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# /sci/ - Science & Math

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File: 65 KB, 992x843, 1589218273373.jpg [View same] [iqdb] [saucenao] [google] [report]

set x=pi.
therefore, y=-cos(pi)=1.
now lets go backwards.
assume that you have 0.999...=-cos(x)
if 0.999...=1, then 0.999...=1=-cos(x) where x=pi

however, this is not the case, because pi is an irrational and completely predefined number for all of its digits associated with it i.e. 3.14159265358979323846264338327950288419716939937510... ad infinitum.

so setting y=0.999... would yield a value of x that is infinitesimally close to pi but not pi. you might ask which digit of pi is altered to achieve such an infinitesimal aberration from the number one, but it less as elusive as asking where is the missing 0.000... ...01 from the whole number 1 to make 0.999...

the existence of pi is indisputable. each number is as important as the number that precedes it towards infinity, and it is wholly unique. if 0.999... = 1, then you are denying the absolute existence of pi and you should be ashamed of yourselves.

if 0.999... = 1, then 1=2 and 0=3.

 >> Anonymous Wed May 13 22:20:46 2020 No.11669549 >>11669397>so setting y=0.999... would yield a value of x that is infinitesimally close to pi but not piThis requires the assumption that 0.999... =/= 1, making your argument circular
 >> Anonymous Wed May 13 22:28:03 2020 No.11669569 >>116693973 < π3.1 < π3.14 < π3.141 < π3.1415 < π3.14159 < π3.141592 < πthis continues endlesslyπ < π
 >> Anonymous Wed May 13 22:50:17 2020 No.11669645 >>11669549see>>11669569y=-cos(3)=0.989992496600445457271572794731261302393679096615588328814...y=-cos(3.1)=0.999135150273279464492376054541466262836641669947942743544...y=-cos(3.14)=0.999998731727539545285114306345049983854508439392120932039...y=-cos(3.141)=0.999999824380866392940839580833975469489338051607740815449...y=-cos(3.1415)=0.999999995707656152283851309987064521145887541258770243337...y=-cos(3.14159)=0.99999999999647923060461239250850048325101828738865122795...y=-cos(3.141592)=0.99999999999978641019108725942917886921117573907654096975...y=1 if and only if x=pi ... exactly
 >> Anonymous Wed May 13 23:02:21 2020 No.11669685 >>11669645Are you retarded? Did you miss the fact that it approaches 1 as the argument approaches pi?
 >> Anonymous Wed May 13 23:34:28 2020 No.11669782 >>11669397Super EZ proof that 0.999... = 11/3 = 0.333...3 x (1/3) = 3 x 0.333...1 = 0.999...
 >> Anonymous Wed May 13 23:39:30 2020 No.11669797 >>11669645Yes and if 0.999... = 1 then arccos(0.999...) = pi exactly. Which it does, so it does.
 >> Anonymous Wed May 13 23:45:01 2020 No.11669820   >>11669569if you proved pi < pi we have bigger issues than 0.99.. not being 1
 >> Anonymous Wed May 13 23:46:18 2020 No.11669826 File: 112 KB, 953x613, 1=.999....jpg [View same] [iqdb] [saucenao] [google] [report] >>11669397SAGED
 >> Anonymous Wed May 13 23:48:06 2020 No.11669837   >>11669826cool image, but "by induction"...? didn't get that
 >> Anonymous Wed May 13 23:53:13 2020 No.11669855 File: 234 KB, 610x610, problem-solver.jpg [View same] [iqdb] [saucenao] [google] [report] >>11669837You've got a lot of reading to do.I'll even give you your first link: https://en.wikipedia.org/wiki/Mathematical_induction
 >> Anonymous Wed May 13 23:54:52 2020 No.11669857 >>11669855You're only proving one case. I don't know what you think induction is, but that isn't it.
 >> Anonymous Thu May 14 06:15:02 2020 No.11670753 >>11669397I can disprove that theorm by make the observation that 0.99... and 1 are not the same numbers. mathtards btfo
 >> Anonymous Thu May 14 07:14:32 2020 No.11670834 >>11670753do it big boi
 >> Anonymous Thu May 14 07:24:10 2020 No.11670847 File: 1.30 MB, 1280x720, duck is perplexed.png [View same] [iqdb] [saucenao] [google] [report] >>11670834I-i...I just did?
 >> Anonymous Thu May 14 07:26:31 2020 No.11670853 File: 331 KB, 300x221, done.gif [View same] [iqdb] [saucenao] [google] [report] >>11670847I make the observation that you're an idiot.>wow it really works
 >> Anonymous Thu May 14 07:33:40 2020 No.11670860 >>11669826>You might think every number has a unique decimal expansion. You would be wrongthe absolute lack of argument - made only worse by the fact that the image clearly contains actual arguments and thus would include support for this claim if it could - only strengthens my suspicions that the 0.999... fags are on to somethingthese threads will continue to be posted until /sci/ actually learns mathematics and produces a satisfying explanation.
 >> Anonymous Thu May 14 07:46:47 2020 No.11670889 $\boxed{0 < p < 1} \\1 = p + (1-p) ~~~~~~ \overset{1}{ \overbrace{[=====p=====|==(1-p)==]}} \\ \text{divide p using x} ~~~~~~ \overset{1}{ \overbrace{ \underset{p}{[ \underbrace{=====x=====|==(p-x)==}]} ~~ + ~~ (1-p)}} \\\\\text{solve x and (p-x), when length ratios must be the same} \\\dfrac{x}{p-x}= \dfrac{p}{1-p} \Rightarrow x- xp = p^2 - xp \Rightarrow \underline{x=p^2} \Rightarrow \underline{(p-x)=p(1-p)} \\\overset{1}{ \overbrace{ \underset{p}{[ \underbrace{=====p^2=====|==p(1-p)==}]} ~~ + ~~ (1-p)}} \\\\\overset{1}{ \overbrace{ \underset{p^2}{[ \underbrace{=====p^3=====|==p^2(1-p)==}]} ~~+ p(1-p)+(1-p)}} \\\overset{1}{ \overbrace{ \underset{p^3}{[ \underbrace{=====p^4=====|==p^3(1-p)==}]} ~~+ p^2(1-p)+p(1-p)+(1-p)}} \\(1-p)+p(1-p)+p^2(1-p)+p^3(1-p)+ \cdots =1 ~~~~ \left | ~ \times \frac{1}{1-p} \right . \\1+p+p^2+p^3+ \cdots = \dfrac{1}{1-p}$
 >> Anonymous Thu May 14 07:48:57 2020 No.11670897 >>11669826TEH MATH.CRINGE. I imagine a fat slob who loves anime and does math to feel cool.
 >> Anonymous Thu May 14 07:54:27 2020 No.11670908 >>11670853Nice b8
 >> Anonymous Thu May 14 08:28:58 2020 No.11670984 >>11670889what is this math evenwritten so neatly i have never seen such style before
 >> Anonymous Thu May 14 08:42:04 2020 No.11671018 >>11669397>Guys I proved that A =/= ALearn2definition
 >> Anonymous Thu May 14 08:43:33 2020 No.11671021 File: 471 KB, 717x768, Retardscreachingexcitedly.png [View same] [iqdb] [saucenao] [google] [report] >>11671018lol retard it clear says there in the op that B =/= A what are you literally brain damaged?
 >> Anonymous Thu May 14 08:47:09 2020 No.11671031 >>11669397pi = lim(n->inf) (cos(360/n) * n)/2
 >> Anonymous Thu May 14 08:49:11 2020 No.11671039 >>11671031sorry, replace cos with sin
 >> Anonymous Thu May 14 09:13:20 2020 No.11671101 >>11669685I'm not approaching 1 I am approaching 0.999... which is an infinitesimal step below 1.>>11669797x=arccos(-y)let us see the iterations as y approaches 0.999... not 1.x=arccos(-0.9999999)=3.141145439990566500477009347399887558935717056958176735465...x=arccos(-0.99999999)=3.141451232233438077827300291442614303329194482853121225407...x=arccos(-0.999999999)=3.141547932230239515888751861631142431400718260085750433840...x=arccos(-0.9999999999)=3.141578511454169389661025165982689624213851967799185604816...x=arccos(-0.99999999999)=3.141588181453838235156470602424130672713759902775571409191...x=arccos(-0.999999999999)=3.141591239376230865249743451392994237261322265928440484832...x=arccos(-0.9999999999999)=3.141592206376197738500977321482269404595357865558939211351...where the exact number pi = 3.14159265358979323846264338327950288419716939937510...looking at it logically, each 9 appended to the number 0.999... adds a greater deal of accuracy to the number pi.relatively speaking (looking at the last arccos iteration), it takes about 19 9's to get 6 correct decimal digits of pi, which isn't very fair. If the resolution of 0.999... is not proportional to the resolution of pi in the limit, then it means that the ideal realization of pi with "catch up" later to all of those 9's appended in the limit or even never.tldr it takes a lot of 9's to make pi, therefore each digit of pi has some amount of (9/10)^n in the function that help build it.to make it clear i am not approaching 1 I am approaching 0.999... in the limit.
 >> Anonymous Thu May 14 09:18:39 2020 No.11671125 File: 145 KB, 720x405, 70b5cd_e588f78e634444c3a45b56418f9dd38f-mv2.jpg [View same] [iqdb] [saucenao] [google] [report] >>11669782>>11670847>>11671018sqrt of minus one (0.000...1) equals minus one
 >> Anonymous Thu May 14 09:38:10 2020 No.11671166 >>11671125so the square root of minus one (0.000...1) = minus one (0.000...1) cause placeholder 0 and negative numbers do not exist
 >> Anonymous Thu May 14 09:56:49 2020 No.11671227 File: 86 KB, 820x995, merlin-magician-royalty-free-clip-art-png-favpng-Z5ZaejkSui63qLKPWsiSUUYcE.jpg [View same] [iqdb] [saucenao] [google] [report] Zero (0) is simply Shorthand for Minus One (0.000...1) and for Infinity (∞) because Both are exactly Equal completing the Definition of so-called 'undefined'.
 >> Anonymous Thu May 14 10:16:18 2020 No.11671280 >>11671039devil
 >> Anonymous Thu May 14 10:50:05 2020 No.11671372 >>11671280cos every1 is a sinner
 >> Anonymous Thu May 14 11:11:10 2020 No.11671425 Here's a simple argument why 0.99... != 1If two numbers a and b are the same, then clearly for any function f, we must have that f(a) = f(b). This is just common sense.Define f to take in any real number, and return the digit in the tenths place.Then f(1) = 0, but f(0.999...) = 9. Therefore 0.999... != 1.
 >> Anonymous Thu May 14 11:23:42 2020 No.11671471 >>11671425american education, folks
 >> Anonymous Thu May 14 11:26:30 2020 No.11671477
 >> Anonymous Thu May 14 11:34:44 2020 No.11671509 File: 254 KB, 512x512, 1588947543986.gif [View same] [iqdb] [saucenao] [google] [report]
 >> Anonymous Thu May 14 11:35:54 2020 No.11671515   0.999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999...
 >> Anonymous Thu May 14 11:36:55 2020 No.11671519   ...9999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999...
 >> Anonymous Thu May 14 11:37:55 2020 No.11671522   ...999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999...
 >> Anonymous Thu May 14 11:38:58 2020 No.11671525   ...99999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999...WHERE'S THE FUCKING ONE, THEN?
 >> Anonymous Thu May 14 11:46:12 2020 No.11671545 >>11671515>>11671519>>11671522>>11671525>let's pretend finite is infinite
 >> Anonymous Thu May 14 11:48:23 2020 No.11671553 >>11671525up your ass
 >> Anonymous Thu May 14 11:51:04 2020 No.11671563   >>11671545I could do it until the end of time and there would still be no 1 faggot.
 >> Anonymous Thu May 14 11:53:34 2020 No.11671571 >>11671563oh sweetie, that's why inf isn't a number
 >> Anonymous Thu May 14 11:55:25 2020 No.11671583 >>11671101One of the most basic properties of the real numbers is the Archimedean property, part of which states that there are no infinitesimally small real numbers. More exactly, it states that for all real numbers greater than zero, there are natural numbers n such that 1/n is less than the real number.This is provable from an even more fundamental property of the reals, the least upper bound property. It states that any nonempty set of real numbers which is bounded above has a least upper bound: a number which is >= all elements of the set, and <= all upper bounds of the set.Let S be the set of infinitesimals in the reals. S is obviously bounded above by 1, because there wouldn't be infinitesimals greater than one. Then, assume by contradiction that S is nonempty. This means that S has a least upper bound I'll call r.r < 2r, and since r is an upper bound, 2r cannot be in S, so can't be infinitesimal. Thus, we can pick a natural n such that 1/n < 2r.r/2 < r, and since r is the least upper bound, there must be at least one infinitesimal i > r/2.However, 1/(4n) < r/2 < i, meaning i is not infinitesimal. By contradiction, S is empty.
 >> Anonymous Thu May 14 11:57:05 2020 No.11671588 >>11671425Let f be the function that returns the denominator of any fraction. f(1/2)=2, but f(2/4)=4. Thus, 1/2 != 2/4.
 >> Anonymous Thu May 14 12:04:21 2020 No.11671614   >>11671571At no point during an eternity is there even the mechanism for a 1 to appear.Face it mathcuck, you've been hoodwinked into believing illogical fantasies.
 >> Anonymous Thu May 14 12:05:43 2020 No.11671618 >>116716146/3Where's the 2?
 >> Anonymous Thu May 14 12:16:38 2020 No.11671653 >>11669826x = 0.333...10x= 3.333...10x-x = 3.333... - 0.333...9x = 33x = 1x = 1/3 = 0.333...BUTx = 0.33oh wait you just realized that the "proof by induction" presented in your picture is fucking retarded and is just an aberration of humans using decimal to represent numbers being unable to deal with that situation very well333...
 >> Anonymous Thu May 14 12:18:46 2020 No.11671661 >>11671614>during an eternity>duringlol, what on earth is going on in that pretty little head of yours
 >> Anonymous Thu May 14 12:36:52 2020 No.11671717   >>116716186/3 is calculation, not a number0.9999... is a numerical expression>>11671661eternity by definition lasts forever. Are you dumb?
 >> Anonymous Thu May 14 12:37:22 2020 No.11671721 >>11671477very neat
 >> Anonymous Thu May 14 12:38:22 2020 No.11671726 >>11671563i could write pi forever and still not be able to make a perfect circle out of itperfect circles must be mathematically impossible
 >> Anonymous Thu May 14 12:43:22 2020 No.11671752 >>116717176/3 is a number, just like 1+1 is a number, 0.5 is a number 7*2 is a number, and the infinite sum from n=1 to infinity of 9/(10n) is a number. It doesn't matter how you label something, as long as it equals a number, it is a number.
 >> Anonymous Thu May 14 12:53:20 2020 No.11671784   >>11671726This is literally correct. Perfect circles are mathematically impossible.
 >> Anonymous Thu May 14 12:58:12 2020 No.11671801 >>11669397why do people still comment on these threads?
 >> Anonymous Thu May 14 13:01:00 2020 No.11671813 >>11669397you just -said- that it's not the case. but it in fact is true that 0.999...=1=-cos(pi).
 >> Anonymous Thu May 14 13:28:42 2020 No.11671918 >>11671717>by definitionok, here's an actual definition:https://www.wolframalpha.com/input/?i=infinityAn unbounded quantity that is greater than every real number.nothing about 'time', nimrod
 >> Anonymous Thu May 14 13:31:31 2020 No.11671929 >>11671784x^2+y^2=r^2>wipes sweat off forehead
 >> Anonymous Thu May 14 13:42:44 2020 No.11671979   >>11671929Nice irrational set you have there. Shame you can't enumerate it.Just tell me you're a midwit next time, things will be a lot quicker.
 >> Anonymous Thu May 14 13:48:17 2020 No.11671997 >>11671979>enumerate itonly losers like you need to do that.it's perfect, cope
 >> Anonymous Thu May 14 14:04:31 2020 No.11672059   >>11671997It's not real if you can't yield it.
 >> Anonymous Thu May 14 15:08:47 2020 No.11672265 >>11669397You are absolutely correct OP, nice proof this shows proof that you have a creative mind.Also it's kind of wierd that this is the exact way that I thought of the .999 problem.
 >> Anonymous Thu May 14 16:33:43 2020 No.11672588 >>11672265OP here.are you... me?
 >> Anonymous Thu May 14 16:57:56 2020 No.11672709 >>11669397>so setting y=0.999... would yield a value of x that is infinitesimally close to pi but not piyou assumed that .999... = 1 so this is a non sequitor
 >> Anonymous Thu May 14 17:01:52 2020 No.11672734 why do these threads survive lol
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