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# /sci/ - Science & Math

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Alright, alright.

Let's settle this as adults with a compromise, now everybody wins!

 >> Anonymous Tue Feb 5 16:52:51 2019 No.10360444 >>10360371In certain circumstances such a limit can make a difference (like in 'chaos theory' some attractors have infinitessimal divisions and can strictly be affected by infinitessimal errors), but for any level of error you want 0.999... will equal 1
 >> Anonymous Tue Feb 5 16:56:25 2019 No.10360460 File: 44 KB, 948x264, 1549401917361.png [View same] [iqdb] [saucenao] [google] [report] >>10360371there will be no compromises. this is a mathematical truth
 >> Anonymous Tue Feb 5 16:56:26 2019 No.10360461 >>10360371Infinitesimals are a trash meme.
 >> Anonymous Tue Feb 5 16:59:21 2019 No.10360476 >>10360460you drive a hard bargain
 >> Anonymous Tue Feb 5 17:00:38 2019 No.10360483 >>10360460high iq thread
 >> Anonymous Tue Feb 5 17:31:45 2019 No.10360588 >>10360460>>10360371both are true
 >> Anonymous Tue Feb 5 17:47:49 2019 No.10360657 File: 14 KB, 200x300, 1493689384887.jpg [View same] [iqdb] [saucenao] [google] [report] >>10360371not so fast
 >> Anonymous Tue Feb 5 23:25:18 2019 No.10361510 >>10360460based
 >> Prof Sai Tue Feb 5 23:30:38 2019 No.10361516 File: 6 KB, 618x175, SlopeProof.png [View same] [iqdb] [saucenao] [google] [report] Infinitesimals are real and a recognized part of mathematics. People who argue that .999... = 1 are arguing from authority and can't really think mathematically on their own.https://www.youtube.com/watch?v=WYijIV5JrKg
 >> Anonymous Tue Feb 5 23:49:14 2019 No.10361540 >>10361516I can think mathematically on their own, and I get the thing why mathematician choose the real over hyperreal when constructing topology on hyperreal
 >> Anonymous Tue Feb 5 23:50:45 2019 No.10361543 >>10360371$1 = \dfrac{3}{3} = 3 \cdot \dfrac{1}{3} = 3 \cdot 0.\bar{3} = 0.\bar{9}$
 >> Prof Sai Tue Feb 5 23:55:38 2019 No.10361554 >>10361543This is the stupidest proof. If you didn't notice the assumption that 1/3 = .333... then that is what I mean by "can't think mathematically on their own."
 >> Prof Sai Wed Feb 6 00:03:13 2019 No.10361565 >>10361540>I get the thing why mathematician choose the real over hyperreal when constructing topology on hyperrealIf you choose the Natural over the Real set, you can 'prove' that 1/2 = 0. I can name a situation where this is the correct answer, but that doesn't mean it is reasnable to assume 1/2 = 0 in all cases.
 >> Anonymous Wed Feb 6 00:06:49 2019 No.10361576
 >> Anonymous Wed Feb 6 00:09:59 2019 No.10361584 >>10361576I'm your side but nigga wtf
 >> Anonymous Wed Feb 6 00:11:48 2019 No.10361589 >>10361554hey prof sai got a questionthen what is (2-.999...)/.999... ?
 >> Anonymous Wed Feb 6 00:14:05 2019 No.10361591 >>10361584>I'm your sideok this is legendary
 >> Anonymous Wed Feb 6 00:16:50 2019 No.10361599 >>103615541/3 = 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 Wed Feb 6 00:20:54 2019 No.10361607 >>10360371Such a statement can only be proven or disproven with a real-world observation, some way of observing this mathematical truth before us. 0.999... what is that exactly? Well, for every n length stick, there’s another stick beside it that has n-1 length. So, a stick of length 10 is beside a stick of length 9. 9/10, 99/100, 999/1000, and so on. The sticks are defined as being different. The fraction is always n-1/n. The second stick never catches up. 0.999... < 1
 >> Anonymous Wed Feb 6 00:22:32 2019 No.10361611 >>10361599>1/inf = 0Right, because a stick of length 1 will some day become absolutely nothing as long as you compare it to a stick of infinite length.
 >> Anonymous Wed Feb 6 00:29:50 2019 No.10361636
 >> Anonymous Wed Feb 6 00:32:35 2019 No.10361646 >>10361611>stick of length 1actually, any real number(graham's number^graham's number)/inf = 0 too
 >> Anonymous Wed Feb 6 00:38:48 2019 No.10361655 >>10361607x = 0.9...10x = 9.9...9x = 9.0...x = 1 = 0.9...
 >> Anonymous Wed Feb 6 00:41:25 2019 No.10361656 >>10361655>a variable can be made equal to a non-terminating ratio>non-terminating ratios can somehow be added to one another >non-terminating ratios can be multiplied by integersI’m gonna need some proof pal
 >> Anonymous Wed Feb 6 00:42:55 2019 No.10361657 >>10361656What is 9.999.../10 ?Is it <1, =1 or >1 ?
 >> Anonymous Wed Feb 6 00:44:01 2019 No.10361659 Two walls. 1 is fixed in place. The other wall approaches the first, covering 9/10 distance between them with each movement. The walls will never meet, because 9/10 will never equal 10/10. There will always be a gap between the walls. Keep zooming in, and it will be as if you have made no progress.
 >> Anonymous Wed Feb 6 00:45:05 2019 No.10361662 >>10361659call it peaches
 >> Anonymous Wed Feb 6 00:49:22 2019 No.10361665 >>10361657What is 9.999...? How is it any different from the examples given >>10361607>>10361659The 0.999... denotes a ratio that, to me, never becomes equal to 1.
 >> Anonymous Wed Feb 6 01:01:23 2019 No.10361675 >>10361665Is it <1, =1 or >1
 >> Anonymous Wed Feb 6 01:02:03 2019 No.10361676 >>10361675It never reaches 1. It will always be less than 1
 >> Anonymous Wed Feb 6 01:04:12 2019 No.10361681 >>10361676ok so you agree that the answer is 0.somethingnext question:Is it <0.9, =0.9 or >0.9
 >> Anonymous Wed Feb 6 01:07:56 2019 No.10361688 >>10360588How the fuck is that true?
 >> Prof Sai Wed Feb 6 01:09:05 2019 No.10361691 File: 115 KB, 437x640, Pope Real set.jpg [View same] [iqdb] [saucenao] [google] [report] Every proof of 1=.999... ultimately has the same flaw:The set of Real numbers was specifically designed to exclude non-zero infinitesimals. As a result, any proof involving the Real set assumes the conclusion you are trying to prove. Infinitesimals don't exist in the Reals for the same reason that fractions don't exist in the Integers. This is the OPPOSITE of a proof. As the video I linked to above shows, infinitesimals have been important since Issac Newton's time. There was an emotional need to deny them for a while, but for serious maths, that is over now. Anyone questioning 1=.999... is thinking about infinitesimals. Responding with "proofs" based on real numbers is obnoxious and undermines people's faith in math and science. It needs to stop.
 >> Anonymous Wed Feb 6 01:11:36 2019 No.10361698 >>10361691>exclude non-zero infinitesimalsduh, that's why we talk about limits if you stick to R
 >> Prof Sai Wed Feb 6 01:12:15 2019 No.10361699 >>10361589.999...
 >> Anonymous Wed Feb 6 01:12:58 2019 No.10361701 >>10361681It can certainly be greater than 0.9.
 >> Anonymous Wed Feb 6 01:14:15 2019 No.10361705 >>10361701ok so you agree that the answer is0.9somethingnext question:Is it <0.99, =0.99 or >0.99
 >> Prof Sai Wed Feb 6 01:14:15 2019 No.10361706 >>10361698>that's why we talk about limits if you stick to RYes, that is what Dr James Grime says in the video. We invented limits (and the Real set) so that we wouldn't have to talk about infinitesimals any more.https://www.youtube.com/watch?v=WYijIV5JrKg
 >> Anonymous Wed Feb 6 01:16:11 2019 No.10361708 0.0 = 00.3... = 1/30.6... = 2/30.9... = 3/3 = 1
 >> Prof Sai Wed Feb 6 01:16:22 2019 No.10361709 >>10361705>Is it <0.99, =0.99 or >0.99Are you trying to use Zeno's paradox as a proof? If you ask an infinite number of questions an endless number of falsehoods will add up to the truth?
 >> Prof Sai Wed Feb 6 01:16:58 2019 No.10361710 >>10361708>0.0 = 0>0.3... = 1/3>0.6... = 2/3>0.9... = 3/3 = 1Prove it.
 >> Anonymous Wed Feb 6 01:17:44 2019 No.10361712 >>10360371Suppose
 >> Anonymous Wed Feb 6 01:21:39 2019 No.10361723 >>10361705This isn’t going anywhere. 0.999... is greater than all terminating values between 0 and 1 but always less than 1. By definition, 0.999... is a ratio that never approaches 1. n-1 will never reach n.
 >> Anonymous Wed Feb 6 01:23:19 2019 No.10361725 >>10361709are you going to answer?
 >> Anonymous Wed Feb 6 01:24:43 2019 No.10361726 0.99 != 1Our number system cannot properly represent 1/3
 >> Prof Sai Wed Feb 6 01:26:46 2019 No.10361730 >>10361725I'm not the poster you asked, so no.
 >> Prof Sai Wed Feb 6 01:27:27 2019 No.10361732 >>103617261/3 = .1 (base 3)
 >> Anonymous Wed Feb 6 01:35:24 2019 No.10361749 1 is the LIMIT of 0.999...It is the same principle as an asymptote. Take the graph 1/x. As x gets infinitely larger, it approaches zero, but never actually touches the x-axis. You can zoom in on the graph for an infinite amount of time and the graph will always be above the x-axis. How is this so hard to understand?
 >> Anonymous Wed Feb 6 02:25:28 2019 No.10361843 >>10361723are you going to answer?
 >> Anonymous Wed Feb 6 02:37:35 2019 No.10361864 one of my professors asked if we could find a number that was between .9999... and 1. one of the fundamental axioms, between any two unique numbers a and b, there exists a unique c between them.
 >> Anonymous Wed Feb 6 02:39:12 2019 No.10361868 >>10361516>can't really think mathematically on their own.>links a memephile video
 >> Anonymous Wed Feb 6 02:42:30 2019 No.10361872 >>10361699...wut?How can a number >1 divided by a number <1 be less than 1?I don't think it's one, but .999... ain't it chief. IMO the expression is irreducible.
 >> Anonymous Wed Feb 6 02:46:28 2019 No.10361878 >>10361864.999.../10+.9ez mode
 >> Anonymous Wed Feb 6 02:49:53 2019 No.10361884 File: 17 KB, 400x400, 1508386795971.jpg [View same] [iqdb] [saucenao] [google] [report] >>10361864>one of the fundamental axioms, between any two unique numbers a and b, there exists a unique c between them.>.999... is a number>infinity is a number
 >> Anonymous Wed Feb 6 02:51:02 2019 No.10361885 >>10361878how is that >0.9... ?
 >> Anonymous Wed Feb 6 02:52:06 2019 No.10361886 >>10361884>infinity is a numberno it isn't
 >> Anonymous Wed Feb 6 02:54:26 2019 No.10361890 >>10361749the expression $\sum_{n=0}^{\infty}a_n$ actually means two things: the series itself and its limit (when it converges), while it's usually clear from the context what is meant. it's a completely harmless abuse of notation, and otherwise it wouldn't really make sense to write $\sum_{n=0}^{\infty}a_n = 3$ for example. whenever you treat the symbol $0.999...$ as a number (e.g. you compare it to other numbers), it actually stands for $1$.
 >> Anonymous Wed Feb 6 03:06:00 2019 No.10361904 >>10361886That's the point. .999.... is just a representation for the limit of a particular series. Just like infinity is.I brought up infinity because it's the easiest analogy that shows how it can't be compared to a real number.
 >> Anonymous Wed Feb 6 03:16:31 2019 No.10361913 >>10361904amount of digits =/= valueexample: 1.000....
 >> Anonymous Wed Feb 6 03:24:02 2019 No.10361926 >>10361913The difference is that 1.000 is completely consistent with the series 1+0+0+0...Are you not aware that treating the series 9/10+9/100+9/1000... as 1 does not always yield the same results?
 >> Anonymous Wed Feb 6 03:35:23 2019 No.10361947 x = 0.9...10x = 9.9...9x = 9.0...x = 1 = 0.9...
 >> Anonymous Wed Feb 6 03:49:50 2019 No.10361968 >>10361947>10x = 9.9...>9x = 9.0...This is wrong. 9x=9 + 9*(.1)*(.1)*(.1)....Why are mathematicians so bad at understanding infinite series?
 >> Anonymous Wed Feb 6 03:53:24 2019 No.10361972 >>10361968Sorry,9x=9 - 9*(.1)*(.1)*(.1)....
 >> Anonymous Wed Feb 6 03:54:18 2019 No.10361975 >>10361968>mathematicians so badunlike shitposters?kek
 >> Anonymous Wed Feb 6 03:59:10 2019 No.10361981 >>10361975I'm feeling pretty good about my stance if that's your argument.
 >> Anonymous Wed Feb 6 04:07:15 2019 No.10361996 >>10361981never met a crazy who wasn't
 >> Anonymous Wed Feb 6 04:12:20 2019 No.10362000 >>10361996Why are you scared, brainlet?
 >> Anonymous Wed Feb 6 04:35:32 2019 No.10362031 >>103619729x=9+0.1^inf9x=9+0x=1
 >> Anonymous Wed Feb 6 04:46:13 2019 No.10362044 >>10362031>9x=9+0.1^inf>9x=9+0prove it. Matter of fact>0.1^inf*10^inf==0*10^inf>(0.1*10)^inf==0>(1)^inf==0>1==0>falsetherefor 0.1^inf!=0Please tell me you already knew you were making a circular argument and just wanted to waste my time.
 >> Anonymous Wed Feb 6 04:57:38 2019 No.10362054
 >> Anonymous Wed Feb 6 05:00:14 2019 No.10362057 >>10362044>0*10^inf0*inf is undefined, mr crazy
 >> Anonymous Wed Feb 6 05:31:31 2019 No.10362094 You brain need some language because your minds are tired of numbers and wibbily letters.A number that is ultra close to one is less than one and despite how infinitely close to one it is, it is not one! This is also known as 0.999...<1
 >> Anonymous Wed Feb 6 05:32:39 2019 No.10362096 >>10362094this post would be cooler if i didn't botch the first two words
 >> Anonymous Wed Feb 6 05:50:55 2019 No.10362117 >>10362094>infinitely close0 distance, so 0.9...=1
 >> Anonymous Wed Feb 6 06:50:00 2019 No.10362174 >>10360444nope
 >> Anonymous Wed Feb 6 06:52:05 2019 No.10362178 >>10361656>non terminating ratios can be multiplied by integers>he doesn't know that the distributive property is one of the axioms>mfw
 >> Anonymous Wed Feb 6 06:52:48 2019 No.10362179 File: 112 KB, 953x613, 1542054335766.jpg [View same] [iqdb] [saucenao] [google] [report]
 >> Anonymous Wed Feb 6 07:25:30 2019 No.10362219 .999...≠1
 >> Anonymous Wed Feb 6 07:27:58 2019 No.10362222
 >> Anonymous Wed Feb 6 07:56:00 2019 No.10362272 >>10362222The image is correct. The bottom left with green ground :>A simple proof of induction:>x = 0.999...>10x = 9.999...>10x - x = 9.999... - 0.999...>9x = 9False; 9x = 8.999...
 >> Anonymous Wed Feb 6 07:57:02 2019 No.10362276 >>10362272>correct*Incorrect*
 >> Anonymous Wed Feb 6 08:15:02 2019 No.10362296 >>10362272 (Addendum, for shitposters)>x = 0.999..>9x = 8.999...because its a infinitely repeating the trailing 1 is never reached. If it wasn't infinite then:>n = 0.999>2n = 1.998>3n = 2.997>...>9n = 8.991
 >> Anonymous Wed Feb 6 08:28:43 2019 No.10362314 There are so many proofs of this is it silly people still argue against it.
 >> Anonymous Wed Feb 6 08:31:41 2019 No.10362320 >>10362314"people"
 >> Anonymous Wed Feb 6 08:34:07 2019 No.10362325 >>10361688they are both true because they say "less than or equal to" and "greater than or equal to". Since the answer is "exactly equal to" they are both true.
 >> Anonymous Wed Feb 6 08:38:20 2019 No.10362333 File: 7 KB, 274x290, Oy+vey+shekels+mah+shekels+_4525f0b974d66219703e161fa294167b.png [View same] [iqdb] [saucenao] [google] [report] so if i am to send you BTC for your proofs, should i send you 1 million x 1 BTC or 1 million x 0.999.. BTC?
 >> Anonymous Wed Feb 6 08:42:12 2019 No.10362342 Imagine not being able to conceptualize why .9999999999... is exactly equal to 1This is why we look down on engicucks
 >> Anonymous Wed Feb 6 08:44:05 2019 No.10362345 >>10361710Prove what? that 1/3 is 0.333...?Just divide by hand yourself.
 >> Anonymous Wed Feb 6 08:45:56 2019 No.10362349 >>10360371π>3.14159265>3.1415927>3.141593>3.141590>3.1416>3.142>3.10>3.0>3π = 3
 >> Anonymous Wed Feb 6 08:46:30 2019 No.10362350 >>10361749There is no "limit" of 0.999... 0.999... is the limit of the sum 9/10**n and if that equals 1, then 0.999... equals 1.
 >> Anonymous Wed Feb 6 08:48:58 2019 No.10362356 >>10362349Great, you're doing the process backwards
 >> Anonymous Wed Feb 6 08:59:20 2019 No.10362378 >>10361611>moves goal posts
 >> Anonymous Wed Feb 6 09:15:02 2019 No.10362414 >>10362333It's the same, so who cares?
 >> Anonymous Wed Feb 6 09:16:57 2019 No.10362418 >0.9... = 1 This is crazy.0.9... = 1 = 0.9... + 0.1... 1 - 0.1... = 10.1... = 00.1... + 0.1... = 0I'm still not buying anyone could believe the above.
 >> Anonymous Wed Feb 6 09:18:28 2019 No.10362421 >>10362418>0.9... = 1 = 0.9... + 0.1... What the fuck are you doing?And don't play the "I was just pretending to be retarded" card.
 >> Anonymous Wed Feb 6 09:23:22 2019 No.10362432 Two real numbers a, b are equal IFF there does not exist a real number c such that a < c < bLet a = .999999999999999999999999...Let b = 1Find a c such that .999999999999999999999999999999... < c < 1Oh wait, you can't.Therefore .999... = 1Its literally that simple and if you don't understand this you are certified retarded
 >> Anonymous Wed Feb 6 09:24:49 2019 No.10362433 >>10362432>b-b-buh 0.999...995 dude
 >> Anonymous Wed Feb 6 09:28:31 2019 No.10362442 >real numbers ah yes the cruel joke of modern mathematics.
 >> Anonymous Wed Feb 6 09:32:03 2019 No.10362448 >>10362442The reals are well defined and objectively exist.You are a certified retardo
 >> Anonymous Wed Feb 6 09:32:36 2019 No.10362449 >>10362448if you say so guy
 >> Anonymous Wed Feb 6 09:33:57 2019 No.10362451 >>10362449It's not "me" saying so there are shitloads of proofs for this.Tell me 1 reason how the reals aren't well defined or what the problem is with them. "I don't like uncountability or the idea of infinite processes" is not an answer
 >> Anonymous Wed Feb 6 09:38:29 2019 No.10362461 >>10360371>"An irrational number is a rational number"Uuuuhhhh... okay buddy
 >> Anonymous Wed Feb 6 09:42:41 2019 No.10362467 >>10362421Well 0.9... + 0.1... = 1 and if like people are arguing in this thread 0.9... = 1 then 0.1... = 0 so 0.1... + 0.1... = 0 also 1 - 0.1... = 1 This 0.1... = 0 is what everyone is arguing in support of aka every number equals zero.
 >> Anonymous Wed Feb 6 09:47:32 2019 No.10362478 >>10362418>0.9... = 1 = 0.9... + 0.1...0.9... = 1 =/= 0.9... + 0.1... = 10/9>1 - 0.1... = 11 - 0.1... =/= 11 - 0.1... = 8/9>0.1... = 0wew lad>0.1... + 0.1... = 0sigh
 >> Anonymous Wed Feb 6 09:49:42 2019 No.10362483 >>103624610.9... is an integer
 >> Anonymous Wed Feb 6 09:51:16 2019 No.10362485 >>10362467>also 1 - 0.1... = 1That's a mistake, I forgot 0.9... = 1 in this thread so 1 - 0.1... = 0
 >> Anonymous Wed Feb 6 09:56:25 2019 No.10362492 >>10362478>0.9... = 1 =/= 0.9... + 0.1... = 10/90.9... ≠ 10.9... + 0.1... = 1Not according to people in this thread but according to reality.
 >> Anonymous Wed Feb 6 10:21:28 2019 No.10362541 >>10362432A small contraption is 1 meter long. At one end is an infinitely thin metal sheet. 0.1 meter away from it, is another metal sheet. 0.01 meter away from it is another metal sheet, and so on. The sum of the distances are then 0.9 + 0.09 + 0.009... etc for infinity. For every terminating number, it will be surpassed by the sum. Yet the sum never reaches 1, because each successive sheet will always be 1/10 distance away from the last sheet. The sheets never touch.
 >> Anonymous Wed Feb 6 10:35:33 2019 No.10362570 0.9... =/= 1Because0.9... + 0.1... = 1.0...>symbol test, there should be a guide on what is filtered Not equal ≠Therefore ∴Because ∵
 >> Anonymous Wed Feb 6 10:41:06 2019 No.10362578 >>10362541>inb4 the sheets magically touch “at infinity”The gap cannot be eliminated. Each section is only different in size. The 9/10 is consistent, and never reaches 10/10. 0.999... is less than 1
 >> Anonymous Wed Feb 6 10:52:09 2019 No.10362607 ITT a bunch of retards claiming 1≠0.999...what a sad state of affairs
 >> Anonymous Wed Feb 6 11:10:35 2019 No.10362645 >>10362570No. On finite lengths of 0.999... adding a 1 to the last digit starts a cascade of carrying over that causes each digit to flip from 9 to 0 and send the 1 to the next digit.For example 0.9999 + 0.0001 = 0.9990 + 0.001 = 0.9900 + 0.01 ... until the 1 rests at the unit digit and the sum equals 1.0000.Now if you extend the trail of 9s infinitely, logically you have to add a 1 digit to the last digit which if infinitely far out in order to get 1. You are adding 1 to every digit meaning there is an extra 1 at every digit except the units digit, so your sum gets 1.11... .The number you have to add is a string of 0s ending with a 1 infinitely far to the right. Now what is that number?
 >> Anonymous Wed Feb 6 11:52:57 2019 No.10362750 >>10362492>people in this threadyou're confusing that with the voices in your head
 >> Anonymous Wed Feb 6 11:56:49 2019 No.10362756 >>10362570>0.9... + 0.1... = 1.0...0.9+0.1=10.09+0.01=0.1etc0.9... + 0.1... = 1.1...1 + 1/9 = 10/9
 >> Anonymous Wed Feb 6 11:59:30 2019 No.10362768 File: 216 KB, 473x477, Screenshot_20190206-115733_Google.jpg [View same] [iqdb] [saucenao] [google] [report]
 >> Anonymous Wed Feb 6 12:06:26 2019 No.10362783 The definition of the reals in terms of the rationals tells us that two reals are equal if their distance is smaller than any positive rational number. 0,000...1 is not a rational number, so 0.999... and 1 are the same real number. They are not the same surreal number, if one wants to explore the consequences of their inequality.
 >> Anonymous Wed Feb 6 12:25:27 2019 No.10362825 Between any two different real numbers, one can take their average, which will be a different real number. So if a
 >> Anonymous Wed Feb 6 12:34:22 2019 No.10362849
 >> Anonymous Wed Feb 6 12:38:29 2019 No.10362863 >>10362492>0.999... + 0.111.. = 1stoopid
 >> Anonymous Wed Feb 6 13:29:44 2019 No.10362976 0.9 + 0.1 = 10.99 + 0.01 = 1...0.999...9 + 0.000...1 = 1
 >> Anonymous Wed Feb 6 13:40:54 2019 No.10363000 >>10362976>0.999...9 + 0.000...1 = 11+0=1
 >> Anonymous Wed Feb 6 13:46:36 2019 No.10363016 >>10362976What's your point?
 >> Anonymous Wed Feb 6 13:47:42 2019 No.10363019 File: 37 KB, 586x578, 1519134466886.png [View same] [iqdb] [saucenao] [google] [report] >>10362057>0*inf is undefinedfucking idiot lmao0*inf0*(10*10*10....)0*10*0*10*0*10...=0>>10362054this isn't a better argument than when it was posted beforeIf you wanted to say 0 or 1, then why don't you just say 0 or 1 you fucking mongrels. An infinite series is not necessarily the same as a real number just because it converges.
 >> Anonymous Wed Feb 6 13:50:51 2019 No.10363028 >>10362314*so many incorrect proofsmeanwhile there are extremely simple numerical counterexamples showing it can't possible be equal to 1.
 >> Anonymous Wed Feb 6 13:52:53 2019 No.10363033 >>10362432>a>real numberwhy can't mathlets use brain?
 >> Anonymous Wed Feb 6 13:53:33 2019 No.10363034 File: 98 KB, 500x282, Wrong ding dong.gif [View same] [iqdb] [saucenao] [google] [report]
 >> Anonymous Wed Feb 6 13:55:31 2019 No.10363039 >>10362578>t. I can't into limits
 >> Anonymous Wed Feb 6 13:57:56 2019 No.10363048 File: 545 KB, 572x703, 1537485316059.png [View same] [iqdb] [saucenao] [google] [report] >>10363034An anime reaction image? That's your proof?Look up Bernoulli trials my based brainlet
 >> Anonymous Wed Feb 6 13:59:06 2019 No.10363054 >>10362418>0.1...You mean 0.0...1
 >> Anonymous Wed Feb 6 14:18:29 2019 No.10363109 >>10363039>literally called limit>he thinks it can be reached1 + 1/2 + 1/4... can never equal 1, or else it would then surpass 1. When does the gap close? Keep zooming in, keep zooming in, it’s always there. You can’t make it go away using definitions and axioms. This is real life, bucko. Mathematics would be just as useful and consistent if the concept of infinity were thrown out completely.
 >> Anonymous Wed Feb 6 14:23:21 2019 No.10363120 >>10362849You're a fucking retard and your "argument" using physical beams is literally irrelevant. If this is how you think it's no wonder you can't do math.
 >> Anonymous Wed Feb 6 14:24:42 2019 No.10363124 >>10363109But even supppsing that an infinite sum can exist, then let us call it what it is: infinite. The sum never ends. You cannot say “at infinity the sun = x” because there is no such thing as “at infinity.” This misconception probably stems from mathematical statements like “as x approaches infinity” etc. But x can never get closer to infinity, it will never “reach” infinity. 0.9 is less than 1 just as 0.999.... is. Take two sticks, one being always one meter less than the other, and stretch them both out at a constant rate for as long as you like, the ratio of their lengths will never equal 1. One will always be in front of the other by one meter.
 >> Anonymous Wed Feb 6 14:26:42 2019 No.10363130 >>103630000.000...1 = 0? How can something which obviously is something, be nothing?
 >> Anonymous Wed Feb 6 14:27:46 2019 No.10363134 >>10363120Not an argument. Math doesn’t require infinity to be useful in our world. The idea that pi can be APPROXIMATED using an infinite sum is neat, but we have to remember that circles don’t actually exist, which is why the number is transcendental. Taking the area under a curve should only require infinite sums of you’ve assumed that the graph is in a transcendent space, unlike everything we encounter in reality.
 >> Anonymous Wed Feb 6 14:29:38 2019 No.10363138 >>10363134>Math doesn’t require infinity to be useful in our world.The physical universe is a proper subclass of mathematics so what you're talking about makes literally no sense.This universe isn't discrete btw it is isomorphic to the Continuum so I have no idea what the motivation for what you're saying is anyway.
 >> Anonymous Wed Feb 6 14:30:04 2019 No.10363140 >>9999999we already settled this shit a few months ago
 >> Anonymous Wed Feb 6 14:32:28 2019 No.10363146 >>10363140based & /thread pilled
 >> Anonymous Wed Feb 6 14:35:11 2019 No.10363153 >>10363138Prove that the “continuum” exists. How can we derive infinity from our discrete perceptions?
 >> Anonymous Wed Feb 6 14:43:00 2019 No.10363167 >>10363153>How can we derive infinity from our discrete perceptions?....crickets
 >> Anonymous Wed Feb 6 14:45:43 2019 No.10363177 >>10363130It is the middle ground between things that are something and nothing.
 >> Anonymous Wed Feb 6 14:50:59 2019 No.10363190 >>10363140holyshit
 >> Anonymous Wed Feb 6 14:58:40 2019 No.10363210
 >> Anonymous Wed Feb 6 15:00:49 2019 No.10363215 >>10363019sure, mr crazyhttps://www.wolframalpha.com/input/?i=0*inf
 >> Anonymous Wed Feb 6 15:04:28 2019 No.10363223 >>103631300.1 = 10^-10.01 = 10^-20.001 = 10^-3;0.000...1 = 10^-inf = 0
 >> Anonymous Wed Feb 6 15:06:47 2019 No.10363228 >>10363223>1/ INF = 0>1>0If the universe is infinite, humans don’t actually exist.
 >> Anonymous Wed Feb 6 15:09:47 2019 No.10363235 >>10363153This was proven over a hundred years ago
 >> Anonymous Wed Feb 6 15:11:58 2019 No.10363240 >>10363235Actually it was disproven 50 years ago. Your move, retard
 >> Anonymous Wed Feb 6 15:14:23 2019 No.10363245 >>10363240>Actually it was disproven 50 years agoNo it wasn't. This level of delusion.
 >> Anonymous Wed Feb 6 15:14:40 2019 No.10363249 >>10363240that turned out to be a false alarm
 >> Anonymous Wed Feb 6 15:17:27 2019 No.10363255 If imaginary numbers exist, then why can't infinitesimals?
 >> Anonymous Wed Feb 6 15:17:47 2019 No.10363257 >>10362325this >>10361688let x = 0.9999...so 10*x = 9.999.....now subtract 1*x:10x = 9.999.... | -x9x = 9 | :9x = 1
 >> Anonymous Wed Feb 6 15:19:31 2019 No.10363263 >>10363255no problem, as long as you don't confuse them with real numbers
 >> Anonymous Wed Feb 6 15:24:50 2019 No.10363280 >>10363228>>10363153>>10363134>>10363124>>10363109>>10362541>>10361749>>10361659Not a single one of these posts has been refuted
 >> Anonymous Wed Feb 6 15:29:14 2019 No.10363295 >>10363280because they belong in >>>/x/
 >> Anonymous Wed Feb 6 15:30:48 2019 No.10363297 >>10363295You only embolden my conviction, and offer no evidence to persuade me. You’re the one who believes in something never yet perceived (infinity) yet you claim I belong on a paranormal board.
 >> Anonymous Wed Feb 6 15:32:13 2019 No.10363304 File: 42 KB, 1920x1872, 1920px-GeometricSquares.svg.png [View same] [iqdb] [saucenao] [google] [report] >>10363280fine i'll refute this one>>10363109pic related, there ain't no gaps. pick any point in this unit square, and it's not too hard to find the term in the geometric series would capture that point. therefore the area of this figure is 1 unit squared exactly
 >> Anonymous Wed Feb 6 15:35:46 2019 No.10363313 >>10363297>me me meno one cares, anon
 >> Anonymous Wed Feb 6 15:36:20 2019 No.10363316 >>10363304The purple squares never connect to the corner, or else there would be a finite amount of them. This is only a rehash of the same problem, the logic still applies. It never actually reaches the goal, hence why it’s an INFINITE sum. It never ends.Btw your English is hardly understandable
 >> Anonymous Wed Feb 6 16:09:46 2019 No.10363396 >>10362645>Now what is that number?0.000...1
 >> Anonymous Wed Feb 6 16:20:06 2019 No.10363424 0.9... ≠ 1 ∵ 0.9... + 0.0...1 = 1.0...>>10362645Thanks.>>10363054I do now, thanks.
 >> Anonymous Wed Feb 6 16:34:54 2019 No.10363482 File: 212 KB, 1281x612, Rafael_Sanzio.jpg [View same] [iqdb] [saucenao] [google] [report] You could argue a lot about how $0.99 \dots$ is unclear, how can the dots be very ambiguous and how can one abuse notation. Well, maybe what is needed is to justify and explain notation and representation. To really understand numbers real analysis is needed, so you will lose your time with someone who only knows up to basic algebra because without any fundaments you can talk very few things about numbers and infinity.Now, what is $0.9999999 \dots$ ?[eqn]0. \bar{9} = \frac{9}{10}+\frac{9}{100}+\frac{9}{1000}+\frac{9}{1000}+\frac{9}{10000} \dots[/eqn]That is your answer. If you really want to know what the dots notation mean, how to take "infinity" into account, you would want to know calculus first and deal with the infinite series. But without topology and analysis, even without a hint of set theory and its axiomatizations, how would you say anything of what mathematicians understand of infinity, only with your "intuition" and your misleading use of notation. What is $0.999 \dots$ and does it is equal to $1$? Solve this:[eqn]0. \bar{9} = \sum_{k=1}^{ \infty} \frac{9}{10^k}=x[/eqn]Where $x$ is your proved solution. But if you don't know what a convergences test or what is a geometric series is, you will only argue over your intuitive notion of the symbols and you will not be arguing over math at all. Semiotics is a thing but is not the central thing in math.Nothing in the world, in science, in humanities and even in abstract systems like math should be like you want it to be, in a way that you feel good about. This desire is irrational. You must accept a fair scientific fact, even if you would want things to be different. You should distinguish between what you see and what you want to see and it is not very different if instead of science you are thinking maths."All the truths of mathematics are linked to each other, and all means of discovering them are equally admissible" Adrien-Marie Legendre.
 >> Anonymous Wed Feb 6 19:58:35 2019 No.10364120 >>10362179wrong. if x = 0.999... then 10x is 9.999...0
 >> Anonymous Wed Feb 6 21:30:27 2019 No.10364392 File: 191 KB, 1600x1584, Pole.jpg [View same] [iqdb] [saucenao] [google] [report]
 >> Anonymous Wed Feb 6 21:41:52 2019 No.10364427 >>10364120That would be the case if it wouldn't be .9999... with infinite decimals
 >> Anonymous Wed Feb 6 23:27:58 2019 No.10364601 >>10363316The purple squares always connect to the corner, or else there would be a finite amount of them
 >> Anonymous Thu Feb 7 12:25:42 2019 No.10366156 bump m'gentlemen
 >> Anonymous Thu Feb 7 15:06:46 2019 No.10366575 >>10366156Why would you do such a thing?
 >> Anonymous Thu Feb 7 15:14:09 2019 No.10366588 >>10361607>strict inequalities hold in an infinite limitgonna need to stop you right there.999... <= 1*
 >> Anonymous Thu Feb 7 17:29:28 2019 No.10366972 >>10363257Would actually be something more like10*x=9.999...subtract 1*x9x=9.999... -xIf you subtract things from one side but not another you prolly have some form of autism
 >> Anonymous Thu Feb 7 18:48:03 2019 No.10367188 File: 15 KB, 1025x693, math.png [View same] [iqdb] [saucenao] [google] [report] >>10360371Now go eat a dick OP
 >> Anonymous Thu Feb 7 19:18:49 2019 No.10367261 >>10366972nothing else was done, everything after the | shows what is done in this step in the line 10x = 9.999... | -xnothing has been subtracted yet; the next line (9x = 9) is the result of that step
 >> Anonymous Thu Feb 7 19:47:03 2019 No.10367312 1/9 = 0.111111...2/9 = 0.222222...1/3 = 0.333333....4/9 = 0.444444...5/9 = 0.555555...2/3 = 0.666666...7/9 = 0.777777...8/9 = 0.888888...9/9 = 0.999999...But 9/9 = 1
 >> Anonymous Thu Feb 7 23:55:13 2019 No.10367810 $x= \frac{1}{10} \\0. \overline{9}=9x+9x^2+9x^3+9x^4+ \cdots \\0. \overline{9}=9x \left (1+x+x^2+x^3+ \cdots \right ) \\0. \overline{9}=(1-x) \left (1+\mathbf{x}+x^2+\mathbf{x^3}+x^4+ \cdots \right ) \\0. \overline{9}=1-x+ \mathbf{x-x^2}+x^2-x^3+ \mathbf{x^3-x^4}+x^4-x^5+ \cdots \\0. \overline{9}=1$
 >> Anonymous Fri Feb 8 08:27:04 2019 No.10368624 >>10361540>I can think [...] on their own I have troubling news for you, anon
 >> Anonymous Fri Feb 8 08:44:33 2019 No.10368662 >>10362349pi=e, by the fundamental theorem of engineering
 >> Anonymous Fri Feb 8 09:27:02 2019 No.10368742 >>10360460Based and analysispilled
 >> Anonymous Fri Feb 8 09:28:03 2019 No.10368745 >>10367312It really boggles the peanut
 >> Anonymous Fri Feb 8 09:28:41 2019 No.10368747 >>10361872It's not less than 1 you idiot. That's the point.
 >> Anonymous Fri Feb 8 09:30:25 2019 No.10368749 >>103616910.9999... doesn't mean 1 minus an infinitesimal, you buffoon. It means the limit of the sequence 0.9, 0.99, 0.999, 0.9999, etc.
 >> Anonymous Fri Feb 8 09:32:14 2019 No.10368753 File: 83 KB, 645x614, 1538528044594.png [View same] [iqdb] [saucenao] [google] [report] >>10361749>limit of a number
 >> Anonymous Fri Feb 8 09:33:43 2019 No.10368758 >>10361926>does not always yield the same results?How so?
 >> Anonymous Fri Feb 8 09:35:44 2019 No.10368765 $x = \lim_{x \to 0}$$0.\overline{9} + x = 1$This is my LAST OFFER.
 >> Anonymous Fri Feb 8 18:33:01 2019 No.10370089 File: 8 KB, 320x240, 1548093440688.jpg [View same] [iqdb] [saucenao] [google] [report] >>10360371>1/3 = 0.3333333...>1/3+1/3+1/3=0.9999999... = 1
 >> Anonymous Fri Feb 8 18:35:13 2019 No.10370092 >>10368765oh ok x=0 i’m good with that
 >> Anonymous Fri Feb 8 20:08:12 2019 No.10370351 >>10364601Finitist BTFO
 >> Anonymous Fri Feb 8 20:26:47 2019 No.10370395 Assume there is some fraction that produces 0.9 repeating.1/x = 0.999...1 = x * 0.999...For anything where 1 = xy, the only solutions are that x is plus or minus 1 (it is 1 here) and y is plus or minus 1, (0.999... is our y), it is obvious that 0.999... is not -1, therefore it is 1.
 >> Anonymous Fri Feb 8 20:28:38 2019 No.10370400 >>10370395>Assume there is some fraction that produces 0.9 repeating.There isn't.
 >> Anonymous Fri Feb 8 20:30:57 2019 No.10370407 >>10370400Exactly
 >> Anonymous Fri Feb 8 20:56:10 2019 No.10370465 All men are equal under God.All numbers are equal under infinity.There is only 1 god. There is only 1 infinity.
 >> Anonymous Fri Feb 8 20:59:50 2019 No.10370472   File: 232 KB, 300x300, 1307889832001.png [View same] [iqdb] [saucenao] [google] [report] >>10370395>>10370400$\sum_{n=1}{\infty} \frac{x}{(x+1)^2} = 0.\overline{9}$
 >> Anonymous Fri Feb 8 21:03:29 2019 No.10370479 >>10370465Your infinity can't be bijected with its powerset.
 >> Anonymous Fri Feb 8 21:03:36 2019 No.10370480 File: 232 KB, 300x300, 1307889832001.png [View same] [iqdb] [saucenao] [google] [report] >>10370400>>10370395>>10370407$\sum_{n=1}^{\infty} \frac{x}{(x+1)^n} = 0.\overline{9}$
 >> Anonymous Fri Feb 8 21:05:15 2019 No.10370483 >>10370479Speak english
 >> Anonymous Fri Feb 8 23:20:42 2019 No.10370789 >>10370465>There is only 1 infinity.ridiculous, even in R you have two, +inf and -infUnder C, you have an infinite amount of infinities
 >> Anonymous Fri Feb 8 23:59:12 2019 No.10370839 >>10370789There is no negative infinity. Hell, there is no positive infinity. Its not a number so it doesn't adopt numeral properties. If it were to be treated as a number though, then all real numbers are equidistant from it, and thus equidistant to each other in relation to it. If there was a positive infinity, even the largest negative number would be no further from it than the same number ×-1. As no enumeration will ever reach infinity under any circumstance, it doesn't matter which value you begin incrementing from, and all values are equally nothing compared to infinity, including all known and knowable values collectively. Theres no useful value in a negative infinity. There isn't even really any useful value in positive infinity either. "Something you can never reach even if you try" explicitly defies any sense of value to be extracted from invoking infinity in math.
 >> Anonymous Sat Feb 9 00:18:59 2019 No.10370880   >>10370839infinity is further from the origin than any real number in R this can happen in two ways, 2D and 3D there are infinite waysinf is not a number, but it is big, duh1/inf = 0inf-inf undefinedlim_x->inf of 1^x, = 1 but 1^inf is undefinedinf isn't a number, but that doesn't mean there aren't some things you can do.
 >> Anonymous Sat Feb 9 00:20:41 2019 No.10370882 >>10370839infinity is further from the origin than any real number in R this can happen in two ways, 2D and 3D there are infinite waysinf is not a number, but it is big, duh1/inf = 0inf-inf undefinedlim_x->inf of 1^x = 1, but 1^inf is undefinedinf isn't a number, but that doesn't mean there aren't some things you can do.
 >> Anonymous Sat Feb 9 00:30:01 2019 No.10370906 >>10360371Recurring decimals hold no meaning in a finite universe. Infinity is a false god
 >> Anonymous Sat Feb 9 01:06:42 2019 No.10370981 >>10370882There is no origin in relation to infinity.
 >> Anonymous Sat Feb 9 01:09:49 2019 No.10370990 >>10370981so? Then it works from anywhere.
 >> Anonymous Sat Feb 9 01:12:15 2019 No.10370993   >>10370906$0.333_{10} = 0.1_{3}$
 >> Anonymous Sat Feb 9 01:14:40 2019 No.10370999 >>10370906$0.333..._{10} = 0.1_3$
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