Tip: one of these is the correct answer. The other is the second option. I will provide proofs on request.
Edit: disappointed in 63.42% of Offtopic.
Edit: 41% of Offtopic is correct.
Edit: can we reach 50/50? Also, thank you for the two or three actual, well-thought-out arguments.
Edit: we've lost ground... We must regain it!
Edit: props to DGO RYAN for reminding me about infinitesimals but this is working with real numbers.
Edit: 521 to 627! we can do it!
English
#Offtopic
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Editado por Jphn_33: 3/29/2016 5:44:29 PMStrictly speaking, 0.99999999 is not 1. It will always be so very close, but will never be 1. However, it can be treated as 1 as we approach infinity.
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5 RespuestasIn the end, it all comes down to personal preference. I already posted down below, and had an intelligent conversation. Personally, my saying is "Close enough for government work"
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9 RespuestasX = 0.9999999... 10X = 9.9999999... 10X - X = 9.9999999... - 0.99999999.... 9X = 9 X = 1 0.9999999... = 1 Checkmate
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1 RespuestaI wonder if there is a correlation between denying this and denying evolution.
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1 RespuestaIt's 48% to 52%. Still not great but better than when this poll started.
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10 RespuestasAt the end of the day, there is still a space in between .9 repeating and 1.
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22 RespuestasEditado por SirBlackened: 3/28/2016 7:39:53 AM0.9999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999≠1
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90 RespuestasAllow me to explain with a wall of logic how .999... = 1. *ehem* All numbers expressible in decimal notation (repeating or non repeating) are real numbers. .999... and 1 are real numbers because they can be expressed in decimal notation (with the former being repeating). Two real numbers with different values have infinitely many other real numbers between them. Is there any number that can be greater than .999... but less than 1? There is none, because you can't get any closer to 1 than .999... Because the two numbers don't have a number between them, in order to keep them as real numbers, they must have the same value. Therefore: .999... = 1.
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2 RespuestasYou guys don't understand what infinite means. You poor petty people...
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5 RespuestasOpen question: Say x=1-.999... What is 1/x?
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My brain hurts...
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19 Respuestas1/3 = 0.333333333..... + 2/3 = 0.666666666..... = 3/3 = 0.999999999..... 3/3 = 1
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Editado por Elundis Core: 3/28/2016 1:13:25 AMHere is an explanation of infinitesimals for anyone who is confused. I'll explain why .9 repeating is equal to 1 in the realm of real numbers. Let's look at a function f(X)=(X(X-1))/(X-1), it's really helpful to graph the function on a calculator that will let you zoom. You will notice that at X=1, there is a hole, or a place where the function does not exist because you will have a value divided by zero. But here is where we see that .9 repeating is actually 1 in the realm of real numbers. We know because 1-.9r is going to be 0.0...1. But you can't have an infinite amount of 0s with a 1 on the end, that would end infinity, and infinity can't be ended. That makes an infinitesimal, a spot where f(X) approaches a value infinitely but can never quite reach it. This is shown if you zoom in right next to the hole in the function. You could zoom in [b][i][u]forever[/u][/i][/b] and the hole would still only be at 1. But that is if somehow infinity ends. The value of .0 with an infinite amount of 0s with a 1 on the end is not real. .9r is not equal to one due to an infinitesimal. But in the realm of real numbers, where we identify .0...01 as unreal (because infinity never ends), we see that .9r will equal 1.
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6 RespuestasEditado por Autolycus: 3/28/2016 10:01:42 AMJust thought of another way to think of it. All repeating decimals are rational numbers: they can be represented as a fraction of two integers. How can you represent 0.9 repeating as a fraction? Well, 1/9 = 0.1 repeating 0.9 repeating = 9 * 0.1 repeating 0.9 repeating = 9 * 1/9 0.9 repeating = 9/9 0.9 repeating = 1
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1 Respuesta2-(1/infinity) =/= or = 2?
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14 RespuestasThere are no numbers in between .9999.... and 1, so .9999....=1.
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.3 recurring is one third. We all know this .6 recurring is two thirds. .9 recurring is three thirds, and is therefore equal to one
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1 RespuestaSince the value requires an infinitely small number to = 1, it already is 1.
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1 Respuesta33/100= 1/3 99.99999/100= 1/1
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1 RespuestaIt's obviously correct 1/3= 0.3 repeating Thus, 1/3*3=0.9 repeating It's equal to 3/3, meaning 0.9 repeating is equal to 1
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27 RespuestasI've already used limits to argue, but it wasn't argued well. So here is a better explanation. In Calculus you learn to identify functions with holes, meaning a place in the function where continuity breaks and the function Does Not Exist. Here is an example. Take the function f(X)=((3X-2)(1-X))/(1-X). There will be a hole at X=1 because anything divided by zero will not exist. This is inarguable, it's factual that there is a hole at 1. I explicitly state this so that you know as you read the next part of this. You say that .9r=1, not the limit, not an estimate, but actual value. So, with that, let me prove you wrong. With the function f(X)=((3X-2)(1-X))/(1-X), the (1-X)s will come out to same value and divide each other out. If X=2, then f(X) will come out to be 4, because you will get ((4)(-1))/(-1). But it would be the same if you just solved 3X-2 by itself. But as stated before, the (1-X)s are there to create a hole at X=1. If you took .9r, then you would come out to a value of 1.9r. You could have an infinite amount of 9s, but no matter what you will have a value of 1.9r, but the moment that X=1, is the moment that the function will not exist. .9r=/=1, because if it did, then our function would not exist. No general algebra bullshit this time OP.
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7 RespuestasFor the sake of time and word count from this point on .99r will be used to indicate .9 repeating. Before we begin I will bring up the most commonly used proofs that .99r = 1. First you have 1/3 = .33 repeating .33 repeating * 3 = .99r 1/3 repeating * 3 = 1.00 1/3 = .33, .99r = 1.00 .99r = 1x 9.99r = 10x subtract x from each side 9 = 9x 1 = x These are the most commonly accepted examples of why .99r = 1, things that your teacher uses to blow your mind in 8th grade, but have no purpose past that, they are mere parlor tricks. The basis for .99r relies entirely on infinity, the basis for all arguments for .99r = 1 are based using the concept of infinity. That's right the Concept. The reason it is a concept is because it doesn't actually exist, your brain cannot comprehend it because everything in our universe is in fact finite. Everything you experience, see, do, its all of the finite nature, how many blades of grass are on earth, how many gallons water are in the ocean, how many hairs are on your head, its a finite number, it can be counted. This is relative because .99r is nine repeating, infinitely, it never reaches 1. PROOF 1: Simple Analysis The number 1 can be written in a variety of ways, but for our case here lets go ahead and right down 1 = 1.00 repeating, the 0s are repeating to infinity, it is another way to write 1. .99r can be rewritten as 0.99r, the 9s are repeating to infinity, another way to write .99r. From simple looking at the numbers, 1.0 > 0.99r simply because 0.99r has a 0, it has a decimal, it has to be less than one. Proof 2: Subtraction Though infinity cannot ever be "reached" depending on how you look at it, I would rather not start a debate on infinity, you can predict the outcome using things such as limits. Because infinity is infinite, I will simply show a pattern that repeats to infinity. 1 - 0.9 = 0.1 1 - 0.99 = 0.01 1 - 0.999 = 0.001 1 - 0.9999 = 0.0001 1 - 0.99999 = 0.00001 Continue however many times you want, literally continue this a trillion times, and you will never reach 0. Repeat this a trillion times to the trillionth power, repeat this for every atom there is in the universe. You will never ever reach 0, you will gain another 0, but the 1 will keep moving and never go away. Proof 3 Limit Lim x = 1/(1-x) The limit of x in this equation is 1. If x Ever reaches the value of 1 then the denominator will turn into 1/(1-1) or 1/0. Because 1/0 is not possible, the value of x can never reach 1, the domain of x is {x:x=/=1} So a limit is defined basically as a value that you can approach but never reach, that's all that you need to do know for this situation. So as I said, the domain of x is ANY number that is not 1. 1/(1-x) you can use the value 1 trillion if you want, you will get 1/-999999999999, a very tiny number, but still in the domain of x. x literally can never equal 1 in this equation. It can reach any other number, and as the definition of the limit is that you are approaching 1 then lets see what the closest number to 1 is. .9, well you are still a tenth off .99, well you are still a hundredth off .999, well you are still a thousandth off .9999, well you are still a ten-thousandth off .99999, well you are a hundred-thousandth off The limit is 1 so you can approach 1 but never cross it So you can approach 1 for how long? Well infinitely, you can continue to go to the next decimal, .99999999999, but you can never cross the threshold between .9999r and 1.000r. so the limit approaches 1, or .99r so if the limit was defined as say a function of y y = .99r and we know from the equation 1/(1-x) that you can never reach 1 y =/= 1 What's that? .99r = y but y =/= 1? .99r =/= 1 I believe this is enough to prove that .99r =/= 1.
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11 RespuestasI think its funny that people will type out whole essays to disprove someone on a (primarily) gaming website.
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12 RespuestasTechnically, it's 1/infinity off of being = 1, but close enough for government work. [spoiler]Especially considering the government doesn't work[/spoiler]
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Editado por Traffic Cone: 3/27/2016 8:27:29 PM.9_ times 10 = 9.9_ 9.9_ - .9_ = 10(.9)-1(.9) = 9*.9 =9 9/9=1 Mind blown [spoiler]it's not true, it's just a math breaking trick[/spoiler]