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# /sci/ - Science & Math

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No.12053975 [Reply] [Original] [archived.moe]

Reminder

 >> Anonymous Thu Aug 27 08:06:05 2020 No.12053976 >>12053975>comic sansImmediately disproved.
 >> Anonymous Thu Aug 27 08:06:40 2020 No.12053977 a delicious thread to hide in my facemouth, yum yum yum
 >> Anonymous Thu Aug 27 08:19:14 2020 No.12053998 This argument comes down to whether you want to use the word "equals" when doing limits.
 >> Anonymous Thu Aug 27 08:31:18 2020 No.12054020 Oh man you're SO close to getting it with argument 2, but you still miss it
 >> Anonymous Thu Aug 27 09:48:10 2020 No.12054180 >>12053976>>12053977>>12053998>>12054020>no argumentonetards btfo
 >> Anonymous Thu Aug 27 09:51:32 2020 No.12054187 >no number between 0.999 and 1There’s also no number between 1 and 2.
 >> Anonymous Thu Aug 27 09:53:45 2020 No.12054195 >>12053975>Argument 2: 'onetards' agree with reality (physicists, engineers) not theoreticians, therefore they are wrong....
 >> Anonymous Thu Aug 27 10:33:38 2020 No.12054292 For argument 1, the result is there is a RATIONAL number between any 2 distinct reals. So which two integers is 0.999... a ratio of?
 >> Anonymous Thu Aug 27 10:52:42 2020 No.12054351 >>12054195It's a windup, mate. Read proof#3.
 >> Anonymous Thu Aug 27 11:10:24 2020 No.12054395 >>120539751/3 = 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 Aug 27 11:11:45 2020 No.12054401 >>12053975What is 1/3 in decimal if it’s not .333333...
 >> Anonymous Thu Aug 27 11:16:40 2020 No.12054412 What is the philosophical motivation for this?
 >> Anonymous Thu Aug 27 11:19:47 2020 No.12054424 >>12054412too btfo .9999... retards with one easy trick.3333.... = 1/3.6666.... = 2/31/3 + 2/3 = 1.3333... + .6666.. = 1>noooo 1/3 does not equal .3333... what does it equal then in decimal?
 >> Anonymous Thu Aug 27 11:23:41 2020 No.12054432 >>12054401>>12054424What is pi in decimal? Don't give me a shortened version I want the exact value in decimal
 >> Anonymous Thu Aug 27 11:25:42 2020 No.12054446 >>12054432pi is not repeating dumb fuck. So it can be shorten to .3333... like 1/3
 >> Anonymous Thu Aug 27 11:32:38 2020 No.12054467 >>12054446Can’t I mean
 >> Anonymous Thu Aug 27 11:32:51 2020 No.12054469 >>12054446Wtf are you even saying. You admit that not all numbers have decimal representations then? What is your argument even?
 >> Anonymous Thu Aug 27 11:33:51 2020 No.12054473 >>12054469No not all numbers do like pi can’t really expressed in decimal only rounded. 1/3 can be expressed like .333333....
 >> Anonymous Thu Aug 27 11:43:08 2020 No.12054504 >>12054473>1/3 can be expressed like .333333..Except that's wrong and those are not equal. Circular reasoning is so ingrained in the mentality of onetards that you can't even imagine making a real argument
 >> Anonymous Thu Aug 27 12:30:10 2020 No.12054668 >>12053975>Here the mistake is that 1/3 does not equal 0.333...So what exactly is 0.333... if not the result of dividing 1 by 3?
 >> Anonymous Thu Aug 27 12:32:21 2020 No.12054674 >>12054424You will also appreciate the two-lines Fermat's theorem proof.
 >> Anonymous Thu Aug 27 12:35:06 2020 No.12054685 File: 41 KB, 640x656, stupid.jpg [View same] [iqdb] [saucenao] [google] [report] >>12054432you see, it's the "..."that makes it non-shortened>calling infinite "shortened", what an idiot
 >> Anonymous Thu Aug 27 12:44:11 2020 No.12054722 >>12054668The result of dividing 1 by 3 is 1/3. Do you onetards try to be this retarded or what?
 >> Anonymous Thu Aug 27 12:45:16 2020 No.12054724 >>120546680.333...+0.000...1/3=1/3
 >> Anonymous Thu Aug 27 12:53:47 2020 No.12054765 File: 134 KB, 1654x2339, 1.000.png [View same] [iqdb] [saucenao] [google] [report] >>12053975Today I will remind them
 >> Anonymous Thu Aug 27 12:55:58 2020 No.12054773 0.9999=1 for most practical purposes. If you need to go further, you are a nerd.
 >> Anonymous Thu Aug 27 13:02:36 2020 No.12054811 >>120547240.000...1/3express this as a decimal please>>12054722well obviously I meant the result expressed as a decimal
 >> Anonymous Thu Aug 27 13:39:15 2020 No.12054923 >>12054765Irrelevant. Once again onetards have nothing to say
 >> Anonymous Thu Aug 27 13:40:19 2020 No.12054926 >>12054811Express the square root of 2 as a decimal please
 >> Anonymous Thu Aug 27 13:42:01 2020 No.12054929 >>12054923Literally all your arguments are stupid if they can be applied to something which is obviously false.
 >> Anonymous Thu Aug 27 13:43:18 2020 No.12054934 >>12054926It's impossible to represent an irrational number in a system which is only capable of representing rational numbers.
 >> Anonymous Thu Aug 27 13:44:22 2020 No.12054938 >>120549261.414... where the nth term in the decimal expansion are given by calculating a finite number of terms in a Cauchy sequence that converges to $\sqrt{2}$
 >> Anonymous Thu Aug 27 13:54:36 2020 No.12054955 >>12054929That also works for 0.(9)=1.(0) crowd.
 >> Anonymous Thu Aug 27 13:54:57 2020 No.12054956 >>12054938"1.414... where the nth term in the decimal expansion are given by calculating a finite number of terms in a Cauchy sequence that converges to √2" is not decimal notation
 >> Anonymous Thu Aug 27 13:56:07 2020 No.12054957 >>12054955what?
 >> Anonymous Thu Aug 27 13:56:45 2020 No.12054961 >>12054956yes it is, I told you how to calculate the nth term in the decimal expansion, you can do this to generate arbitrarily many terms in the decimal expansion
 >> Anonymous Thu Aug 27 13:56:50 2020 No.12054962 A reminder that you can represent decimals as infinite list without maximal index and infinite list with maximal index. In the second case it is possible to have number standing just before 1.
 >> Anonymous Thu Aug 27 13:56:53 2020 No.12054964 >>12054395PWNed!
 >> Anonymous Thu Aug 27 13:57:55 2020 No.12054968 >>12054957>Literally all your arguments are stupid if they can be applied to something which is obviously false.
 >> Anonymous Thu Aug 27 13:59:01 2020 No.12054972 >>12054964>1/infWow, such rigor, much self-praise.
 >> Anonymous Thu Aug 27 14:01:20 2020 No.12054978 >>12054961So? Decimal notation consists of a series of numbers, a decimal point and another series of numbers plus an optional line indicating a repeating series of numbers. A formula isn't decimal notation.
 >> Anonymous Thu Aug 27 14:02:28 2020 No.12054980 >>12054962Yes, but the second case isn't the real numbers.
 >> Anonymous Thu Aug 27 14:03:57 2020 No.12054985 >>12053975So close. Algebraic manipulation does not work for non-convergent sequences/series. All internally consistent expressions of 0.999... converge, and the number they converge to is 1.
 >> Anonymous Thu Aug 27 14:09:22 2020 No.12055002 >>12054968That's indeed what I wrote, but it doesn't help me understand what you mean by "That also works for 0.(9)=1.(0) crowd.".
 >> Anonymous Thu Aug 27 14:12:35 2020 No.12055012 I don't really get this. 1/3 would only work in a number system based around 3's. In a 10 digit system, the best you can do is an approximation, which is .333 to infinite. It should be understood that .333 is a representation of 1/3, but if you're interested in being exact, 1/3 should be used. There's a reason we use different systems, as they allow specificity and flexibility depending on the task.
 >> Anonymous Thu Aug 27 14:15:09 2020 No.12055020 >>12055002The "Literally all your arguments are stupid if they can be applied to something which is obviously false." also works for 0.(9)=1.(0) crowd.
 >> Anonymous Thu Aug 27 14:18:14 2020 No.12055030 >>12054985>All internally consistent expressions of 0.999... convergeAll of them? That's a very bold claim.
 >> Anonymous Thu Aug 27 14:20:30 2020 No.12055038 >>12055012I would say this is incorrect. The decimal notation we were taught in school allowed for putting lines above digits to indicate them repeating indefinitely, and this allows you to exactly represent fractions like 1/3 (as 1.3 (repeating the 3 indefinitely)) and 1/7 (as 0.142857 (repeating the 142857 indefinitely)). However it should be noted that in this system, representations aren't unique, so the real number 1 can be represented both by 1 and by 0.9 (repeating the 9 indefinitely)
 >> Anonymous Thu Aug 27 14:21:50 2020 No.12055041 >>12055020Are you actually interested in having a discussion with me or do you just want to throw poop around?
 >> Anonymous Thu Aug 27 14:22:18 2020 No.12055042 >>12055038You can also proclaim that 0.999999 is equal to 1, and that will be true when no precision is needed, but not true metaphysically.
 >> Anonymous Thu Aug 27 14:23:49 2020 No.12055046 >>12055042Precision? We're talking about exact representations. And 0.9 (with the 9 repeating indefinitely) is mathematically exactly equal to 1.Please, I challenge anyone thinking this is false to give a precise definition of the number "0.999..." which I can't prove to be equal to 1.
 >> Anonymous Thu Aug 27 14:24:09 2020 No.12055047 >>12055041Your argument is "I don't like some arguments. If I'll apply arguments which vaguely look like them to the different task, they supposedly will be wrong. Therefore initial arguments are wrong". With such a method you can disprove absolutely everything.
 >> Anonymous Thu Aug 27 14:24:55 2020 No.12055053 >>12054978A told you how to calculate the sequence of numbers you're referring toSince there are an infinite number of digits in the sequence following the decimal place, I can't include the entire sequence, but I can tell you how to calculate the nth term, which is a way of specifying every term in that sequence.That is to say, [eqn]\sqrt{2} = 1.d_0d_1d_2...[/eqn]where [eqn]d_n = \lfloor 10^n \times x_{2^n} \mod 10 \rfloor, \\x_0 = 1, \\x_{n+1} = \frac{x_n}{2} + \frac{1}{x_n}[/eqn]Here, I'll do it for the first few terms in that sequence1.414213562373095...I've written done this in haskell so you can calculate the full expression since haskell supports infinite lists which you can evaluate here, but note it will take an infinite amount of time and memory to runhttps://repl.it/repls/SuperficialSadQueryoptimizer
 >> Anonymous Thu Aug 27 14:25:46 2020 No.12055055 >>12055047It's not a proof, more of showing you how stupid you sound. Also, please tell me which of the arguments isn't a literal exact translation of your original arguments.
 >> Anonymous Thu Aug 27 14:25:48 2020 No.12055056 >>12055046Here: a number is an infinite sequence of integers. If two integers in this sequence differ, then two numbers are not equal.
 >> Anonymous Thu Aug 27 14:26:54 2020 No.12055061 >>12055053This is very great, but it is not decimal notation. Based Monad Wizard though.
 >> Anonymous Thu Aug 27 14:27:55 2020 No.12055063 >>12055055None of them because they talk about different things.
 >> Anonymous Thu Aug 27 14:28:08 2020 No.12055064 >>12053975>he doesnt accept the proof of $1 + 2 + 3 + ... = -\frac{1}{12}$fucking retard>hurr moving parentheses make badhttps://en.wikipedia.org/wiki/Riemann_series_theoremyou cant move parentheses moron
 >> Anonymous Thu Aug 27 14:29:08 2020 No.12055065 >>12055038>The decimal notation we were taught in school allowed for putting lines above digits to indicate them repeating indefinitely, and this allows you to exactly represent fractions like 1/3To me, that's more of a compromise in a system that can't really represent that particular number, so a vinculum is used to make it work so we're not constantly jumping between decimals and fractions. A base 3 system could represent 1/3 accurately, but then a vinculum would be require for other fractions that don't work in base 3. What really matters is that people agree about the representation, which they generally do unless they feel like arguing on /sci/.
 >> Anonymous Thu Aug 27 14:29:36 2020 No.12055066 >>12055056I assume this is supposed to define the real numbers 0 <= x < 1 ?
 >> Anonymous Thu Aug 27 14:29:50 2020 No.12055068 >>12055064Let's define "=x" as "equals x or equals x+1". Then 2+2=5.
 >> Anonymous Thu Aug 27 14:30:46 2020 No.12055071 >>12055063??? How is saying "0.999... is real because (0.999... + 1)/2 exists" different from saying "1.000... is real because (1.000... + 1)/2 exists" ???
 >> Anonymous Thu Aug 27 14:30:50 2020 No.12055072 >>12055056youre still wrong, a number can be represented as an infinite sequence of numbers 0 to 9two numbers are equal if their difference is 0>>12055068lets define (You) as "a retard", then youre a retard.
 >> Anonymous Thu Aug 27 14:31:24 2020 No.12055073 >>12055066You can also add the index of the decimal point. Or take another sequence for the integer part.
 >> Anonymous Thu Aug 27 14:32:03 2020 No.12055074 >>12055068This Anon is actually right. Ramanjuan Summation isn't the same thing as normal Summation.
 >> Anonymous Thu Aug 27 14:32:46 2020 No.12055076 >>12055071They both can be real?
 >> Anonymous Thu Aug 27 14:33:18 2020 No.12055078 >>12055073That would allow for infinite numbers like ...111. Certainly a cool system, but not the same as the real numbers.
 >> Anonymous Thu Aug 27 14:34:22 2020 No.12055081 >>12055078Real numbers will be their subset.
 >> Anonymous Thu Aug 27 14:34:42 2020 No.12055083 >>12055076Yes, and they're both equal to 1.
 >> Anonymous Thu Aug 27 14:35:26 2020 No.12055084 >>12055083Is 0.9 equal to 1? Is 1.0 equal to 1?
 >> Anonymous Thu Aug 27 14:35:54 2020 No.12055085 >>12055081No. A subset would imply them being defined the same way. You could define a mapping though and depending on how that mapping worked, either 0.999... wouldn't map to a real number just like ...111 or it would map to 1.
 >> Anonymous Thu Aug 27 14:36:21 2020 No.12055086 >>12055084no, yes
 >> Anonymous Thu Aug 27 14:37:30 2020 No.12055089 >>12055085...111 would be larger than every finite number, unlike 0.999...
 >> Anonymous Thu Aug 27 14:37:35 2020 No.12055090 >>12055084>Is 0.9 equal to 1?Obviously, no>Is 1.0 equal to 1?Obviously, yesYou know the answers to these questions. Are you trying to tell me because these hold for all finite lengths, they hold for infinite lengths too? That argument doesn't work. All the approximations of pi are rational and yet pi itself is irrational.
 >> Anonymous Thu Aug 27 14:38:37 2020 No.12055097 >>12055089No, whatever ...111 mapped to wouldn't be larger since it wouldn't even be part of the real numbers. You can't compare real numbers with things that aren't real numbers.
 >> Anonymous Thu Aug 27 14:38:38 2020 No.12055098 >>12055086Ok, let's go a bit further:Is 0.99 equal to 1? Is 1.00 equal to 1?
 >> Anonymous Thu Aug 27 14:39:42 2020 No.12055102 >>12055097Ah, so we can't say that 2>1.5?
 >> Anonymous Thu Aug 27 14:40:48 2020 No.12055108 >>12055090Now you can see why applying argument fit for a number starting with 0. to the number starting with 1. is being faulty.
 >> Anonymous Thu Aug 27 14:41:44 2020 No.12055109 >>12055098Read >>12055090, faggot
 >> Anonymous Thu Aug 27 14:42:23 2020 No.12055111 >>12055109Read >>12055108, faggot
 >> Anonymous Thu Aug 27 14:42:56 2020 No.12055113 >>12055102No, I'm not saying that. 2 can be defined by a Dedekind Cut and is thus a real number. It can also be defined as a natural numbers, but comparing the natural number 2 with the real number 2 makes no sense.
 >> Anonymous Thu Aug 27 14:44:20 2020 No.12055119 >>12055108Do you have some sort of brain damage? Whether a number has 0 or 1 as integer part is literally completely irrelevant. I could make the argument that 0.000... is not equal to 0 too.
 >> Anonymous Thu Aug 27 14:45:39 2020 No.12055123 >>12055113>It can also be defined as a natural numbers, but comparing the natural number 2 with the real number 2 makes no sense.But it's pretty obvious that two apples are more than one and half.
 >> Anonymous Thu Aug 27 14:47:17 2020 No.12055128 >>12055119Since 0 is equal to 0.0 or 0.00, that will not be very convincing.
 >> Anonymous Thu Aug 27 14:49:21 2020 No.12055136 >>12055128So? Maybe it's not equal in the limit. As I said, properties can change in the limit.
 >> Anonymous Thu Aug 27 14:50:28 2020 No.12055138 is this the best /sci/ meme?
 >> Anonymous Thu Aug 27 14:51:43 2020 No.12055141 >>12055136Yes, you can also define functions which will have vastly different value at the point than their limits at that point. That still will be pretty arbitrary and not some metaphysical truth.
 >> Anonymous Thu Aug 27 14:52:16 2020 No.12055144 >>12055108if the distance between .999... and 1 is 0, then theyre the sameregardless of what they start with
 >> Anonymous Thu Aug 27 14:52:20 2020 No.12055145 >>12055123What even is your point here now?"I can easily compare two apples to one and a half applethusit makes sense to compare natural and real numbersthusit makes sense to compare any two numbers from any two arbitrary number systemsthus0.999... defined as a sequence can be compared to the real number 1 and is not equal to it"?
 >> Anonymous Thu Aug 27 14:52:47 2020 No.12055147 >>12055144The distance is infinitesimal though.
 >> Anonymous Thu Aug 27 14:53:24 2020 No.12055151 >>12055141The irrationality of pi is not a metaphysical truth?
 >> Anonymous Thu Aug 27 14:53:34 2020 No.12055152 >>12055147no its notthe distance between 1 - 1/w and 1 is infinitesimal.000...1 is not an infinitesimal
 >> Anonymous Thu Aug 27 14:53:55 2020 No.12055153 >>12055145>it makes sense to compare any two numbers from any two arbitrary number systemsThen what was the demand to bring the number equal to 1/3 about? Fractions are fractions, decimals are decimals.
 >> Anonymous Thu Aug 27 14:54:28 2020 No.12055158 >>12055147There are no infinitesimal real numbers.
 >> Anonymous Thu Aug 27 14:54:56 2020 No.12055161 >>12055152>.000...1 is not an infinitesimalThen what is it? Finite number? Infinite number?
 >> Anonymous Thu Aug 27 14:56:04 2020 No.12055165 >>12055158Great, you can also have a system where numbers less than 1/1000000 don't exist. It will even be practically useful.
 >> Anonymous Thu Aug 27 14:56:20 2020 No.12055168 File: 79 KB, 550x543, Brainlet.png [View same] [iqdb] [saucenao] [google] [report] >>12055152>.000...1
 >> Anonymous Thu Aug 27 14:57:08 2020 No.12055170 >>12055138Yes, you can discuss it forever.
 >> Anonymous Thu Aug 27 14:57:21 2020 No.12055171 >>12055153>Then what was the demand to bring the number equal to 1/3 about? Fractions are fractions, decimals are decimals.That wasn't me. >>12054765 was my first post in this thread.
 >> Anonymous Thu Aug 27 14:58:17 2020 No.12055174 >>12055171Ok, so if you think that there is no need to map everything on everything, then the problem does not even exist.
 >> Anonymous Thu Aug 27 14:58:24 2020 No.12055175 >>12055161Please, define that number. It's not valid decimal notation. It's not a real number. It's not even validly definable by an infinite sequence of integers.Retard.
 >> Anonymous Thu Aug 27 15:00:06 2020 No.12055184 >>12055175It's an infinite sequence of zeros followed by 1. If you don't like infinite sequences, then stop discussing them, be they 1.(0), 0.(9) or 0.(0)1.>It's not valid decimal notation. It's not a real number. It's not even validly definable by an infinite sequence of integers.How do you declare infinitesimals with these things?
 >> Anonymous Thu Aug 27 15:00:47 2020 No.12055187 >>12055165>equating some arbitrary system with the real numbersHoly fuck, you're actually retarded. Centuries of mathematical work has been based on the real numbers. It is the standard system. Nowhere in this thread have you mentioned or defined a system which would allow for infinitesimal numbers.
 >> Anonymous Thu Aug 27 15:02:07 2020 No.12055194 >>12055174Actually, I'm interested in you number system now if we can at least agree for the reals. What would the difference of 0.999... and 1 be in your number system? 0? So, two numbers that aren't real could have difference 0. Doesn't seem very useful or nice at all.
 >> Anonymous Thu Aug 27 15:03:01 2020 No.12055197 File: 80 KB, 1280x720, clownfeels.jpg [View same] [iqdb] [saucenao] [google] [report] Can we stop having these discussions as it just makes these retards orgasm more? We needn't stoop down to their level.
 >> Anonymous Thu Aug 27 15:03:41 2020 No.12055200 >>12055184>It's an infinite sequence of zeros followed by 1.>infinite>followed byPlease google what the word "infinite" means. (Tip: It comes from the prefix "in-" and the word "finite", meaning "not finite". Without end. You can't follow something up if there's no end to it)
 >> Anonymous Thu Aug 27 15:03:41 2020 No.12055201 >>12055187In practice you constantly use systems with limited precision. That's actually pretty obvious unless you can count to infinity and remember infinite digits of pi (in which case you must be a God).>It is the standard system.Standard system may be simply convenient, not metaphysically true. Just like you can ignore relativity effects in most cases, but that does not disprove the relativity theory.
 >> Anonymous Thu Aug 27 15:04:43 2020 No.12055205 >>12055200There is an infinity of numbers in the interval [0,1], yet it still has an end.
 >> Anonymous Thu Aug 27 15:05:13 2020 No.12055207 >>12055201>In practice>Standard system may be simply convenient, not metaphysically true. Just like you can ignore relativity effects in most cases, but that does not disprove the relativity theory.What? Are you basing your arguments on engineering practices or """metaphysical truth""" now? These are completely different things.
 >> Anonymous Thu Aug 27 15:05:46 2020 No.12055211 >>12055194>What would the difference of 0.999... and 1 be in your number system?0.000...1 of course.
 >> Anonymous Thu Aug 27 15:06:16 2020 No.12055214 >>12055205Yes, we call the interval [0,1] infinite because if we were to put the numbers in there into a sequence (which isn't possible anyways) it would have no end.
 >> Anonymous Thu Aug 27 15:07:13 2020 No.12055219 >>12055207If you argue then it's just convenient to equate 0.(9) to 1.(0), then no problems, continue to do that if you wish. If you argue that it is an Ultimate Metaphysical Platonic Truth, then we have some questions.
 >> Anonymous Thu Aug 27 15:07:20 2020 No.12055221 >>12055211THATS NOT A SEQUENCE YOU FUCKING IDIOT REEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEE 0.000...1 IS NOT A THING. NOT A THING. NOT A THING.GOD I HATE YOU FAGGOTS IM LEAVING THE THREAD NOW
 >> Anonymous Thu Aug 27 15:07:51 2020 No.12055224 >>12055214Anon, stop arguing with him. They try to understand it. You're honestly just wasting your time on this thread.
 >> Anonymous Thu Aug 27 15:08:19 2020 No.12055226 >>12055214You can also replace some zeros in 0.000...1 with infinite sequence of digits you like more.
 >> Anonymous Thu Aug 27 15:08:53 2020 No.12055229 >>12055224>try*never try
 >> Anonymous Thu Aug 27 15:09:21 2020 No.12055231 >>12055221It's a number, which is also infinitely small. But bye-bye!
 >> Anonymous Thu Aug 27 15:10:24 2020 No.12055236 >>12055214>>12055224Is the set of negative integers infinite?
 >> Anonymous Thu Aug 27 15:12:52 2020 No.12055241 >>12055061how is it not decimal notation? it's a sequence of integers of numbers, a decimal point followed by another sequence of integersjust because one has to be creative in order to specify that sequence of integers doesn't mean it isn't a sequence of integers.
 >> Anonymous Thu Aug 27 15:14:54 2020 No.12055248 Anons, embrace the ultrafinitism.
 >> Anonymous Thu Aug 27 15:23:57 2020 No.12055281 0.(9) < 0.(9)9 < 0.(9)(9) < 0.((9))
 >> Anonymous Thu Aug 27 15:31:54 2020 No.12055310 >>12055281>0.(9)9 < 0.(9)(9) < 0.((9))not real numbers
 >> Anonymous Thu Aug 27 15:36:31 2020 No.12055325 >>12055310What about 0.(...(9)...)?
 >> Anonymous Thu Aug 27 15:40:14 2020 No.12055335 File: 104 KB, 832x1024, omegas.png [View same] [iqdb] [saucenao] [google] [report]
 >> Anonymous Thu Aug 27 15:41:47 2020 No.12055342 >>12055335>omegasnot real numbers
 >> Anonymous Thu Aug 27 15:43:35 2020 No.12055349 >>12055342They are more real than reals.
 >> Anonymous Thu Aug 27 15:55:04 2020 No.12055397 >>12054187Heh. I like this criticism of naively using the word number without defining it.
 >> Anonymous Thu Aug 27 16:05:22 2020 No.12055422 >>12055349so what?
 >> Anonymous Thu Aug 27 16:08:11 2020 No.12055433 >>12053975Sigh, why do I even...Counterargument 1: So this number is bigger than 0.999... but smaller than 1? How would you write this? 0.999...+?What about the next number in the sequence?Counterargument 2: Being an engineer is not even an argument.Counterargument 3: That example doesn't converge. 0.999... does. Pay attention next time in Analysis 101.
 >> Anonymous Thu Aug 27 16:12:19 2020 No.12055445 >>12055433Stop falling for bait and let the thread die.
 >> Anonymous Thu Aug 27 16:13:59 2020 No.12055450 >>120554331: 0.(9)52: If you are en engineer, then it's OK to ignore precision questions.3: What does your converging definition say about infinitesimals?
 >> Anonymous Thu Aug 27 16:20:00 2020 No.12055472 >>12055422Ask that about >>12055342
 >> Anonymous Thu Aug 27 16:42:40 2020 No.12055551 Open Python and enter>print(0.9999999999999999999==1)Get >TrueQ.E.D.
 >> Anonymous Thu Aug 27 16:46:08 2020 No.12055566 >>12055551stfu and stop bumping
 >> Anonymous Thu Aug 27 16:46:35 2020 No.12055568 It's impossible to calculate a difference between the 1 and whatever the object described by 0.999... can possibly represent.1 - 0.999... = 0.000...No difference = same thing.
 >> Anonymous Thu Aug 27 16:47:00 2020 No.12055570 >>12055566nineist btfo
 >> Anonymous Thu Aug 27 16:48:01 2020 No.12055574 >>120555680.000...1
 >> Anonymous Thu Aug 27 16:48:11 2020 No.12055575 >>12055568>t. retard falling for bait
 >> Anonymous Thu Aug 27 16:55:36 2020 No.12055599 >>12055575kill yourself you retarded janny wannabe
 >> Anonymous Thu Aug 27 16:56:39 2020 No.12055600 >>12055574no, that would be the answer to 1 - 0.999...9 not 1 - 0.999...1 - 0.999...9 = 0.000...11 - 0.999... = 0.000...
 >> Anonymous Thu Aug 27 16:57:47 2020 No.12055604 >>12055599The more you talk about how 0.99=1, the more they will post, the more they love the attention.
 >> Anonymous Thu Aug 27 16:58:25 2020 No.12055606 >>12055604stfu
 >> Anonymous Thu Aug 27 17:05:16 2020 No.12055627 >>12055600Well, 0 is 0, 0.0 is 0, so is 0.000, but is 0.000... 0?
 >> Anonymous Thu Aug 27 17:10:33 2020 No.12055645 >>12055604>0.99=1Truth.I mean, knowing the difference between 0.9 and 0.95 can be useful in some rare cases, but 0.99 is 1 by all means.
 >> Anonymous Thu Aug 27 17:12:13 2020 No.12055650 >>12055627There's never any difference between 0.000... and 0.
 >> Anonymous Thu Aug 27 17:16:00 2020 No.12055661 >>12055645It's essentially either trolls or NEETs living in their mom's basement, wearing a t-shirt covered with cheeto dust. The amount of effort they put in to 'not' understand math, they could've put all of it into actually understanding it.
 >> Anonymous Thu Aug 27 17:17:27 2020 No.12055668 >>12055661Conclusions looking for corroboration is the post-modern scientific method.
 >> Anonymous Thu Aug 27 17:19:12 2020 No.12055677 >>12055661It's fun to troll dorks who finished half of analysis 101 and now think that they are the source of divine truth.
 >> Anonymous Thu Aug 27 17:22:08 2020 No.12055686 >>12055677It is. But these threads bait newfags who then spend their effort convincing these monkeys rather than doing actual /sci/.
 >> Anonymous Thu Aug 27 17:31:09 2020 No.12055702 >>12055335holy shit that is obsessed with 3s
 >> Anonymous Thu Aug 27 17:35:57 2020 No.12055711 >>12053975how many people with any math background beyond calculus believe this shit
 >> Anonymous Thu Aug 27 17:39:53 2020 No.12055724 >>12055686They actually create threads like this, so they want that.
 >> Anonymous Thu Aug 27 17:42:55 2020 No.12055733 >>12055711All of them.
 >> Anonymous Thu Aug 27 17:44:12 2020 No.12055738 >>12055686Spending a bit of effort is justified when you get fun stuff like >>12055221 in return.
 >> Anonymous Thu Aug 27 17:47:30 2020 No.12055748 what number is before 0.999...? you cant put anything therethe truth is that infinity is a meme
 >> Anonymous Thu Aug 27 17:51:50 2020 No.12055762 >>12055748Can't put any number right before 1 either. Same thing.
 >> Anonymous Thu Aug 27 18:01:33 2020 No.12055792 >>120539750.333=1/3 is trivially easy to proveLiterally just do the long division lmao
 >> Anonymous Thu Aug 27 18:04:55 2020 No.12055806 >>120557620this post was made by integer gang
 >> Anonymous Thu Aug 27 18:07:07 2020 No.12055820 >>12055792Sure, if you have infinity of time to spare.
 >> Anonymous Thu Aug 27 18:08:14 2020 No.12055826 bros what if 1/3 is not infinite but we just havent discovered it?
 >> Anonymous Thu Aug 27 18:10:32 2020 No.12055835 >>120558261/3 is surely finite, just eat 1/3 apple.
 >> Anonymous Thu Aug 27 19:27:22 2020 No.12056026 >>12054504>can be expressed as>BUUUTTT IT'SH NAWT EEKWALand?
 >> Anonymous Thu Aug 27 19:34:56 2020 No.12056037 >>12056026Ok, then 1 can be expressed as 0.999.... (or 0.999 if needed), but isn't equal to that.
 >> Anonymous Thu Aug 27 19:49:34 2020 No.12056066 >>12056037But it is.
 >> Anonymous Thu Aug 27 19:54:43 2020 No.12056081 >>12056066>BUUUTTT IT'SH EEKWAL
 >> Anonymous Thu Aug 27 20:02:15 2020 No.12056105 infinitesimals are purely algebraic objects, and as such, never turn up in limitslimits are geometric, infinitesimals are notthe limit of $1/2^n$ is literally just 0, by how limits are definedan infinitesimal is a nonzero element which squares to 0which means it satisfies $a^2 = 0$$.000...1$ cannot even be an infinitesimal, since it does not square to 0$a = .000...1$ means that $a^2 = .000...1$so $a^2 = a \implies a^2 - a = 0 \implies a(a-1) = 0$so $a$ is either equal to 0 or to 1and it cant be 1, since $a$ has a 0 in the ones placeproblem?>>12056081.999... is not 1 minus an infinitesimal$1 - 1/\omega \neq .999... = 1$
 >> Anonymous Thu Aug 27 20:11:10 2020 No.12056119 >>12056105>an infinitesimal is a nonzero element which squares to 0>.999... is not 1 minus an infinitesimal>1/ωSo what is it? 1/ω or thing which squares to 0?
 >> Anonymous Thu Aug 27 20:13:35 2020 No.12056127 >>12056105>limits are geometricHow are they not analytical objects? Genuinely curious, I don't have a stake in this contest of yours.
 >> Anonymous Thu Aug 27 20:21:21 2020 No.12056145 >>12056127geometry and analysis are the same in my mind>>12056119if you want to write it as epsilon then be my guestone over omega or epsilon are both not .999... anyway
 >> Anonymous Thu Aug 27 20:26:50 2020 No.12056165 >>12056145$(1/ω)^2=1/ω^2$, not 0.
 >> Anonymous Thu Aug 27 20:31:04 2020 No.12056178 >>12056165yeah, its just a habit of mine to write 1/wbut its still fine, since 1 - 1/w is not .999... anyway
 >> Anonymous Thu Aug 27 20:36:47 2020 No.12056194 >>12056178You say that 1-0.999...is not infinitesimal because it is not 1/ω. But you also say that infinitesimal must always square to 0. So what is it?
 >> Anonymous Thu Aug 27 20:43:04 2020 No.12056215 The answer can literally be either or depending on how you want to define the conditions of something "equaling" another thing. I don't even know math but I'm apparently better at it than all of you retards. /thread
 >> Anonymous Thu Aug 27 20:49:32 2020 No.12056235 >>12056194the retards in this thread cant fucking handle a definition of infinitesimal besides "squares to 0"im not going to get into dealing with it more properly>>12056215>The answer can literally be either or depending on how you want to define the conditions of something "equaling" another thing.no it cantwe already have a definition of that, you dont get to change it willy nilly you dumb pseud
 >> Anonymous Thu Aug 27 21:02:49 2020 No.12056263 >>12056235>cant>we already have a definition of that, you dont get to change it willy nilly you dumb pseudSorry kid, but just did. /thread
 >> Anonymous Thu Aug 27 22:14:01 2020 No.12056398 Reminder that 0.999... is still not equal to 1, no matter how much you want to believe otherwise.
 >> Anonymous Thu Aug 27 22:17:03 2020 No.12056404 >>12053976Wasn't the Higgs Boson announcement also in Comic Sans?
 >> Anonymous Thu Aug 27 23:49:44 2020 No.12056618 >>12055738I feel bad for him lol.
 >> Anonymous Thu Aug 27 23:57:02 2020 No.12056635 I have speaking to God recently. God tells me that infinity does not exist ( except for Him, obviously ).
 >> Anonymous Thu Aug 27 23:59:03 2020 No.12056640 >>120539750.99999999... is the cauchy sequence that converges to 1, however this is not equivalent to 1, rather 1 is the least upper bound of the former sequence, though on its own makes an equivalence class that could be represented as [1]
 >> Anonymous Fri Aug 28 00:02:29 2020 No.12056647 >>12056635God doesn't exist. I'm sorry anon, you might be schizophrenic.
 >> Anonymous Fri Aug 28 00:03:50 2020 No.12056649 >>12056635>I have speaking to God recentlyprove it.
 >> Anonymous Fri Aug 28 00:14:52 2020 No.12056670 Can we make a compromise? For example 0.(9)=1, but 1.(9)<2?
 >> Anonymous Fri Aug 28 04:33:49 2020 No.12057064 >>12053975I agree OP. The only people who say that 0.999... = 1 are trolls
 >> Anonymous Fri Aug 28 04:37:22 2020 No.12057075 >>12054765Problem with this "no u" post is that mathematical operations used in OP can not be applicable to this example. They just don't make sense here.
 >> Anonymous Fri Aug 28 04:42:40 2020 No.12057084 >>12057064worst and cringiest bait I have ever seen
 >> Anonymous Fri Aug 28 04:47:06 2020 No.12057090 >>12057084Stop baitingWhy do retards like to pretend 0.999...=1 so much? Do you have anything else going on in your life??
 >> Anonymous Fri Aug 28 04:48:06 2020 No.12057091 >>12053975Based post.If 0.999... were equal to 1, pseudorandom number generators would have a chance of outputting 1 and potentially causing system to crash as it depends on the fact that all numbers are generated in range of [0; 1), or in other words, [0; 0.999...].
 >> Anonymous Fri Aug 28 04:59:48 2020 No.12057111 >>120539751/3 = 0.333...(1/3) * 3 = 0.333... * 33/3 = 0.999...1 = 0.999...
 >> Anonymous Fri Aug 28 05:03:46 2020 No.12057114 >>12057111but 1/3 is not 0.3333....
 >> Anonymous Fri Aug 28 05:12:34 2020 No.12057126 File: 51 KB, 1280x720, maxresdefault.jpg [View same] [iqdb] [saucenao] [google] [report] >>12057114The absolute state of /sci/
 >> Anonymous Fri Aug 28 05:13:29 2020 No.12057128 >>12057114When these faggots will understand the difference between approximation and real value?
 >> Anonymous Fri Aug 28 05:14:31 2020 No.12057130 It's so difficult to distinguish who's a moron and who's baiting for shits and giggles.
 >> Anonymous Fri Aug 28 05:24:24 2020 No.12057139 >>12057130Everyone who assumes 1/3 = 0.(3) for their argument is baiting.1/3 is finite, 0.(3) by definition is not, the latter approaches 1/3 when amount of digits is going towards infinity, but interesting property of limits is that end value is purely theoretical and requires perfect conditions.You can be a retard and say 1/x = inf, because that's the limit of x approaching 0, but everyone will laugh at you.Say that 1/3 = 0.(3) and you're a genius...Go back to fundamenrals, retards.
 >> Anonymous Fri Aug 28 05:49:08 2020 No.12057186 >>12057090I was wrong. this is the worst and cringiest bait I have ever seen.
 >> Anonymous Fri Aug 28 08:59:51 2020 No.12057645 0.999... is an algorithm that keeps appending nines.It is not equal to one since it will never reach 1.However, the LIMIT of 0.999... is 1.
 >> Anonymous Fri Aug 28 16:31:44 2020 No.12058980 >>12053975Against my better judgement (and also because I'm bored) I will answer these. The first one, (0.999...+1)/2 would be great if you could actually produce such a number. As it stands, no decimal can conceivably be imagined that represents this. The argument also goes more like this: 1-0.999... is less then every single rational number-since there exists a rational less then a real[simply take a new number by a termination of that reals decimal sequence], then any real number which 1-0.999... supposedly is, would mean I can find a rational less then it-in turn, 1-0.999... is not less then every rational, a contradiction. I would like to see you worm your way out of the properly stated form of this proof rather then the strawman.The second one is to ask what it means for a number to correspond to it's decimal expansion: the answer is the limit of the partial representations of the decimal and in that case 1/3 certainly equals 0.333... To ask such a question without even being clear how the decimal sequence (0,3,3,3,...) relates to the number 1/3 is a pointless exercise. 0.333... isn't a decimal approximation-it is the true to goodness calculated value of 1/3-at any given termination at point n,The third one, from a formal perspective, is a bit iffy [namely, on the multiplication by 10-this needs to be better elaborated on[. However, to claim 9.999... - 0.999... =/= 9 is to reach mount stupid, since this is how decimals have always worked. Also, your DIVERGENT series is a red herring since these series are convergent, absolutely so, in fact. The sum of two convergent series is the series of the summed terms-this is a basic proof.Basically, fuck off and learn math. All your tripe objections are easily, easily answerable if you actually care to learn.
 >> Anonymous Fri Aug 28 16:37:16 2020 No.12058998 >>120571391/3 and 0.(3) are both finite you fucking idiot, since they are both less then 1. The totality of the sequence of digits to represent them in decimal format are both infinite.The decimal expansion isn't a real number but a sequence-there is an assignment to a real number by its infinite series as a decimal, which is defined as a limit.This isn't even comparable (if you write it out in full you lazy bastard) to your 1/x case, and you still get it wrong since lim x-> 0 1/x isn't inf, only if you approach it from the positive.Pretty rich for you to tell someone to 'go back to fundamentals'. This is real analysis 101.
 >> Anonymous Fri Aug 28 16:39:49 2020 No.12059007 >>120543951/inf isn’t a number, and it never becomes 0
 >> Anonymous Fri Aug 28 16:43:58 2020 No.12059026 >>12058998I still think he's winding you up, anon.Incidentally, does no one write it $0.\dot3$ anymore? That's how we learnt it in school.
 >> Anonymous Fri Aug 28 16:48:24 2020 No.12059046
 >> Anonymous Fri Aug 28 16:51:47 2020 No.12059060 >>12053975What a brainlet thread.
 >> Anonymous Fri Aug 28 23:56:28 2020 No.12061187 >>120589801-0.999...=0.000...1 which is less than every positive rational0.333... is simply a decimal approximation of 1/3 and no amount of whining and feet stomping will change that, child
 >> Anonymous Sat Aug 29 00:04:21 2020 No.12061196 0.iii...
 >> Anonymous Sat Aug 29 00:04:41 2020 No.12061199 >>12053975this is funny OP, thanks for making it>1this one is funny because its circular, but then claims the counterargument is circular>2this one is not really an argument, but its funny, i like it>3this one is sneaky, but the key is the difference between convergent and divergent series
 >> Anonymous Sat Aug 29 00:06:07 2020 No.12061201 >>12059060What a brainlet post
 >> Anonymous Sat Aug 29 00:10:13 2020 No.12061207 is there a mathematical application for which it is necessary to distinguish between 0.999... and 1? does it have anything to do with "surreal numbers"?
 >> Anonymous Sat Aug 29 01:07:36 2020 No.12061272 >>12053975here's my proof:2 - (2 x 0.9999...) = 1 - (1 x 0.9999...)+ (2 x 0.9999...) + (2 x 0.9999...)2 = 1 + 0.9999...-1 -11 = 0.9999...
 >> Anonymous Sat Aug 29 02:00:07 2020 No.12061380 >>12061187>approximationno, it's exact>>12054395
 >> Anonymous Sat Aug 29 02:01:11 2020 No.12061385 >>120590070 is a number, virgin1/inf = 0
 >> Anonymous Sat Aug 29 02:06:04 2020 No.12061407 >>120613801 is less than 1002 is less than 100...100 is less than 100101 is less than 100
 >> Anonymous Sat Aug 29 02:07:46 2020 No.12061413 >>12061385He never said 0 is not a number. Learn to read kiddo
 >> Anonymous Sat Aug 29 02:19:10 2020 No.12061447 >>12053976Comic sans is a good font, begone redditor.
 >> Anonymous Sat Aug 29 03:09:17 2020 No.12061580 >>12061187"1-0.999...=0.000...1 which is less than every positive rational"Which would be a direct violation of the archimedean property. I will simply point you to a proof that for every two real numbers, there is a rational inbetween: http://fulviofrisone.com/attachments/article/453/Principles%20Of%20Mathematical%20Analysis%20-%20W.Rudin.pdf#page=18.Alternatively, another way to view it is that the rationals are dense in the reals[simple fact of topology]-if 0.000...1 and 0 don't have a rational inbetween, then clearly the interval (0,0.000...1) consists of points in which are not rationals nor are limit points of rationals, a contradiction..
 >> Anonymous Sat Aug 29 03:10:19 2020 No.12061582 >>12061580Also, it should be clear that '0.000...1' means a bunch of 0, and THEN a 1.[the sequence is of order type w+1] '0.999...' means a bunch [countably infinite] number of 9's, there is no 'after'. [sequence of order type w] Summing these in the only meaningful way would give 0.999... 1 [again, this is assuming 0.000...1 means anything which there is no system I am aware of that it does]. As you might have noticed, this does not produce 1....And to that, it should be noted that '0.000...1' has no meaningful definition. For a positive real number r, let a_0 be largest integer not 0 such that. r-a_0>0, then a_1 largest integer such that r-a_0-a_1/10>0, and so forth. This defines a sequence (a_1,a_2,...) called the decimal expansion. So, you have the 'decimal' (0.000...1), for what value of n in the sequence do you get this 1? If you were to actually carry this out for 1-0.999..., you would get (0,0,0,0,...), which, as you may have noticed, is just a string of 0's. And, the infinite sum a_0+a_1/10+a_2/100+... is equal to r, as the limit of the partial sums (the definition of infinite series) is r by the above algorithm. So the real number defines the decimal and vice versa-so since we do this for 1-0.999... and get decimal (0,0,0,...), what real number do you think we'll get? I am putting my money on... 0.Also, 0.333... is 1/3 and it always has been and always will be. It's you whining against pretty much the most obvious concepts of mathematics. The left is infinite series with terms 3/10^n, which sums to... 1/3. What do you think it sums to, it is a geometric series so should converge to some number, if it isn't 1/3 done by basic plug and chug, what is it? Again, learn real analysisAnyway you cut it, you are wrong from practically every angle imaginable
 >> Anonymous Sat Aug 29 03:12:30 2020 No.12061588 >>12061413lrn2math boomer
 >> Anonymous Sat Aug 29 03:15:57 2020 No.12061596 >>120615821/3 is finite, 0.333... approaches 1/3 but never quite gets there because neither infinity nor a limit is a number and you cannot plug either of those into a sum you faggot.
 >> Anonymous Sat Aug 29 03:20:54 2020 No.12061613 The countably infinite number of 9s in the series is equal to the cardinality of the series.x=.9999...10x=9.999...10x-x=99x=9x=11=.9999...
 >> Anonymous Sat Aug 29 03:55:34 2020 No.12061752 >>12061596>never quite gets there0.999... is static, the length is aleph_0 from the get go.Your naive cartoon vision of a diesel engine chugging along is ridiculous. Embarrassing even.
 >> Anonymous Sat Aug 29 04:14:39 2020 No.12061797 >>12061752Write down the value of aleph_0 for us.
 >> Anonymous Sat Aug 29 04:15:51 2020 No.12061799 >>12061797aleph_0
 >> Anonymous Sat Aug 29 04:19:19 2020 No.12061807 >>12061799So you can't tell me because you aleph_0 is not a real number?Is this faggot so fucking retarded that he will use English definition of "real" to dismiss mathematical fact that aleph_0 is not a real number and cannot be used in mathematical operations? Stay tuned to find out.
 >> Anonymous Sat Aug 29 04:49:50 2020 No.12061874 >>12061596I am a faggot indeed but that is besides the point.Let us make this as clear as I possibly can. Grab paper and pencil and try doing this and let me know exactly where I mess up because I think I've made it stupidly clear. Please be very specific, not some vague stuff about 'you set sum equal to limit', point to a specific logical fallacy.Forget about decimal notation. Based on the above process, call the decimal of that number the sequence (a_0,a_1,a_2,...). It has, as of yet, no connection to a specific real number. There is a real number r, and an algorithm that produces the above sequence.You now DEFINE a_0.a_1 a_2 a_3... as this real number by what I did above-as the limit of the given series. Still following? 0.333... is a NUMBER, and 0<0.333...<1-it is less then a FINITE number and therefore is finite. It isn't 'oo'-now, the amount of non-zero numbers in the sequence IS infinite, but that isn't what we mean when we say a number is infinite. And, the algorithm for numbers with terminating decimals still is infinite, just with redundant zeroes.0.333... is therefore DEFINED to be the series 3/10+3/100+... which is DEFINED to be its limit of the partial sums. The limit of its partials sums is the number 1/3, so 0.333... is by definition 1/3.
 >> Anonymous Sat Aug 29 04:53:59 2020 No.12061885 >>12061807'Real numbers' is just a term based its contrast to 'complex numbers'. If you want to say 'these aren't number', fine-I will call them a mathematical structure called the real and complex field respectively. It doesn't fucking matter.Is aleph_0 a number? Well, if you don't want it to be a number, then so be it. I will consider it as a cardinal in the 'monoid of cardinals'. Whatever I call it, who cares-it acts like a number, doing arithmetic operations so we call it a number.To illustrate the absurdity of your objection... write down the value of 1. Stupid question, it's 1. Exactly-the value of aleph_0 is aleph_0.
 >> Anonymous Sat Aug 29 06:28:09 2020 No.12062035 >>120618071/inf = 01 + inf = inf1- inf = -infinf + inf = infinf/inf undefinedinf-inf undefined1^inf undefinedyou can't do everything with inf as with a number, doesn't mean you can do nothing tho
 >> Anonymous Sat Aug 29 06:35:29 2020 No.12062043 > 1What is the N, such that 10^-N plus 0.9999... is below 1 then?> 2Absolute brainlet tier> 3An equation is not an infinite, divergent sequence.
 >> Anonymous Sat Aug 29 13:23:34 2020 No.12062946 >>12053975By what do you mean equal? As symbols? As sequences? as real numbers? The true interpretation of the real numbers is as equivalence classes of Cauchy sequences. The two sequences in question are[eqn] 0.999\ldots \sim (0, 0.9, 0.99, \ldots) [/eqn]and[eqn] 1 \sim (1, 1, 1, \ldots).[/eqn]As sequences, we see that they are not literally equal. However, both belong to the same class of Cauchy sequences since for any $N \in \mathbb{N}$, there exists some $K \in \mathbb{N}$ such that for all terms beyond the $K^{th}$ term, any values from either sequence are withing $1/N$ of each other. So as sequences, no, but as real numbers (equivalent sequences), yes.
 >> Anonymous Sat Aug 29 13:31:02 2020 No.12062961 >>12062035>1 + inf = inf1+inf = -1(-1 -inf) since (-inf) = (+inf)1+inf = 1-inf
 >> Anonymous Sat Aug 29 14:10:36 2020 No.12063072 >>12062961>inf = -infcongratz, largest error possible
 >> Anonymous Sat Aug 29 14:29:35 2020 No.12063138 File: 23 KB, 500x603, 500px-Real_projective_line.svg.png [View same] [iqdb] [saucenao] [google] [report] >>12063072how is this still not common knowledge?
 >> Anonymous Sat Aug 29 14:32:29 2020 No.12063149 >>12063138because it's bullshit
 >> Anonymous Sat Aug 29 14:36:12 2020 No.12063160 >>12063138There is no -oo in the real projective line. There is only a single point at infinity, oo. Now, -oo can refer to two things... it can refer to an element -oo such that -oo+oo=0 [an inverse element], which does not exist in this number system. Or, it can be (-1)*oo by formal arithmetic properties of this system, which is just oo and so really doesn't need a new symbol.
 >> Anonymous Sat Aug 29 14:42:38 2020 No.12063181 >>12063149>real world applications>bullshit>>12063160So there is no number at that point, just a point used as a number. got it.
 >> Anonymous Sat Aug 29 17:02:18 2020 No.12063738 >>12053975I know the image is bait because argument 1 relies on circular logic while calling out circular logic.
 >> Anonymous Sat Aug 29 17:09:04 2020 No.12063761 >>12063138So that's why they call (R,*,+) a ring.......
 >> Anonymous Sat Aug 29 20:33:25 2020 No.12064370
 >> Anonymous Sat Aug 29 21:13:03 2020 No.12064479 >>12063761But it isn't the real number line, it is the projective real number. The real number line is a ring whereas the projective one isn't.
 >> Anonymous Sun Aug 30 02:43:12 2020 No.12065146 >>12054765what you wrote is a nonsense since 0.9999... is not equal 1 so it not possible to replace one by another
 >> Anonymous Sun Aug 30 04:09:56 2020 No.12065296
 >> Anonymous Sun Aug 30 04:12:13 2020 No.12065299 >>12064370>aynrandllol
 >> Anonymous Sun Aug 30 04:21:10 2020 No.12065329 File: 123 KB, 1440x1715, b80.jpg [View same] [iqdb] [saucenao] [google] [report] >>12065146>>12065296When will infinitesimals be taken seriously?Even faggot wolfram alpha says 0.999... = 1 because that engine is too retarded to represent infinitely small difference between two numbers and assumes equality because of it.It's not even such hard concept to grasp, all you need to know is limits. The only reason anyone could proudly say that 0.999... = 1 is limits, because yes, the former is approaching 1, but it will never be 1, no matter how many 9's there are, even aleph_0, it will still be less than 1 because of it, because if we could know value of aleph_0 + 1, it would still get 0.999... closer to 1, but also aleph_0 + 2... what about if we added 4? 5? 100...?We came up with limits exactly to approximate these values despite them never actually being what the limit is, and yet people misuse undergrad level math to come up with retarded shit like this, what the fuck?
 >> Anonymous Sun Aug 30 05:02:28 2020 No.12065420 >>12065329They're like virtual particles in physics, a nice lubricant for equations. In the end however you return to real numbers. So 1/inf=0 to all non-autists.
 >> Anonymous Sun Aug 30 05:04:35 2020 No.12065427 >>12065329>0.999... = 1 is limitsno you retard, "limits" is when you see "lim" written."0.9..." is just as static as "1" is
 >> Anonymous Sun Aug 30 05:10:06 2020 No.12065437 >>12065427So is 0.000...1
 >> Anonymous Sun Aug 30 05:15:46 2020 No.12065450 >>12065329>We came up with limits exactly to approximate these values despite them never actually being what the limit is,Keep dreaming
 >> Anonymous Sun Aug 30 05:17:43 2020 No.12065454 File: 3.66 MB, 256x256, watch-and-learn.gif [View same] [iqdb] [saucenao] [google] [report] >>12065427You niggers always argue that 0.999... = 1 because 1 - 0.999... = 0.000...1In other words, because apparently you can just plug in value[eqn]\lim_{x \to \infty}\frac{1}{10^x}=0[/eqn]like a retard and be right.
 >> Anonymous Sun Aug 30 05:26:09 2020 No.12065459 >>12065454>You niggers always argue that 0.999... = 1 because 1 - 0.999... = 0.000...1Actually we argue 0.999... = 1 because it follows from the definition of 0.999... as a sum of an infinite series
 >> Anonymous Sun Aug 30 05:28:27 2020 No.12065463 >>12065459And the series depend on limits, yet somehow manage to introduce this retarded inconsistency. There's no real x where equatiin I mentioned becomes absolute 0, meaning that 1 - 0.999... > 0, faggot.Come up with something less retarded.
 >> Anonymous Sun Aug 30 05:34:25 2020 No.12065475 >>12065463So your point is that you dont accept 0.999... to be well defined as a number?
 >> Anonymous Sun Aug 30 05:36:08 2020 No.12065477 >>12065475I accept the fact that 0.999... is a well defined number that is infinitely close to 1 but is not exactly the same as 1 because of infinitely small difference.Its irrelevant to me how small the difference is, it isn't 0, because infinitely small difference is approaching 0, but is not 0, and I will not ignore it.
 >> Anonymous Sun Aug 30 05:50:10 2020 No.12065506 Suppose you have three equal spheres A, B, C with infinite points. Suppose you are able to remove a point from sphere B and two points from sphere C. How would you define the integer values of sphere B and C assuming A is 1.
 >> Anonymous Sun Aug 30 06:16:54 2020 No.12065541 >>12065437" 0.000...1" is just as static as "0" is
 >> Anonymous Sun Aug 30 06:18:20 2020 No.12065543 >>12065463>real xright, inf isn't a number
 >> Anonymous Sun Aug 30 06:19:23 2020 No.12065545 >>12065477>infinitely close to 1 but is not exactly the samelet's pretend finite is infinite
 >> Anonymous Sun Aug 30 06:22:50 2020 No.12065554 >>12065545Just a reminder that all real numbers between 0 and 1 make up a bigger set than all countable integers.0.999..., ironically, is not a part of countable integer set.
 >> Anonymous Sun Aug 30 06:26:59 2020 No.12065562 >>12065554nope,1 is part of the countable integer set
 >> Anonymous Sun Aug 30 06:32:44 2020 No.12065572 >>12065562if 0.999... = 1, then 0.999... is a part of countable integer set.This is everything that's wrong with niggers trying to do anything related to science.
 >> Anonymous Sun Aug 30 06:42:59 2020 No.12065591 >>12065572yeah, that's what I just saidlrn2read
 >> Anonymous Sun Aug 30 06:45:56 2020 No.12065603 >>12065591And its objectively wrong, you nigger.
 >> Anonymous Sun Aug 30 07:30:22 2020 No.12065695 >>12065463in other words, you don't understand the definition of 0.999... as a sum of an infinite series
 >> Anonymous Sun Aug 30 07:34:48 2020 No.12065703 >>12065695Infinite series rely on limits themselves and what you really can't grasp yourself is inconsistencies your retarded concept introduces.
 >> Anonymous Sun Aug 30 07:37:05 2020 No.12065706 >>12065703>inconsistenciesname one
 >> Anonymous Sun Aug 30 07:40:02 2020 No.12065711 >>12065706Your brain, you fucking faggot>Infinite series are defined as the limit of the infinite sequence of partial sums.Do you know what limit means?You faggots literally continue repeatedly telling us that 0.999... = 1, only because1 - 0.999... = 0 eventually, because that's the approximated limit.How fucking retarded do you have to be to not comprehend such trivial concept?
 >> Anonymous Sun Aug 30 07:42:34 2020 No.12065715 >>12065603ok sweetie
 >> Anonymous Sun Aug 30 07:43:37 2020 No.12065717 >>12065711>that's the approximatednope, exact
 >> Anonymous Sun Aug 30 07:44:39 2020 No.12065718
 >> Anonymous Sun Aug 30 07:47:30 2020 No.12065727 File: 65 KB, 1000x988, math.jpg [View same] [iqdb] [saucenao] [google] [report] >>12065717>>12065718[eqn]1 - 10^{-x} = 0[/eqn]And the value of x is?
 >> Anonymous Sun Aug 30 07:49:13 2020 No.12065729 >>12065727oh honey, it's right there under the "lim"
 >> Anonymous Sun Aug 30 07:51:02 2020 No.12065731 >>12065729By definition,[eqn]\infty[/eqn]is not a number you nigger.I don't even have to try, you faggots out yourselves as retards on your own.
 >> Anonymous Sun Aug 30 07:52:57 2020 No.12065735 >>12065731so?1/inf=0
 >> Anonymous Sun Aug 30 07:57:44 2020 No.12065742 >>12065735For [eqn]\frac{1}{\infty}=0[/eqn] to hold, [eqn]\frac{1}{0}=\infty[/eqn] needs to hold, also what the fuck does [eqn]1=0\cdot\infty[/eqn] even mean?You're a fucking retard.
 >> Anonymous Sun Aug 30 07:59:30 2020 No.12065746
 >> Anonymous Sun Aug 30 08:00:58 2020 No.12065750 >>12065742no, because that's manipulating inf like it is a numberyou just said that it isn't a number, wtf is wrong with you
 >> Anonymous Sun Aug 30 08:03:22 2020 No.12065754 >>12065746>>12065750Infinity is not a number so you can't do anything with infinity as a number.[eqn]\color{red}{\infty~is~not~a~number}[/eqn]Get that into your thick skull, retard.I'm showing you that it makes no sense to manipulate it like a number.If you treat it as a number but avoid inconsistencies by saying "doen't matter", you probably should realize that this isn't >>>/x/chizo board.
 >> Anonymous Sun Aug 30 08:04:50 2020 No.12065758 >>12065754>you can't do anything with infinitysure you can>>12062035
 >> Anonymous Sun Aug 30 08:06:03 2020 No.12065762 >>12065711in other words, you don't understand what limits are. okay
 >> Anonymous Sun Aug 30 08:06:59 2020 No.12065766 >>12065754>can't do anythinglol, schoolkids do it all the time$\displaystyle\lim_{x \to \infty} \dfrac{x+1}{x} =\lim_{x \to \infty} 1+ 1/x = 1+0 = 1$
 >> Anonymous Sun Aug 30 08:09:58 2020 No.12065777 >>12065758>>12065762>1^infinity=undefinedThen you look at math and realize that[eqn]\lim_{x \to \infty}1^x=1[/eqn]Care to explain why you blindly quote someone as retarded as you and try to pass it as a fact?>>12065766>only in context of limitsAre you seriously trolling or just that fucking braindead?
 >> Anonymous Sun Aug 30 08:10:39 2020 No.12065782 >>120657110.999... is not an infinite series, it's a real number. You want to know what's an infinite series? The retarded "proof" in number three of the OP.
 >> Anonymous Sun Aug 30 08:11:45 2020 No.12065785 >>12065782So you agree that it's a real number that's not in a set of integrals and that it doesn't equal to 1.Why the fuck are you even replying to me if you agree?
 >> Anonymous Sun Aug 30 08:15:38 2020 No.12065799 >>12065777yes, it's an example where the lim is different from the valuefeed it into wolfram alpha or go read a math book
 >> Anonymous Sun Aug 30 08:16:47 2020 No.12065805 >>12065785It's a real number that equals 1.Just another way of writing one.The same way 20/20 is another way of writing one.I'm replying to you because you are spouting retarded bullshit. 0.999... is not an infinite series.
 >> Anonymous Sun Aug 30 08:17:18 2020 No.12065807 File: 512 KB, 480x270, autism.gif [View same] [iqdb] [saucenao] [google] [report] >>12065777>only in context
 >> Anonymous Sun Aug 30 08:19:27 2020 No.12065816 >>12065799>wolfram alpha isn't retarded like me and knows that inf isn't a number>go read a math bookyeah go read up on what a number is and isn't and what limits are, you nigger.>>12065805>>>/x/
 >> Anonymous Sun Aug 30 08:21:10 2020 No.12065821 >>12065816WA vs random 4chan schizolol
 >> Anonymous Sun Aug 30 08:22:24 2020 No.12065827 >>12065754>Infinity is not a number so you can't do anything with infinity as a number.non sequitur
 >> Anonymous Sun Aug 30 08:23:25 2020 No.12065831 >>12065821You absolute nigger, WA tells you that[eqn]1^\infty=undefined[/eqn] exactly because its not a number, and you can't raise 1 by something that isn't even a number.
 >> Anonymous Sun Aug 30 08:24:48 2020 No.12065835 >>12065831how exactly is this related to your retarded opinion that 0.999... is not 1 ?
 >> Anonymous Sun Aug 30 08:25:10 2020 No.12065838 >>120658311/inf = 01 + inf = inf1- inf = -infinf + inf = infinf/inf undefinedinf-inf undefined1^inf undefinedfeed them all in WA
 >> Anonymous Sun Aug 30 08:25:26 2020 No.12065840 >>12065754It is possible to consider infinity as as number. One needs only to compactify the complex plane with a point added at infinity. This is called the Riemann sphere.However, this ends up not having the nice algebraic structure we would like it to have.But i agree, the arbitrary usage of infinity as a number is super retarded.
 >> Anonymous Sun Aug 30 08:25:28 2020 No.12065841 >>12065827>pretentious words his philosopher professor mentioned eventuallyThis is /sci/, not >>>/his/
 >> Anonymous Sun Aug 30 08:26:22 2020 No.12065842 >>12065841>i have no argument
 >> Anonymous Sun Aug 30 08:26:48 2020 No.12065844 >>12065840what "arbitrary usage" do you have in mind? for example 1/inf = 0 is completely fine.
 >> Anonymous Sun Aug 30 08:27:47 2020 No.12065847 >>12065840It is also possible to consider that 1 = 2 and be a >>>/x/ chizoposter and I don't give a fuck to humor that idea.>>12065842Then reply when you will have one, nigger.
 >> Anonymous Sun Aug 30 08:27:50 2020 No.12065848 >>12065841>Infinity is not a number so you can't do anything with infinity as a number.doesn't follow
 >> Anonymous Sun Aug 30 08:29:05 2020 No.12065849 >>12065848>can't use non-number as a number doesn't follow because my schizo says otherwise
 >> Anonymous Sun Aug 30 08:29:48 2020 No.12065853 >>12065847>Then reply when you will have one, nigger.go back if you don't even know how to greentext
 >> Anonymous Sun Aug 30 08:30:53 2020 No.12065856 >>12065853You literally greentexted yourself, what is there to know?
 >> Anonymous Sun Aug 30 08:30:55 2020 No.12065858 >>12065844In the context of riemann sphere, yes it is true. However, we lose the field structure. 0/infinity is no longer defined, for example. So one can no longer do arbitrary operations that would be valid in a field wihtout being careful.>>12065847Compactification is no pseudo-mathematics, retard. It has a real valid point when talking about topology.
 >> Anonymous Sun Aug 30 08:31:13 2020 No.12065859 >>12065849feed them all in WA
 >> Anonymous Sun Aug 30 08:31:24 2020 No.12065860 >>12065816>He thinks numbers with repeating decimals are infinite series>He doesn't realize we wouldn't be able to operate on fractions without using limits if this was the case>He uses basic Math terms wrong>He sends *me* to /x/0.999... = 1 Seethe harder.
 >> Anonymous Sun Aug 30 08:32:21 2020 No.12065862 >>12065856lol, so cluelesstypical schizo
 >> Anonymous Sun Aug 30 08:34:26 2020 No.12065872 >>12065862>cluelessDo you always talk in 3rd person or only on 4chan?
 >> Anonymous Sun Aug 30 08:38:15 2020 No.12065881 >>12065859At this point you may aswell tell me to feed 0.999... into WA.Talk to me when WA will respect infinitesmals.
 >> Anonymous Sun Aug 30 08:42:13 2020 No.12065888 >>12065849X is not a number => arithmetic operations are not necessarily defined for X (but they might) and if they are, they don't necessarily obey all usual rules (but they might)X is not a number => arithmetic operations are automatically not defined for Xone is true, one is false
 >> Anonymous Sun Aug 30 08:47:13 2020 No.12065900 >>12065888Your brain is false.[eqn]1^\infty = 1[/eqn] could very easily be defined with no issues but some faggot arbitrarily decided that nah, that just won't do it.And why won't it do? Nobody knows because the whole thing is retarded.
 >> Anonymous Sun Aug 30 08:48:20 2020 No.12065902 >>12065881>i am better than WA in mathtopkek
 >> Anonymous Sun Aug 30 08:48:32 2020 No.12065903 >>12065900there's a perfectly sane reason for why it's not defined this way
 >> Anonymous Sun Aug 30 08:49:23 2020 No.12065904 >>12065900your Fields medal is in the mail
 >> Anonymous Sun Aug 30 08:49:33 2020 No.12065905 >>12065900Exponentiation would lose continuity.Suppose x^infinity is defined.Then for all x < 1, x^ infinity = 0However, 1 ^ infinity = 1.One desires exponentiation to be continuous. Literally as simple as that
 >> Anonymous Sun Aug 30 08:51:04 2020 No.12065908 >>12065905>one desires consistency>rounds 0.999... up to 1
 >> Anonymous Sun Aug 30 08:51:54 2020 No.12065910 >>12065908Imagine literally being this retarded.I'm surprised you can solve captchas.
 >> Anonymous Sun Aug 30 08:53:17 2020 No.12065915 >>12065905Wait, hold on...[eqn]2\cdot2\cdot...\cdot2=0[/eqn]??? Guess I'm just being trolled here.>>12065910my indian friend solves them for me
 >> Anonymous Sun Aug 30 08:54:19 2020 No.12065919 File: 112 KB, 953x613, 1494195814627.jpg [View same] [iqdb] [saucenao] [google] [report]
 >> Anonymous Sun Aug 30 08:55:56 2020 No.12065924 >>12065919>infinitesmals don't existSomeone told me that I'm not smarter than WA, so I went to WA and found out that they do https://mathworld.wolfram.com/Infinitesimal.html
 >> Anonymous Sun Aug 30 08:59:36 2020 No.12065935 >>12065924more like they're not real
 >> Anonymous Sun Aug 30 09:04:34 2020 No.12065938 >>12065935And? They're extension of real numbers, part of hyperreals[eqn]^*R[/eqn]
 >> Anonymous Sun Aug 30 09:05:19 2020 No.12065939 >>12057645it's not an algorithm idiot. CS fags gtfo
 >> Anonymous Sun Aug 30 09:06:55 2020 No.12065942 >>12065939>use WA to see ur wrong>shits on CSOkay so can you make an argument that doesn't depend on "look it up on WA"?
 >> Anonymous Sun Aug 30 09:16:41 2020 No.12065959 >>12057645>0.999... is an algorithm that keeps appending nines.don't make stuff up, anon
 >> Anonymous Sun Aug 30 09:25:22 2020 No.12065969 >>12065942read a book
 >> Anonymous Sun Aug 30 09:27:05 2020 No.12065976 >>12065969I've read Nietzsche.
 >> Anonymous Sun Aug 30 09:36:11 2020 No.12066001 >>12056105reee all rings are integral domains
 >> Anonymous Sun Aug 30 09:40:04 2020 No.12066007 >>12056105[eqn]\lim_{x \to \infty}10^{-x}=0.000...1=0[/eqn]Do I need to explain or will you come to your own conclusions?
 >> Anonymous Sun Aug 30 17:25:10 2020 No.12067573 >>12066007youve not contradicted anything i said
 >> Anonymous Sun Aug 30 17:26:30 2020 No.12067577 >>12067573Everything you wrote is complete bullshit.Whatever retarded shite you wrote literally has nothing to do with infinitesmals.
 >> Anonymous Sun Aug 30 18:06:59 2020 No.12067719 >>12067577thats exactly my point you dumb retardI was showing that .000...1 ISNT an infinitesimalcan you read?
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