Why is 3/3 equal to 1?Ok, so 1/3 is 0.33333 forever. 2/3 is 0.6666 forever. So, if that's the case, why is 3/3=1 and not 0.99999 forever? Where does the last little bit get added to 3/3 to have it equal 1?
Math is 2-dimensional; a line isn't real.
>>16986939Our monkey brains tend to see 0.999... as a process that is getting closer and closer to 1 but never quite getting there. However, in mathematics, the infinite string of 9s represents a fixed value, and that value is exactly 1. 0.999... is just a different way of writing 1, similar to how 1/2 and 0.5 are the same thing.
My brain simply isn't wired for math. I suspect OP is similar
>look, mom, I posted it again
>>16986939Answer me this OP. what is 1 - 0.9999(repeating)Checkmate
>>16986963Its obviously .0 followed by infinite zeros then a 1. whereas 1-1 and also .99-.99 is .0 followed by infinite zeros and then a 0.
The implication is that if .99999... is 1 then might as well say .9 is 1 and if that's the case then what isn't 1. 10 might as well be 1
>>16986939I guess because infinity isn't real
>>16987009when do you think the infinite stream of zeros stops so that you can put a 1?
It is tautological. To divide a quantity into a number of groups equal to that quantity itself thus equals one part per group. Or, in reverse, to take however many groups there are and then multiply it by the number of members in that group (1 per group) yields a quantity equivalent to however many groups there were. The reason 0.999 repeating can be used to represent 1 (or 1.000 repeating) is because the repeating implies an infinite series of decimal places. Following each decimal place, the leftover bit needed to get from 0.9 to 1.0 gets smaller by a factor of ten. So, after one reaches an infinite number of decimal places, that leftover bit has gotten smaller and smaller to the point where it can be considered to have vanished. Though I guess the trouble then is, where did the infinitesimal end up, if it only ever got smaller and never actually reached (nor could ever reach) zero? I'd argue that this is an artifact of the language/notation used to represent and convert different concepts between each other, but that's just intuition and not a fleshed out, formal reasoning.
>>169869630.1111...But why does 0.1111...=0
>>16986939>Why is 3/3 equal to 1?For the same reason 1/1 = 1 and 2/2 = 1 and 4/4= 1
>>16986939>Where does the last little bit get addedthere is nothing addedtwo numbers are differrent if there's at least 1 number between themthere is nothing between 0.999... and 1, therefore they are the same number
>>16987075if there was nothing between them and they were the same number then they wouldn't be different numbers in the first place, but given that they are different numbers then there must be something between them to distinguish them, as such they cannot be the same number as otherwise they wouldn't have separate identities.
>>16987039>where did the infinitesimal end upif the field s archimedean, id ceased to exist, if it ain't archimedean then somewhere that's for sure... depending of how many of the non-standard integers where used, if you used all of them then once more you are left with no infinitesimal, hence why 0.999...=1 even in said non-archimedan field, take care
>>16987100>given that they are different numbersbut they are not different numbersit's the same number, just written differentlylike 1/2 and 0.5
>>169869630
>>16986948>However, in mathematics, the infinite string of 9s represents a fixed value, and that value is exactly 1. 0.999... is just a different way of writing 1Hmm, not quite sure about that, if I can prove you that there is an exception, your whole assertion would be proved wrong.In maths :If A=BThen f(A)=f(B) (the other way is not true, f(A)=f(B) =/=> A=B like with A^2=B^2 =/=>)Let's write :f(x)=1/(1-x)x=1 => f(x)=undefinedx=0.999... => f(x)=+infinityTherefor :1=/=0.999...Same with :>>16987039>>16987075>>16987100If I can give you a number between 0.999... and 1, you'd be proven also wrong.By convention in any base :1 = 0.111...(base2) = 0.222...(base3) = ... = 0.999...(base10) = ... = 0.AAA...(base11) = 0FFF...(base16)But, the speed at which each base goes to infinity is different :0.111(base2) = 0.1(base2) + 0.01(base2) + 0.001(base2) 0.111(base2) = 0.5(base10) + 0.25(base10) + 0.125(base10)0.111(base2) = 0.875(base10)Etc.0.11111(base2) = 0.96875(base10)Etc.So 0.111...(base2) goes to 1 slower than 0.999...(base10) at infinity.Same with 0.999...(base10) and 0.AAA...(base11) : 0.999...(base10) goes to 1 slower than 0.AAA...(base11)And if it goes slower, that means that there is some quantity between them... Even the smallest quantity.Same with any other bases after :base12 < base13 < base14 <...< base(infinity+1)
>>16987110>it's the same number, just written differentlylet x = 0.999... and y = 1for | x = y | show that for every decimal of x the equation ( x/y + y/y ) = 2y is truethrough process of elimination we can determine that 0.999.. indeed is not equal to 1, just because you approach 1 forever in infinitely small amounts doesn't mean you'll ever get therein shortyou will never be a oneman
>>16987176>x=0.999... => f(x)=+infinityWrong.By Definition[math]0.999... = \lim_{n \to \infty} \left(1 - \frac{1}{10^n}\right) = 1[/math]So [math] f(0.999...) = f \left( \lim_{n \to \infty} \left(1 - \frac{1}{10^n}\right) \right) = f(1) [/math] which is undefined.This is not the same as [math]\lim_{n \to \infty} f\left(1 - \frac{1}{10^n}\right)[/math]>If I can give you a number between 0.999... and 1, you'd be proven also wrong.Okay, show us the number
>>16987009Incorrect, and impossible. You're stupid, eat a bag of nigger dicks please. >>16987061Wow, somehow even more stupid and wrong then the guy above you, impressive, but you as well need to eat a bag of nigger dicks.>>16987140This is of course the correct answer, you are not retarded and may have an extra snack at lunch. Good job anon.
>>16987019None of my business. I just know that there's a 1 at the end instead of a 0.
Perhaps we don't know exatly what's 1/3 or 2/3 are. 0.3333... and 0.6666... are always are an aproximation and never were a constant. But we already know 3/3 are 1.
Because we know in fact that any n/n always results in 1 except 0. Black magic am i right?
>>16986939because the 10-adic representation of 1/3 is ...66667 and ...66667+33333... =1. Whenever an infinity crops up while evaluating a real number in its n-base it can usually be cleared up when analyzing it in its n-adic complement.
>>16987230You're saying :>By definition>ThenIt's circle reasoning.I've just given you an exception with those basic maths :>A=B>f(A)=f(B)If I have an exception, then it's false.There is at least one exception with f(x)=1/(1-x)>If I can give you a number between 0.999... and 1, you'd be proven also wrong.Okay, show us the number0.AAA...(base11) is closer to 1 by an epsilon than 0.999...(base10).0.A(base11) = 0.9090909...(base10) > 0.9(base10)0.AA(base11) = 0.9917355371900...(base10 > 0.99(base10)0.AAA(base11) = 0.9992486851990984...(base10) > 0.999(base10)And so on...0.AAA...(base11) > 0.999...(base10) at infinity.
>>16987474>It's circle reasoning.0.999... is a shorthand for the limit I wrote down by definition. The limit being one just follows from the rules of limits.With this the rest of your arguments falls apart.If you don't accept the definition then that's a (You) problem
>>16987491Hey buddy, I know you are right.I've just given you an exception if you sort direct reasoning above common acceptance in definitions.With basic maths, there is an exception, but with the teachings of limits, those exceptions are no more.Same with 1 = 0.AAA...(base11) = 0.999...(base10)If you dont use the definitions of limits, you could say :1 > 0.AAA...(base11) > 0.999...(base10)
>>16986939Because you're using base 10 numbering system
Because base 10 is a trick of the jews to keep us from the higher realm. use base 12 from now on and you will hear colors
Omg goys67/99ths
>>16987502what is the number 0.AAA....'s decimal representation?
>>16987075>there is nothing between 0.999... and 1there is though
