151 They aren't equal. Any proof using 1/3 is invalid because we ALSO can't represent 1/3 appropriately.
 >> Anonymous Sat Oct 12 05:57:49 2019 No.11052184 >>110521510.1 in base 3, exactly
 >> Anonymous Sat Oct 12 06:01:48 2019 No.11052194 >>11052151>They aren't equal.No they're approximately equal. Close enough.
 >> Anonymous Sat Oct 12 06:05:12 2019 No.11052196 >>11052194I agree but I will rearend the next fag youtuber to tell me they are equal
 >> Anonymous Sat Oct 12 07:10:46 2019 No.11052264 >>11052151>>11052194Are you guys really this stupid?The repeating decimal means[eqn]9\times 10^{-1}+9\times 10^{-2}+9\times 10^{-3}+\dots[/eqn]This is a geometric series[eqn]9\times 10^{-1}(1+10^{-1}+ 10^{-2}+\dots)=9\times 10^{-1}\left(\frac{1}{1-10^{-1}}\right)=1[/eqn]I'm sorry but if you are one of those crackpots that doesn't believe in infinite series, you don't get to talk about non-terminating decimals, since that is exactly what they are
 >> Anonymous Sat Oct 12 08:04:12 2019 No.11052329 Gay, 0.9... = 1
 >> Anonymous Sat Oct 12 08:05:12 2019 No.11052331 >>11052264Brainlet hereWouldn't the right side of the equations solve to be 00,81?
 >> Anonymous Sat Oct 12 08:06:34 2019 No.11052333 >this thread againWhy are you all such dull stupid faggots. You'd think with all the self professed 200+ IQ's around here there'd be a spark of some creativity.
 >> Anonymous Sat Oct 12 08:46:58 2019 No.11052390 >>11052329this. how is if so hard to understand
 >> Anonymous Sat Oct 12 08:49:12 2019 No.11052393 >>11052098If I have an infinite number of dice and roll all of them an infinite number of times, will there exist a die that rolled a 6 every single time?
 >> Anonymous Sat Oct 12 08:52:18 2019 No.11052399 $\frac{1}{3}=0.1_3 \\0.1_3 +0.1_3 = 0.2_3 \\0.2_3 +0.1_3 = 1_3=1_{10}$
 >> Anonymous Sat Oct 12 09:04:43 2019 No.11052414 >>11052393Yes, since the opportunity exists. Otherwise the opportunity wouldn't exist
 >> Anonymous Sat Oct 12 09:08:22 2019 No.11052419 >>11052393Yes
 >> Anonymous Sat Oct 12 09:15:05 2019 No.11052425 >>11052393>>11052419Taking this a bit further, you'd have an infinite number of dice that rolled a 6 every single time.
 >> Anonymous Sat Oct 12 09:51:48 2019 No.11052489
 >> Anonymous Sat Oct 12 09:57:13 2019 No.11052498 >>11052399BasedNo, multi-radix based
 >> Anonymous Sat Oct 12 18:52:50 2019 No.11053551 >>11052489based grimeposter
 >> Anonymous Sat Oct 12 20:08:34 2019 No.11053712 >>11052264infinity doesn't actually end. even 10^-1(1/(1-10^-1)) in your equation is only an approximation for the set the infinitesimally small number is just disregarded. but disregarding it to make an equivalence is false, it'll always be an approximate. it's just the limit of the numeric system that mathematicians cheat over
 >> Anonymous Sun Oct 13 01:50:30 2019 No.11054326 >>11053712>I'm sorry but if you are one of those crackpots that doesn't believe in infinite series, you don't get to talk about non-terminating decimals, since that is exactly what they are
 >> Anonymous Sun Oct 13 02:28:01 2019 No.11054391 >>11053712>infinity doesn't endnooo really?next: water is wet
 >> Anonymous Sun Oct 13 02:54:52 2019 No.11054424 >>11053712brainlet
 >> Anonymous Sun Oct 13 02:59:10 2019 No.11054430 Define 0.999... to be 1.QED
 >> Anonymous Sun Oct 13 04:22:10 2019 No.11054541 >>11052098Suppose 0.99... is strictly less than 1Therefore 1-0.99... =x where x is strictly greater than 0.So 1-x=0.99...Now let's consider 1-0.1x, this expression is at least as large as 1-x, but definitely smaller than 1. So, either it's 1-x<1-0.1x<1 or 1-x=1-0.1x<1. If 1-x=1-0.1x then x=0 which is a contradiction. If 1-x is less than 1-0.1x, then there exists a number between 0.99... and 1, which will call y. Y must be strictly smaller than 1 and strictly larger than 0.99... so there exists numbers 1-Y and Y-0.99.. that sum to x. These numbers must be stricty nonzero and smaller than x, and their absolute difference must be smaller than either, call it z so that 1-z is greater than 1-y and greater than 1-x. You can do this forever and find an infinite amount of numbers larger than 0.99.. and smaller than 1. So either 0.99... is equal to 1 or it's totally meaningless because there's always a number closer to 1 than it.
 >> Anonymous Sun Oct 13 04:28:15 2019 No.11054548 >>11052098 NO. It is NOT "approximately" 1. It is EXACTLY one.There is NO difference between 0.999... and 1.000...
 >> Anonymous Sun Oct 13 05:04:00 2019 No.11054598 Found the guy responsible for the 737MAX's crashing: >>11052098
 >> Anonymous Sun Oct 13 05:05:02 2019 No.11054601 >>11054548>There is NO difference between 0.999... and 1.000...So what's 0.999... - 1.000... ?
 >> Anonymous Sun Oct 13 05:10:37 2019 No.11054611
 >> Anonymous Sun Oct 13 05:12:14 2019 No.11054614 >>11054611Prove it. xD
 >> Anonymous Sun Oct 13 05:13:39 2019 No.11054617 >>11054548>he probably thinks it's okay to say pi is equal to """exactly""" 3, since it's """close enough"""
 >> Anonymous Sun Oct 13 05:19:13 2019 No.11054624
 >> Anonymous Sun Oct 13 05:21:11 2019 No.11054628 >>11054624Nonsense. Only 1=1. You're a brainlet if you believe anything else.
 >> Anonymous Sun Oct 13 06:57:34 2019 No.11054730 >>11054601>So what's 0.999... - 1.000... ? Zero.What is "4 quarters" - "1 dollar bill" ?Also Zero.A number can have many different symbol representations. Just like money can have many different representations.
 >> Anonymous Sun Oct 13 07:09:00 2019 No.11054743 >>11052414If the opportunity has an infinitely small chance of happening, doe the opportunity exist?
 >> Anonymous Sun Oct 13 07:14:22 2019 No.11054753 >>11052393>will there exist a die that rolled a 6 every single time? Yes, in fact an infinite number of them.
 >> Anonymous Sun Oct 13 07:16:15 2019 No.11054755 >>11052098>>110522640.9 < 10.09 < 0.10.9 + 0.09 < 1 + 0.1QED
 >> Anonymous Sun Oct 13 07:51:43 2019 No.11054786 File: 26 KB, 499x499, facebook.jpg [View same] [iqdb] [saucenao] [google] [report] >>11054326>>11054391>>11054424Ah yes, it is abundantly clear by your responses that you have run out of rational responses to this argument. What's wrong? The reality of infinite sets too difficult for you?
 >> Anonymous Sun Oct 13 07:59:06 2019 No.11054789 >>11052098Why can't faggots understand this? It's not that hard, are you really that stupid?
 >> Anonymous Sun Oct 13 08:36:32 2019 No.11054824 >>11052393Countable or uncountable infinities?If countable infinities, number the dice 1, 2, 3, ….Let A(n) be the event that die #n rolls a 6 every single time. It has probability 0. Let B(n) be the event that die #n is the first die (in this enumeration) to roll a 6 every single time. It is a subset of A(n), so also has probability 0. The B(n) are all disjoint events. The event that at least one die rolls a 6 every single time is the countable union of the B(n), so also has probability 0. If the number of dice were uncountable the answer would be different.
 >> Anonymous Sun Oct 13 08:48:50 2019 No.11054841
 >> Anonymous Sun Oct 13 09:02:47 2019 No.11054870 >>11054755Yes continue your argument and you will have proven that 1 < something greater than 1Wow you really showed me>>11054786Why am I required to humor your silly delusions? If you want you can learn from my post, and if not that's your choice then. This isn't an argument between equals
 >> Anonymous Sun Oct 13 12:08:11 2019 No.11055246 1/9 = .111...2/9 = .222...3/9 = .333...4/9 = .444...5/9 = .555...6/9 = .666...7/9 = .777...8/9 = .888...9/9 = .999... = 1
 >> Anonymous Sun Oct 13 13:09:42 2019 No.11055404 File: 73 KB, 1024x576, 1568058561681.jpg [View same] [iqdb] [saucenao] [google] [report] >>11054755based af
 >> Anonymous Sun Oct 13 13:25:10 2019 No.11055451 File: 15 KB, 307x400, image-3.jpg [View same] [iqdb] [saucenao] [google] [report] Disclaimer: I do actually agree with the ignorant, barely literate pajeets in these threads who say that the 1/3=0.33... => 3/3 = 0.999... = 1 is not a valid proof, at least in a sense. Because disagreement over whether 0.999...=1 or not comes from the DEFINITION of what the "..." part means, and manipulations of these expressions before agreeing what it means get you nowhere. In the following, I will give the standard definition of what it means (at least for anyone aware of mathematics) and then prove that 0.99...=1.Read and understand this proof to get smart:By the Cauchy sequence definition of real numbers, a real number is an equivalence class of rational sequences a:N->Q, whose n'th member is a_n, with the equivalence relation being a~b <=> |a_n-b_n|-> 0 as n-> infinity. This says that for every rational x>0, there is a natural number N such that for all n>N, |a_n - b_n|
 >> Anonymous Sun Oct 13 13:26:12 2019 No.11055454 >>11055451For an infinitely long decimal expression, we define the real number that it represents by taking a sequence of increasing finite truncations of the decimal expression. In particular, we write 0.9999... to denote the real number represented by the sequence (0, 0.9, 0.99, 0.999, and so on). To make sense of the real number 1, we inject rational numbers into reals by letting the real number q' by (q,q,q,q,....) for a rational number q. Then, in order to prove that the real numbers 1=[(1,1,1,1,...)] (where [x] denotes the equivalence class of the sequence x), and 0.9999...=[(0.9, 0.99, ...)] are equal, it suffices to show that they lie in the same equivalence class (because gain, real numbers are equivalence classes, not elements in those classes themselves). The n'th term in the canonical sequence for 0.999... is 1-(10^-n). The n'th term in the sequence for 1 is 1. Hence it suffices to prove that |1-(10^-n) - 1 | = 10^(-n) -> 0 as n->infinity. Looking back at the definition of a limit, let x>0 be any positive rational number. We want to find an N such that for all n>N, 10^-n < x, or 10^n > 1/x. But that is simple, just take any N such that 10^N > 1/x. Hence, the limit is proved and 0.9999... = 1.Note that by similar arguments, we also have [(0.97, 0.997, 0.9997,...)]= 1 etc.Keep in mind that everything I just explained is not complicated. In fact, it's elementary mathematics that is often left as an exercise in introductory analysis books. That means you should be able to understand what I just explained and accept that 0.999..=1.retards
 >> Anonymous Sun Oct 13 13:27:29 2019 No.11055457 File: 317 KB, 500x375, b9f0210a0eefbccae719772f2f0ce74b.png [View same] [iqdb] [saucenao] [google] [report] I understand that my post was probably the first time a lot of people here saw what real numbers actually were. I will take this opportunity to teach you some more. We will continue with the Cauchy definition of real numbers. How do we define the field operations?Simple. From now on, we will refer to real numbers by arbitrary elements in their equivalence classes. This means you have to prove that the definitions are well defined independent of the choice of element in the equivalence class, but that can be done without too much effort.The most basic operation is addition. We define (a_n)+(b_n) be (a_n + b_n) (essentially sum each entry in the sequence. so (1,1,1,1,1,1,...) + (1, 1/2, 1/4, 1/8,...) will be (1, 1.5, 1.25, ....). We need to prove that this defines a unique real number independent of choice of sequences (a_n) and (b_n) in their respective equivalence classes. This is easy: assume (a_n) ~ (a'_n) and (b_n) ~ (b'_n). We need to show that (a_n + b_n)~(a'_n + b'_n), or equivalently that |a_n + b_n - a'_n + b'_n | -> 0 as n-> infinity. But |a_n + b_n - a'_n + b'_n | = | (a_n - a'_n) + (b_n - b'_n)| <= |a_n - a'_n| + |b_n - b'_n| (here we used the triangle inequality |a+b| <= |a| + |b|). Hence since |a_n - a'_n| tends to 0, as does |b_n - b'_n| , their sum does too, hence (a_n + b_n)~(a'_n + b'_n) and addition of real numbers is well defined. This is actually not the complete proof yet: we need to establish that addition actually defines a real number by showing that (a_n + b_n) is also a Cauchy sequence, but that proof is similar and left as an exercise to the reader :)Now that you've seen how addition is defined, try and yourself define: addition, multiplication and division. Not just tell us how to do it, but show that your definition actually works, as I did.
 >> Anonymous Sun Oct 13 13:38:51 2019 No.11055510 >>11052098>>11055451>>11055454>>11055457There we go, all sorted out.
 >> Anonymous Sun Oct 13 16:49:14 2019 No.11056063 >>11052264Finally, some sanity
 >> Anonymous Sun Oct 13 17:23:07 2019 No.11056226 >>110521510.999... = X10X = 9.999...9X = 10X - X = 9X = 9X/9 = 1Nigga
 >> Anonymous Sun Oct 13 17:49:25 2019 No.11056340 >>11052194No they are equal
 >> Anonymous Sun Oct 13 18:18:54 2019 No.11056448 >>11056226>10X = 9.999...Multiplying by 10 results in a product ending in 0
 >> Anonymous Sun Oct 13 18:24:46 2019 No.11056469 >>110521511/3 is a valid representation though>>11056226so many things wrong with this
 >> Anonymous Sun Oct 13 18:32:39 2019 No.11056495 >>11054870>continuethere is nothing to continue, you are wrong by definition
 >> Anonymous Sun Oct 13 18:38:16 2019 No.11056515 >>11052264>1+10−1you can't insert a 1 anywhere retard, it's all 9's
 >> Anonymous Sun Oct 13 18:42:12 2019 No.11056528 >>11056448Is this the new shitpost?
 >> Anonymous Sun Oct 13 18:43:44 2019 No.11056536 >>11056528it's correct.0.9 x 10 = 9.0 =/= 9.9
 >> Anonymous Sun Oct 13 18:57:06 2019 No.11056587 >>11056536Please take your meds.
 >> Anonymous Sun Oct 13 19:27:20 2019 No.11056699 >>11052098therefore 0.9999(...) is a natural number
 >> Anonymous Sun Oct 13 21:18:50 2019 No.11056983 >>11056469theres literally nothing wrong with it>>11056515take your meds
 >> Anonymous Sun Oct 13 22:13:23 2019 No.11057122 >>11054870Yes I understand my concept is difficult for you but I will at least try to treat you as an equal.
 >> Anonymous Sun Oct 13 22:31:48 2019 No.11057160 >>11055457I would love to understand what you're talking about. It feels like I walked in halfway into a story
 >> Anonymous Sun Oct 13 23:10:42 2019 No.11057231 >>11056699>therefore 0.9999(...) is a natural numberYes.Why does it bother you that the same number can be represented in different ways?4 quarters = 10 dimes = 20 nickels = 1 dollar here the same amount of money is represented in 4 different ways but they all represent the same amount of money0.999... = 10/10 = 1.00.... = 1The same number represented 4 different ways.
 >> Anonymous Sun Oct 13 23:16:43 2019 No.11057240 >>11057231u havent done anything to prove it's an equivalency you fucking idiot
 >> Anonymous Sun Oct 13 23:30:04 2019 No.11057263 This thread rages on haha0.999... is a symbol for 0.99999 and then infinite 9s,. This is because you cannot represent infinite 9s.You will run out of paper.So if you graph 0.999... it will form an infinite curve known as an asymptote. With the line forever approaching 1, but with 1 as the limit.No matter how close you get to one, the line never touches 1.The same as how if you weigh out 0.999999 grams on a scale. It doesn't equal 1 gram.No matter how many decimals you go to, it's still not equal to 1
 >> Anonymous Sun Oct 13 23:58:38 2019 No.11057318 >>11057263>cannot representnope$1 = \dfrac{3}{3} = 3 \cdot \dfrac{1}{3} = 3 \cdot 0.\bar{3} = 0.\bar{9}$
 >> Anonymous Mon Oct 14 00:00:45 2019 No.11057322 File: 5 KB, 812x388, infinity.png [View same] [iqdb] [saucenao] [google] [report] >>11057263>No matter how many decimals you goyeah that's why infinity isn't a number,by definition it's bigger than all of them
 >> Anonymous Mon Oct 14 00:21:17 2019 No.11057360 >>110520980.9 repeating = 1The bit that's missing between 0.9 repeating and 1 is just the operator. (The equal sign itself contains the missing amount between 0.9 repeating and 1, because these are relative math concepts that can not be compared without an operator. 0.9 repeating |Absolute =| 1 can not exist.0.9 repeating = 1 is fine, and correct, as the automatic forebearance is that the equal sign provides the missing amount to make the statement true, or the statement is false.Sorry for you finite, solid math, and non-theoretical cucks that can't actually deduce that on your own.
 >> Anonymous Mon Oct 14 00:21:30 2019 No.11057361 >>110573181/3 =/= 0.333....
 >> Anonymous Mon Oct 14 00:22:21 2019 No.11057364 >>11052264Ok jackass, post an infinite series in long form.As soon as you do that, I'll believe they exist.
 >> Anonymous Mon Oct 14 00:23:48 2019 No.11057365 >>11057322The argument is infinitesimal there, not infinity.
 >> Tuba Jam Mon Oct 14 00:30:18 2019 No.11057369 >>11052151>they aren't equalThen what's their mean?>>11052393No matter how large the number of rolls becomes, you'll always be able to find an arbitrarily large number of dice who have always come up with a 6.
 >> Anonymous Mon Oct 14 01:07:00 2019 No.11057431 >>11057369>Then what's their mean?0.999.... + 0.000...1 / 2
 >> Anonymous Mon Oct 14 01:08:50 2019 No.11057434 >>11057365>infinitesimalnot a real number
 >> Anonymous Mon Oct 14 01:09:53 2019 No.11057437 >>110573611/3 = 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 Mon Oct 14 01:10:00 2019 No.11057438 >>11057434neither is infinity
 >> Anonymous Mon Oct 14 01:11:18 2019 No.11057441 File: 28 KB, 488x463, retardClap.png [View same] [iqdb] [saucenao] [google] [report] >>11057431so 0.5
 >> Anonymous Mon Oct 14 01:11:19 2019 No.11057442 >>11057437>1/inf>x = y
 >> Anonymous Mon Oct 14 01:12:23 2019 No.11057444 >>11057438exactly, that's why it works
 >> Anonymous Mon Oct 14 01:13:47 2019 No.11057446 >>11057442r u ok?your post reads like you just had a stroke
 >> Anonymous Mon Oct 14 01:13:59 2019 No.11057447 >>11057444you can't just write 0.999... and say it's an infinite number of 9's
 >> Anonymous Mon Oct 14 01:14:59 2019 No.11057450 0.999... = 19.999.../9 = 9/99 = 8.9998.999.../9 = 9/90.888... = 1hmm
 >> Anonymous Mon Oct 14 01:22:38 2019 No.11057460 >>11057450>9 = 8.999nope
 >> Anonymous Mon Oct 14 01:23:40 2019 No.11057461 >>11057447[citation needed]
 >> Anonymous Mon Oct 14 01:25:07 2019 No.11057463 >>11057460According to >>11052489 it is
 >> Anonymous Mon Oct 14 01:25:26 2019 No.11057464
 >> Anonymous Mon Oct 14 01:26:58 2019 No.11057469 >>110574638.999... = 9, yeslrn2write
 >> Anonymous Mon Oct 14 01:35:40 2019 No.11057482 Alright anon, let's get a Cartesian number plane.A horizontal plane we call X, Now this plane ranges from 0 to 1Plot the point "0" one the planeNow plot "1" on the plane.Now plot 0.999...Is it equal to "1"?No.It's a different number.Just because you can imagine it, doesnt make it real.
 >> Anonymous Mon Oct 14 01:37:15 2019 No.11057486 >>11057450>8.999.../9 = 0.888...holy shit that's retardedhttps://duckduckgo.com/?q=8.9999999999999999999999999999999999999%2F9&t=h_&ia=calculator
 >> Anonymous Mon Oct 14 01:38:18 2019 No.11057487 >>11057482>Is it equal to "1"?yes
 >> Anonymous Mon Oct 14 01:39:10 2019 No.11057489 Lol does 9=10 Hahaha
 >> Anonymous Mon Oct 14 01:41:54 2019 No.11057493 >>11057489either one could be your iqreally no difference there
 >> Anonymous Mon Oct 14 01:48:39 2019 No.11057503 >>11052264$\sum_{i=1}^{\infty}\frac{9}{10^{i}}=1$is a much better way to say it
 >> Anonymous Mon Oct 14 01:55:55 2019 No.11057511 >>11057503$\displaystyle\sum_{i=1}^{\infty} \dfrac{9}{10^{i}}=1$Optimized.
 >> Anonymous Mon Oct 14 02:02:47 2019 No.11057519   >>11052098This shit can be solved with basic algebra.$x = \sum_{i=1}^{\infty}\frac{9}{10^{i}} = 0.99\bar{9}$$10x = 10 \times\sum_{i=1}^{\infty}\frac{9}{10^{i}} = 9.99\bar{9}$$10x-x= 9x = 9 \times\sum_{i=1}^{\infty}\frac{9}{10^{i}} = 9.99\bar{9}-x=9.99\bar{9}-0.99\bar{9}$$9x=9$$x=1$But we started with $x = 9.99\bar{9}$Therefore, $9.99\bar{9}=1$THERE. That's your proof. You don't even need a geometric series to figure this shit out.
 >> Anonymous Mon Oct 14 02:06:44 2019 No.11057526 $x = \sum_{i=1}^{\infty}\frac{9}{10^{i}} = 0.99\bar{9}$$10x = 10 \times\sum_{i=1}^{\infty}\frac{9}{10^{i}} = 9.99\bar{9}$$10x-x= 9x = 9 \times\sum_{i=1}^{\infty}\frac{9}{10^{i}} = 9.99\bar{9}-x=9.99\bar{9}-0.99\bar{9}$$9x=9$$x=1$But we started with $x = 0.99\bar{9}$Therefore, $0.99\bar{9}=1$THERE. That's your proof, plain as day, in algebra no less.
 >> Anonymous Mon Oct 14 02:08:10 2019 No.11057530 >>11057511So it approaches the limit of 1, but never actually reaches 1.Hey guys if i have a savings account and I invest $900 000, then 90 000, then 9 000, then 900, then 90, then 9, then 90cents, then 9 cents, then 0.9 cents, then 0.09 cents forever, deciding each amount by ten, do I eventually get a$1 000 000?Go and learn about limits.This is why you can't understand infinity.Stop pretending to be a mathematician if you don't understand limits.
 >> Anonymous Mon Oct 14 02:14:31 2019 No.11057534 File: 112 KB, 953x613, 0.999 = 1.jpg [View same] [iqdb] [saucenao] [google] [report] >>11057530>So it approaches the limit of 1, but never actually reaches 1.No, it's *exactly* 1. It's not a computer program that iterates. Moreover, it's not even remotely different. Numbers can be expressed in many ways and $0.99\bar{9}=1$ is just as valid as saying $\frac{6}{3}=2$. Just because they *appear* to be different (to you) doesn't mean they actually are. The repeating decimals is just an artifact of our decimal number system. It's a flaw in representing it in logarithmic base. The fact is if we had a base 12 number system that artifact wouldn't even show up.
 >> Anonymous Mon Oct 14 02:16:19 2019 No.11057536 >>11057530Stop pretending to know infinity if you believe any limit can be proven in this Universe.We hit entropy death before either one of us can prove a limit, that includes infinity, to be true or false.You understand mathematics, but we don't exist in your world that infinity can be practically applied.
 >> Anonymous Mon Oct 14 02:18:04 2019 No.11057538 >>11057534I prefer sexagesimal, but exactly what this guy said.PS - Ancient Sumerians used a sexagesimal number system.
 >> Anonymous Mon Oct 14 02:21:12 2019 No.11057540 >>11052098If $0.99\bar{9} \ne 1$ then there must exist some number $x$ such that $0.99\bar{9} < x < 1$So, what is $x$? Go on. I'll wait.Here, I'll even use your logic against you. if the 9s go on forever without terminating, then when you subtract so do the 0s in $0.00\bar{0}...$ Remember, those 0s *never*, *ever* terminate. There is no room for a difference greater than zero which means they have to be the same.
 >> Anonymous Mon Oct 14 02:24:12 2019 No.11057545 Anyone who still thinks 0.999... \neq 1 is such a brainlet they can't comprehend how brainlet they are. I wouldn't bother trying to convince them.
 >> Anonymous Mon Oct 14 02:34:39 2019 No.11057555 0.1 ~= 0.20.2 ~= 0.3...0.9 ~= 1Does that mean 0.0 ~= 0.1? And thus 0 = infinity?
 >> Anonymous Mon Oct 14 02:53:52 2019 No.11057577 Hey anon,If I borrow 1 Bitcoin from you,And agree to pay back one tenth of what I owe per day,As I the first day I pay 0.9 Bitcoin, the. 0.09, then 0.009, then 0.0009, then 0.0009, then 0.00009 etc.How long until the total of 1 Bitcoin is paid paid.ie how long until the amount in your account becomes equal to 1 Bitcoin?I can't believe this is still a debate.You never reach 1, it's a limit. You get closer and closer for ever but never reach.It's called a limit.
 >> Anonymous Mon Oct 14 03:55:51 2019 No.11057666 >>11057577Your practical argument is MEGA FLAWED.Do your research plebian. You can't pay me back past 1 satoshi limit.Thus, you default on your debt, and owe me more money after interest.God damn, go to the fucking accounting thread, trash.
 >> Anonymous Mon Oct 14 07:35:42 2019 No.11058107 >>11052098Perfect because nobody would actually be stupid enough to confuse a numbers limit to what the actual number exactly is.
 >> Anonymous Mon Oct 14 07:46:34 2019 No.11058122 >>110520980.999...99*10=9.99...909.99...90-0.999...99=8.999...918.999...1/9=0.999...Fuck all this 10x bullshit
 >> Anonymous Mon Oct 14 07:52:09 2019 No.11058128 >>11057530>approachesinfinity isn't approaching anything, it's way out there already from the get-go.
 >> Anonymous Mon Oct 14 08:00:07 2019 No.11058136 >>11058128He is talking about the geometric series you fucking red nosed cock retard fuck face mother fucker shit
 >> Anonymous Mon Oct 14 08:06:04 2019 No.11058142 >>11057666But you just said that 0.999...=1So I only have to pay you back 0.9999999 Bitcoins and you will have 1 Bitcoin ;););).......unless 0.999..=1 is incorrect :0Which it it....you fucking idiot.Way too agree with me because you don't understand maths.
 >> Anonymous Mon Oct 14 08:11:17 2019 No.11058147 >>11057240>prove it's an equivalencyNO, YOU prove they are not.You are an idiot, you refuse to believe anyone's proof, so if you are so fucking positive they are different numbers then YOU provide a proof.Prove how 0.999... is a different number than 1
 >> Anonymous Mon Oct 14 08:11:44 2019 No.11058149 >>11058136yes, we all are, little dipshit
 >> Anonymous Mon Oct 14 08:12:47 2019 No.11058153 >>11058149Yes so I was right you fuck
 >> Anonymous Mon Oct 14 08:13:49 2019 No.11058154 >>110581530.999... = 1nice to agree
 >> Anonymous Mon Oct 14 08:14:07 2019 No.11058155 >>110581470.999...=1-10^-n1=1-0unless 0=10^-n which is just retarded
 >> Anonymous Mon Oct 14 08:15:10 2019 No.11058159 >>11058154check this if you can read subspecie:>>11058155
 >> Anonymous Mon Oct 14 08:17:22 2019 No.11058163 >>11058155What is the value of 'n'? You need to fix 'n' to a specific value, then your argument falls apart.
 >> Anonymous Mon Oct 14 08:17:26 2019 No.11058164 >>110581591/(10^inf) = 0no problemo
 >> Anonymous Mon Oct 14 08:18:20 2019 No.11058165 >>11058164lol hahahahahahahaha ok, so 1/0=10^infinity?
 >> Anonymous Mon Oct 14 08:20:29 2019 No.11058172 >>110581651/0 = undefined10^infinity = infso, not the same
 >> Anonymous Mon Oct 14 08:21:05 2019 No.11058173 >>11058163n is the largest number, it is just to illustrate the difference between 1 and 0.999..., it's infinatly small but existant.
 >> Anonymous Mon Oct 14 08:22:07 2019 No.11058174 >>11058172so how isn't 1/10^n also not undifined
 >> Anonymous Mon Oct 14 08:22:17 2019 No.11058175 >>11058173>largest numberno such thing
 >> Anonymous Mon Oct 14 08:23:19 2019 No.11058177
 >> Anonymous Mon Oct 14 08:25:28 2019 No.11058179 >>11052399absolute madmannever saw it proven that way, for some reason, really nice
 >> Anonymous Mon Oct 14 08:26:07 2019 No.11058182 >>11058173>n is the largest number WTF? What is "the largest number"???Please pick it, then add one to it, and what is the new number called?? "the largest number PLUS one?"
 >> Anonymous Mon Oct 14 08:26:32 2019 No.11058183 >>11058175yes becuase infinity is undifined but obs that means we still know that the number im talking about is not zero
 >> Anonymous Mon Oct 14 08:27:34 2019 No.11058185 >>11058177infinity
 >> Anonymous Mon Oct 14 08:28:37 2019 No.11058189 >>11058182try adding one to infinity you fucking pleb
 >> Anonymous Mon Oct 14 08:28:58 2019 No.11058190 >>11058183>infinity is undifinednopeDefinition is:An unbounded quantity that is greater than every real number.
 >> Anonymous Mon Oct 14 08:30:04 2019 No.11058192 >>11058189but inf isn't a number
 >> Anonymous Mon Oct 14 08:30:06 2019 No.11058193 >>11058190Omg are you stupid?Yes it has a definition but it is not a defined NUMBER.
 >> Anonymous Mon Oct 14 08:31:08 2019 No.11058195 >>110581851/inf = 0
 >> Anonymous Mon Oct 14 08:31:08 2019 No.11058196 >>11058192Ok so?
 >> Anonymous Mon Oct 14 08:32:13 2019 No.11058198 >>11058195no 0 is the limit, do you think 0*infinity=1?
 >> Anonymous Mon Oct 14 08:32:14 2019 No.11058199 >>11058193so?
 >> Anonymous Mon Oct 14 08:33:18 2019 No.11058201 >>11058196inf isn't the largest number
 >> Anonymous Mon Oct 14 08:33:35 2019 No.11058203 >>11058199So it is undefined
 >> Anonymous Mon Oct 14 08:34:19 2019 No.11058206 >>110581980*inf is undefined
 >> Anonymous Mon Oct 14 08:34:37 2019 No.11058207 >>11058201what is?
 >> Anonymous Mon Oct 14 08:34:42 2019 No.11058208 >>11058185>infinityinfinity is not a number, it is an idea.There are lots of infinities and they differ greatly in size. There are in infinite number of natural numbers, but there are far more irrational numbers than natural numbers.
 >> Anonymous Mon Oct 14 08:36:01 2019 No.11058211 >>11058203>Yes it has a definition>it is undefinedhurr durrpick your lane
 >> Anonymous Mon Oct 14 08:36:29 2019 No.11058212 >>11058206ok so 1/infinity=0 exactly but 1/0=is not infinity and 0*infinity is undifined is what you are saying?
 >> Anonymous Mon Oct 14 08:37:04 2019 No.11058214
 >> Anonymous Mon Oct 14 08:37:33 2019 No.11058216 >>11058208ok so i can't use it to prove that the diffrence between 1 and 0.999... is real only very small because the number doesn't have a exact value?
 >> Anonymous Mon Oct 14 08:38:18 2019 No.11058219 >>110582121/0 undefined0*infinity undefined1/inf = 0
 >> Anonymous Mon Oct 14 08:38:51 2019 No.11058220 >>11058211Ok einstein tell me, what is infinity?exactly in numbers if it is a defined number?
 >> Anonymous Mon Oct 14 08:40:14 2019 No.11058225 >>11058214ok so lets say i have a number bigger than all other numbers and it is because i say so, it has this symbol ∞
 >> Anonymous Mon Oct 14 08:41:20 2019 No.11058227 >>11058216>diffrence between 1 and 0.999...Infinitesimal, which by definition isn't real
 >> Anonymous Mon Oct 14 08:41:42 2019 No.11058229 >>11058219Well I can only disagree, if you would divide an apple in to infinitly small parts they would just be that, infinetly small parts, not non existant.
 >> Anonymous Mon Oct 14 08:42:44 2019 No.11058231 >>11058227wow it's like we are talking about surreal numbers.
 >> Anonymous Mon Oct 14 08:43:57 2019 No.11058233 >>11058225nope, the definition is at >>11058190
 >> Anonymous Mon Oct 14 08:45:04 2019 No.11058235 >>11058229ignorance is bliss
 >> Anonymous Mon Oct 14 08:46:01 2019 No.11058237 >>11058233I don't understand what you are trying to say?Are you annoyed because I didn't pick you definition you looked up?
 >> Anonymous Mon Oct 14 08:47:03 2019 No.11058238 >>11058235Funny but you can't prove shit either so really I can say the same thing in your book.
 >> Anonymous Mon Oct 14 08:49:02 2019 No.11058240 >>11058237Your definition is flawed because it claims that inf is a number.The definition at >>11058190 results in infinity NOT being a number.
 >> Anonymous Mon Oct 14 08:49:09 2019 No.11058241 >>11058231>surreal numbers.Yes, EXACTLY, you have NO physical means of understanding infinity, it is an idea.ONE is easy to understand you can hold one object, you can easily understand a million or even a billion, but infinite is far beyond common understanding. It is not just a "Really really big number", it is far larger than that.
 >> Anonymous Mon Oct 14 08:49:19 2019 No.11058242 File: 256 KB, 768x960, 1568511972774.jpg [View same] [iqdb] [saucenao] [google] [report] >mfw all the people here trying to "prove" 0.99.. = 1 using infinite series and rephrasing the problem in many ways>mfw they all fail to see that the core of the disagreement stems from whether or not we allow infinitesimals, and that the real numbers by their definition don't allow infinitesimals.> mfw my 3 effortposts explaining all this in detail and proving that 0.999... = 1, get 0 replies.>mfw 99% people here don't realize the core of their disagreement stems from difference in definition of what 0.999... is, or lack of definition altogether.>mfw a sizeable portion of people here think they're arguing about maths and not notation, and think this is what maths is aboutjust kill me already
 >> Anonymous Mon Oct 14 08:50:20 2019 No.11058244 >>11058240It is a number, a undifined number.
 >> Anonymous Mon Oct 14 08:51:12 2019 No.11058246 >>11057364t. low IQ animal who can't grasp basic mathematical abstractions
 >> Anonymous Mon Oct 14 08:51:22 2019 No.11058247 >>11058241Yes so the distance between 0.999... and 1 is surreal (not real) and therefor maybe it doesn't apply the same rules as 1 and 2
 >> Anonymous Mon Oct 14 08:53:39 2019 No.11058250
 >> Anonymous Mon Oct 14 08:54:43 2019 No.11058251 >>11058244if it's undefined, it isn't anything
 >> Anonymous Mon Oct 14 08:55:23 2019 No.11058252 File: 42 KB, 591x570, b0a.jpg [View same] [iqdb] [saucenao] [google] [report] Alright. I will provide the answer, if I must.infinity = 1/(1/(1-0.99...))infinity != 1/0.'. 1!=0.99....
 >> Anonymous Mon Oct 14 08:55:31 2019 No.11058254 >>11058247Define what you mean by 0.999..., faggot.
 >> Anonymous Mon Oct 14 08:55:51 2019 No.11058255
 >> Anonymous Mon Oct 14 08:55:53 2019 No.11058256 >>11058247>so the distance between 0.999... and 1But there is your flaw, there is NO distance between the two. For two numbers to be different there needs to be a value that they differ by. So what is the value that 0.999... differs from 1??
 >> Anonymous Mon Oct 14 08:58:32 2019 No.11058260 >>110582540.999....a zero and dot followed by infinite nines.aka the biggest number smaller than 1
 >> Anonymous Mon Oct 14 08:59:35 2019 No.11058264 >>110582560.000...1
 >> Anonymous Mon Oct 14 09:00:49 2019 No.11058268 >>11058264>0.000...1That is NOT a number.
 >> Anonymous Mon Oct 14 09:01:42 2019 No.11058269 >>11058250What is 0^0? Hint it's one by definition, know your cool calculator seems to disagree so maybe its just a program made to show specific awnsers to certain calculations done by the programmers
 >> Anonymous Mon Oct 14 09:02:44 2019 No.11058271 >>11058268Yes like how infinity isn't and like how 0.999... isn't and how 1/0 isn't and the sqrt(-1)
 >> Anonymous Mon Oct 14 09:05:45 2019 No.11058274 >>110582680.000...1 = 0
 >> Anonymous Mon Oct 14 09:07:34 2019 No.11058276 >>11058271>infinity isn'tok> and like how 0.999... isn't .999... = 1>1/0 isn't ok>sqrt(-1)i
 >> Anonymous Mon Oct 14 09:07:37 2019 No.11058277 >>11058274Prove it, seems like you are just assuming
 >> Anonymous Mon Oct 14 09:09:18 2019 No.11058280 >>110582770.1 = 10^-10.01 = 10^-20.001=10^-3:0.000...1=10^-inf = 0
 >> Anonymous Mon Oct 14 09:12:42 2019 No.11058282 >>11058269depends on how the limit is calculated.doing the limit with x^x is the simplest and gives 1
 >> Anonymous Mon Oct 14 09:13:18 2019 No.11058283 >>110582760.999... is as undifined as infinite and 1/0 and i they all are not real
 >> Anonymous Mon Oct 14 09:14:21 2019 No.11058284 >>11058282?2^2=4 not 1
 >> Anonymous Mon Oct 14 09:15:38 2019 No.11058287 >>11058283>2019>being baffled by a geometric serieskekhttps://en.wikipedia.org/wiki/Geometric_series
 >> Anonymous Mon Oct 14 09:15:43 2019 No.11058288 >>11058280You are just saying it is, you dont prove it.
 >> Anonymous Mon Oct 14 09:16:42 2019 No.11058292 >>11058284awww it's retarded
 >> Anonymous Mon Oct 14 09:18:09 2019 No.11058295 >>11058288ok hun
 >> Anonymous Mon Oct 14 09:20:53 2019 No.11058300 >>11058292Ok whatever you say but 0^0=1 and your calculator that obs doesnt know that maybe could be subjektive like you
 >> Anonymous Mon Oct 14 09:22:08 2019 No.11058303 >>11058300thanks ESL, that laugh felt good
 >> Anonymous Mon Oct 14 09:23:08 2019 No.11058304 >>11058287Wow im so baffled i haven’t sen this a houndred Times and it is a theory at most since there is no proof of it.
 >> Anonymous Mon Oct 14 09:44:48 2019 No.11058333 >>11058304>i can't read so books don't existoh i am laffin
 >> Anonymous Mon Oct 14 10:30:13 2019 No.11058408 >>11058274That’s not an infitesimal. That number terminated with a 1, and by extension is a real number.
 >> Anonymous Mon Oct 14 10:36:00 2019 No.11058416 >>11058408anything after ... is irrelevantit's zero
 >> Anonymous Mon Oct 14 10:38:36 2019 No.11058421 >>11058304Mathematical theorems have very rigorous proofs, idiot.https://www.purplemath.com/modules/series7.htmAnd the geometric series is one of the easier things to prove
 >> Anonymous Mon Oct 14 10:41:15 2019 No.11058428 >>11058416My point is that notation is logically incorrect. There is no 0.000...1That “1” at the end is a lie. That, or the “...” is not really infinite. There cannot be both infinite zeros and have the set terminate with a 1. There is no room for that “1” at the end. It’s JUST 0.000...., which is, in fact, 0
 >> Anonymous Mon Oct 14 10:52:11 2019 No.11058450 >>110582881/3 = 0.333....2/3 = 0.666....3/3 = 0.999....3/3 = 1Just because two representations of values *look* different or use different numbers doesn’t mean they *are*. I don’t see anyone arguing that 6/2 =\= 3.0.999... = 1 is just as valid as valid as 3/3 = 1If you cannot see this intuitively, you are just being a brainlet. If you cannot believe rigorous proofs provided, you are just in denial and your intuition betrays you.
 >> Anonymous Mon Oct 14 11:02:20 2019 No.11058465 >>11058450>6/2 =\= 3$\sqrt[]{(-1)^6} \neq (-1)^3$
 >> Anonymous Mon Oct 14 11:14:35 2019 No.11058496 >>11058269>done by the programmersaka actual mathematicians
 >> Anonymous Mon Oct 14 13:11:47 2019 No.11058747 >>11058465That’s stupid Square root X is just X^(1/2)
 >> Anonymous Mon Oct 14 13:14:22 2019 No.11058754 >>11058282Wrong. 0^x is simplest and that limit approaches 0
 >> Anonymous Mon Oct 14 13:46:35 2019 No.11058827 >>11058754x^x is the purest, "just the function & x"
 >> Anonymous Mon Oct 14 13:53:59 2019 No.11058845 >>11058827You are incoherent. Plus, we’re not even talking about “purity”, whatever that means, we are talking about simplicity, and a constant raised to a variable is simpler than a variable raised to a variable
 >> Anonymous Mon Oct 14 14:08:28 2019 No.11058873 >>11058242your post is good and completely correct.
 >> Anonymous Mon Oct 14 14:12:16 2019 No.11058886 >>11058845bs, that hand-picked zero is biasing it
 >> Anonymous Mon Oct 14 14:29:08 2019 No.11058915 >>11058142>then 0.00009 etc.>then 0.00009 etc.>etc.You do not go full infinitesimal.Your argument is brainlet mode.Get BTFO.
 >> Anonymous Mon Oct 14 14:30:23 2019 No.11058916 >>11058242Your post is gay and completely heteromathematical.
 >> Anonymous Mon Oct 14 14:49:16 2019 No.11058951 File: 1.52 MB, 2000x2264, 1565750750437.jpg [View same] [iqdb] [saucenao] [google] [report] >tfw posting about the inane fundamentals to thwart orthodoxy and make the scientifically indoctrinated enlightened to the nature of logic and reasoning itself. Infinity is stipulated, what other systems can be stipulated, and what unexplored worlds do they give rise to? Perhaps there exists one that approximates reality even closer than the current consensus... who knows?
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