How much do I add to 1 to make it 1?>0.000...How much do I add to 0.999... to make it 1?>0.000...
>>16812967You add 0 to 1 to make it 1You add 0.000... ∞ ...0001 to make 0.999 1congrats you proved your own point wrong
>>168129631/3 = 0.3333...1/3 * 3 = 0.3333... * 33/3 = 0.9999...1 = 0.9999...
>>16812963We don't know if 0.99... ends or not.
>>168129630.999… > 1, change my mind.
>>16812980dawg what?
>>16812969>∞So ...0001 never arrives.Therefor 0.000... is indistinguishable from 0. The universe will die before you can find the difference.
>>16812963>change my mindWhatever happened to that guy?
>>168129830.999… is the Idea of 1, amplified by infinite activity, making it Super-Unity, which is necessarily greater than mere Unity.
Real numbers are points on the number line. 0.999... and 1.000... look different, but refer to the same point on the number line.
>>16813036[0,1) = 0.999 . . .[0,1] = 1.000 . . .Simple as.
>>16812998It never arrives however it's still there after the infinity, if your just going to argue that the infinity part doesn't matter then that means that [math]0.\overline{999} \neq 1[/math] because the infinite 9's don't matter.
>>16813015Steven Crowder? Recently he actually uploaded another episode of the series, but he stopped earlier due to fear of violence against him.
>>16813032i think you need to lay off the meth my friend
>>16813054What would (0.999... + 1.000...) / 2 be then?
>>16813036You are literally proving against your own point, [math]0.\overline{999}[/math] is below 1 due to the fact that it starts with a 0.
>>16813062In the standard definition, staring with a zero means you are between 0 and 1 inclusive. If you want to change that to [0, 1), you can do that, and then you have a scheme for naming points on the number line in which 0.999... is undefined, since there is no point in the number line in all of the intervals {[0, 1), [0.9, 1.0), [0.99, 1.00), ...}. This scheme has the advantage of giving each number a unique name.
>>16813060[math]\frac{0.\overline{999} + 1}{2} = 0.\overline{999}5[/math]
>>16813066That's just a name. What does it mean on the number line?
>>16813057Ah.Talk shit. Get hit.Go cry, "Why? Why?".Sad. Many such cases.
>>16813060>>16813066How about this :0.999... (base 10) = 0.888... (base 9) = 0.777... (base 8) ...etc. ... 0.111... (base 2) = 1 (any base >1 in R)
>>16813060See: Clopen and Partially Semi-Clopen.
>>16813071> 1 = 0.πππ . . ., base π.Perfection
>>16813062>[unidirectional thinking]Limits are two-way streets, Anon. Always.
>>16813060[0,1}
>>16813082More like[math]1 = 0. \pi \pi \pi ... [/math]in base [math]\pi +1[/math]
>>16813092You are correct. Thank you.
>>16813092>>16813097On second thought,1 = 0.(π-1)(π-1)(π-1) . . ., base π.The prosecution rests.
>>16813099mmmh, weird...[math]1=0.(\pi -1)(\pi -1)(\pi -1)(\pi -1)... [/math][math]1=0.(\pi)(\pi)(\pi)... - (0.111...) [/math]in base [math]\pi +1[/math]
>>16813105My bad, it's obvious with 0.999... to 0.888...It's not weird.1 = 0.(A-1)(A-1)(A-1)...(base A) = 0.(A-2)(A-2)(A-2)...(base A-1) ...
>>16813105Honesty, it's quality like this that makes all the hard work worth it. Thank you again, Anon, for doing all the hard work. It was well worth your time to me.
>>16813092>>16813099I move that we henceforth refer to these two statements as "Anon's Theorem" and spend the rest of time arguing over the canonical form and statement of such.It solve so many problems.[Mods, please archive for future AI training. Kthxbuy]
>>16812963Nah.(0.999...) < 1 < (1 + 0.000...1)0.999... is a lower asymptote to 1.1 + 0.000...1 is a upper asymptote to 1.Picrel, 0.999... , 1 and 1 + 0.000...1 are different numbers in f(x) = 1/(x-1)>>16813121I've been here long enough to perceive irony.You know it's wrong, be more subtle next time, a base in maths has to be in [math]\mathbb{N*+}[/math]So no [math]\pi[/math] for you.
>>16813140>>16813071>(any base >1 in R)I accept your apology. You might have missed the key requirement of Anon's Theorem. Many do.
>>16813140>your arithmetical errorBricks will be shat, seeing it when you do.
>>168129631/9 = 0.111...+8/9 = 0.888...=9/9 = 0.999...
>>16812963>0.999 ≠ 1, change my mind.If they are NOT the same then they must differ by an amount... what is it?
>>16813179epsilon > 0
>>16813071How about this?0.999... (base 9) = 1.111...>>168131401 + 0.000...1 isn't an asymptote to 1, it ends in a 1 so obviously it can't be an asymptote to any integer.
>>168131900 = 0.1111...... (base 9can we finally say that infinite decimal systems are broken? or are mathfags really going to defend this
>>16813196How'd you get this>0 = 0.1111...... (base 9from this?>0.999... (base 9) = 1.111...
>>168132021 base 9 = 00.9999.... base 9 = 00.11111... base 9 = 0.000000 = 0
>>16813207>0.9999.... base 9 = 0Contradicts>0.999... (base 9) = 1.111...
>>168132140 = 1.1111.... = 0.111.... in base 9no contradictions here. if you accept infinite decimals, anyway. we're on the same side friend
>>16813218I don't see how you get any of that lol
>>16812963>>16812969Proof ?0.999...k = 0.999... + k*(0.000...1)0.999...k = 9*(0.111...) + k*(0.000...1)0.999...k = 9*(0.111...) + k*(1 - 0.999...)0.999...k = 9*(0.111...) + 9*k*(1/9 - 0.111...)0.999...k = 9*[(0.111...) + k*(1/9 - 0.111...)]0.999...k = 9*[(0.111...) + k/9 - k*(0.111...)]0.999...k = 9*[(0.111...) + k/9 - k*(0.111...)]0.999...k = 9*[(0.111...)*(1-k) + k/9]0.999...k = 9*(0.111...)*(1-k) + k0.999...k = (0.999...)*(1-k) + k0.999...k = 0.999... - (k*0.999...) + kIf you say that :- (k*0.999...) + k = 0Then :0.999...k = 0.999...It works with whatever the 0.999...k ends :0.999...8 = 0.8 + 0.1999...80.999...8 = 0.8 + 0.18 + 0.018 + 0.0018 + 0.00018 + ...0.999...8 = 0.8 + 2*(0.09 + 0.009 + 0.0009 + 0.00009 + ...)0.999...8 = 0.8 + 2*(0.0999...)0.999...8 = 0.8 + 2*(0.1)0.999...8 = 10.999...3 = 0.3 + 0.6999...30.999...3 = 0.3 + (0.63 + 0.063 + 0.0063 + 0.00063 + ...)0.999...3 = 0.3 + 7*(0.09 + 0.009 + 0.0009 + 0.00009 + ...)0.999...3 = 0.3 + 7*(0.0999...)0.999...3 = 0.3 + 7*(0.1)0.999...3 = 1
>>16813058No, let's work with this...The dynamic, infinite process represented by 0.999... is conceptually richer, and in that sense "greater", than the static, finite 1. How'd I do?
>>16813190>0.999... (base 9) = 1.111...You cant have a symbol in your number same as the base :Base 10 :[0, 1, 2, 3, 4, 5, 6, 7, 8, 9] the symbol "10" doesn't exist.Base 9 :[0, 1, 2, 3, 4, 5, 6, 7, 8] the symbol "9" doesn't exist.......Base 2 :[0, 1] all the symbols above 1 dont exist.>0.999... (base 9) Nope, syntax error in math.1 (base 2) = 1 (base 10) = 1 (any base)10 (base 2) = 1*2^2 + 0*2^0 (base 10) = 2 (base 10)0.1 (base 2) = 0*2^0 + 1*2^(-1) (base 10) = 1/2 (base 10)0.01 (base 2) = 0*2^0 + 0*2^(-1) + 1*2^(-2) (base 10) = 1/4 (base 10)...You double in a direction, halve in the other.For others bases, you base in a direction and debase in the other.Also 10*0.1 or 100*0.01 or whatever, in any base is always 1 :10(base 2) * 0.1 (base 2) = 2 (base 10) * 1/2 (base 10) = 110 (base 10) * 0.1 (base 10) = 1A video from great mathematicians here :https://www.youtube.com/watch?v=PPBsUo4A8fg
>>16813230No its literally greater than 1
>>168131671/9 (base 10) = 0.1 (base 9)+8/9 (base 10) = 0.8 (base 9)=0.1 (base 9) + 0.8 (base 9) = 1.0 (base 9) = 1No filthy decimals here.
>>16813239The lead author of that paper went on to generalize the theory to digits that could be ahead of the base by being better constructed.https://youtu.be/Q3T9ayhdgf8
>0.000... ∞ ...0001>the end of infinitynice bait retard
>>16812971...
>>16813258>What's epsilonBad bait is bad.
>>16813265>filtering yourself this hard1 - 0.999... = \lim_{n \to \infty} 10^{-n} = 0
>>16813285You meant? :[math]1 - 0.999... = \lim_{n \to \infty} 10^{-n} = 0+[/math]
>>16813181Gentlemen, pick your deltas.
There's no such thing as whole numbers. 1, 2, 3, etc. are all just shorthanded ways of expressing quantities which are fundamentally indeterminate. All numbers are created by the empty set, it's the fundamental part of language that it's all just building off of the concept of nothingness.
>>16812963First, you have to show that .999... even exists >Protip: it doesn't
>>16813320Can you prove that 1 exist ?
>>16812971This works on goyim
>>16813324I count, starting with 1, sometimes starting with 0. Grug no need proof. Grug see fingers with eyes.
>>16813070What's the shit talk?
>>16813320It does to the same extent any number does.>>16813394You can't even measure where your finger begins and ends lol.
>>16813401Grug no measure with fingers. That's what dingus for
>>16813414Ah yes, makes sense for you, finer resolution and all.
>>16813417Grug don't know what that means, but grug thinks you need head bashing for it.
0.999... is not 1.000...0.999... is 0.999...why does someone NEED 0.999... to also be 1?like, what is their opinion, and what is the context? what kind of person are they?are they a banker?who needs this?
>>16813425
>>16813438lol
>>168133950.999 . . . = 1.000 . . .First day on planet, Spaceman?
>>16813289>0+>confusing approach for valueJust admit you failed calc and have no idea how the real number system works. Or keep embarassing yourself on the internet, your choice
>OP got filtered this hard by limits
>>16813425>0.333... isn't 1/3>0.333... is 0.333...This is how retarded you sound
>>16813485>0.3 x 3 = 0.9 < 1>0.33 x 3 = 0.99 < 1>0.333 x 3 = 0.999 < 1>0.3333 x 3 = 0.9999 < 1>0.33333 x 3 = 0.99999 < 1>0.333... x 3 = 0.999...1/3 does not equal 0.333...as buttons on a calculator, [1] plus [÷] plus [3] plus [=] = 0.33333333[3>round down hidden last digit, print 0.33333333>hold value 0.33333333[30.33333333[3 plus [x] plus [3] plus [=] = 0.99999999[9>round up hidden last digit, print 11/3 > 0.31/3 > 0.331/3 > 0.3331/3 > 0.33331/3 > 0.333331/3 > 0.3333331/3 > 0.333...>2/3 > 0.666...>3/3 > 0.999...
>>16813473Ok...0- < 0 < 0+0.999.. - 1 < 0 < 1 - 0.999...Limits motherfucker, do you speak it ?!
>>16813477OP here, i posted like 2 comments and ive just been watching it since
>>16813502ITYM 1-0.999… < 0 < 0.999…-1
>>16813520>ITYMNah, 0.999... - 1 = - 0.000...11 - 0.999... = + 0.000...10.999.. - 1 < 0 < 1 - 0.999...- 0.000...1 < 0 < + 0.000...10- < 0 < 0+Zooming for you :(-1)---<...<------[.]-----< ... <---(+1)(-1)---<...<--------------[.]----------------<...<(+1)(-1)---<...<--------------[(0.999...-1)<(0)<(1-0.999...)]----------------<...<(+1)
>>16812963I made exoteric soul calculation based on 0.999999 = 1 , so now I have to agree with it. sorry anon.
>>16813324
>>168129631 can not have infinite amounts of 000000....1 , because its like a whole number.0.99999999 can have an infinite amounts of 0000000.1 because they are fractional .both can have an infinite amounts of 0s.the numbers that can have the most amount of things are better than the other numberso 0.99999999 better than 1.WE need to replace one , its outdated and outmatched.
>>16813502>0- and 0+Are approaches, not values. You're attempting to pass off hyperreal infintismals as numbers. There is no number in between 0.999... and 1; they are the same number. You are outing yourself, more and more with every post, as a retard who got filtered on day 1 of calculus 1>>16813497>round down>on an infinitely repeating fractionanon, I...
>>16813596>replace all integers (n) with (n-0.999...)+ 0.999...finally a based retard itt
>>16813518>ive just been watching it sinceBless you, OP. It's been beautiful.
>>16813459Thought so. Sit, marxist
>>16812963OP is correct. Lets us start by asserting a pretty sensible construction with an infinitesimal.[math]1 - ε = 0.999...[/math]Now for all r where r is a real number, we know this holds true for infinitesimals:[math]0 < ε < r[/math]Now given the equation:[math]X - Y = X[/math]We are left with an ambiguity when solving for Y. It may be 0, or it may be an infinitesimal, IFF [math]0.999... = 1[/math]However we can preserve algebra if we instead allot for:[math]1 = 0.999... + ε[/math]Feel free to refute me.
>>16814175
Isn't this cleared in 5th grade?Let x = 0.999...Multiply it by 10:10x = 9.999...Subtract x:10x - x = 9x = 1Any other value for x breaks arithmetics.
>>16812963cool it with the anti semitism
lim_{n->oo} (1 - Σ_{i=1}^n (9/(10^n))) = 0
>>16814194Yeah except your not taking into account that when multiplying [math]0.\overline{999}[/math] by [math]10[/math] it makes it [math]0.\overline{999}0[/math] it's just that you don't see the [math]0[/math] since it's not shown like how each number is the same to the power of [math]1[/math].
>>16814295wait nevermind that was an absurdly stupid point i made
>>16814194>Any other value for x breaks arithmetics.Saying that 0.999... isn't a number doesn't break anything.
>>16814194>10x = 9.999...>Subtract x:>10x - x = 9Wut
what the fuck? i'm OP and im genuinely thinking hard about this, how the hell is a random anon making me think about math
>>16814307damn it, i keep blurting out stupid shit i don't mean
>>16814314my brain is hurting i should've payed attention back in math class
>>16814299It's capricious and gay to let numbers have unlimited zeros after a digit but not unlimited nines. It breaks all sense of logic and decorum.
>>16814175>no counterargumentsI accept acadaemia's concession. /g/ sends its regards.... ;-)
>>1681430310x = 9.999...which is just9 + 0.999...that is9 + xso10x - x = 9
Really it's the same trick you use when converting a periodic decimal to a fraction. It's EXACTLY the same thing.Like, which fraction is 0.(23)?You write:x=0.(23)100x=23.(23)100x - x = 2399x = 23x = 23/99Apply the same exact procedure to 0.(9) and you get 1.
>>16814299... is an operator
>>168129631/3 > 0.333..2/3 > 0.666..3/3 > 0.999..3/3 = 1
>>16814433Shouldn't it be >=?
>>16814443They should all be =, he’s retarded
>>16814401>I accept [ ] concession.Indian debate syntax. (/g/ is implied)
>>16814401>/g/ sends its regards.... ;-)>regardshttps://www.youtube.com/watch?v=kjEAqrFmAXM
>>16814476>>16814492And yet, no refutation was produced to earn the right to call me a retard. Eating pudding before porridge, tsk tsk.
>>16814502See >>16814180
>>16814506Can you actually not refute it though, I legitimately want to know
>>16814502>>16814175>Lets us start by asserting
>>16814526And is it an unreasonable assertion? What makes it so?
>>16814519It's explicit in the edit. Look closer. If you're still stuck after 12 hours, come back for another hint.
>>16814443No
>>16814544Let us start by reasonably asserting 0.999...=1.
>>16814633Fair enough, but how do you account for an infinitesimal difference in this case?
>>16814684Just add the limit of 1/X as X approaches infinity
>>16814684Let us start by asserting that an "infinitesimal difference" is 0.
>>16814706So in effect, we can't? This equality relies on restricting our domain to the reals? I was always curious about this. It's why I always thought the equality was sus, I knew of the surreals before I knew of the equality.
>>16814739That's a common misunderstanding. No, 0.999... = 1 in either system.
>>168131791 - 0.(9)
>>16814871What representation would you use for the following:[math]\{ 0, \frac{9}{10}, \frac{99}{100}, \frac{999}{1000},...|1\}[/math]Which is decidedly not equal to one.
>>16815011Says who?
>>16815119Me, abiding a representation of the surreals where surreal X is commonly written as:[math]X = \{ A | B \}[/math]and[math]X > {\forall}n {\in} A [/math][math]X < {\forall}n {\in} B [/math]
>>16815301So "max A"?
>>16815301>>16815460Actually with max A < X < min B, you can't even write that. Your expression is just ill-defined gibberish lol.
>>16814299Saying it doesn't. But saying it, and truly meaning it in your heart, that's what really hurts.
>>16814719>infinitesimal = 0Kekerino
>>16815460>>16815473No, A and B are sets. Time to go study the surreals anon!
>>16815606I would love to hear what he thinks infinity is.
>>16815612Your B is well-defined. Your A is gibberish.
>>16815606NTA but in every text on nonstandard analysis, 0 is indeed formalized as the only infinitesimal in the standard reals.
I hate this problem.Here's my cold take.Opinion A>1 - 0.999...9 = 0.000...1>0.000...1 infinitely approaches 0... so it IS 0.Opinion B>0.999...9 is 1 - 0.000...1>Since 0.000...1 always ends in 1 no matter what, for eternity, it can never equal 0 exactly, so 0.999...9 cannot be 1 exactly.Lol.
>>16815615I can forgive not having studied the surreals, but have you seriously never seen a dedekind cut in standard analysis?
>>16815631One of us is certainly talking out of his ass lol.
>>16815646It's neither. I'm holding your hand and spoonfeeding you and you're being an indignant baby about it.
>>16815653That’s what you think you’re doing?
>>16815657>eu wee... goo goo... bleh!The cute sounds of anon spitting his carrots out for the 10th time!Here comes the train! Choo choo!
>>16815662You know you could always just read a text on nonstandard analysis and learn something about it instead of embarrassing yourself with this stuff.
>>16815668You're literally bitching about a standard notation for defining surreals and now are going to pretend like you know shit about non-standard analysis? Holy shit get a grip dude.
>>16815677Or don’t learn and keep embarrassing yourself, I guess, lol.
>>16812963nah, you deserve to be retarded, now if you pay me i'll try
>>16813167/thread
>>16815618>Nonstandard Into the trash it goes.
>>16815876This, but its me throwing everything out that doesn't deal in the surreals which are the only valid number system
>>16815907You're the guy who can't speak a word of some language but says ZOMG that language is so beautiful, it's my favorite. Except it's worse in your case because then you go on the internet and pretend you do.
>>16813032>invents his own term of super-unity before your eyes
>>16816075>>16813032>activity infinite0.999... = 1 + AIIndia strikes again
You retards need to read Hegel's Science of Logic. You're treating a qualitative quantity as a pure quantity.
>>16816116"qualitative quantity"Top google results>viXra.org>marxists.orgThanks but no
>>16816092Close, but I think AI might be the magic, not the residual.Ahem,0.999... + AI = 1.No apply Euler's Identity and we'll have it.
>>16815959nigga how are you blown out this fucking hard kek
>>16816361>nigga how are you blown out this fucking hard kek
>>16814175ah, but 1 - 2ε = 0.999... as well
