0.9999 recurring is equal to 1
Voting Style:  Open  Point System:  7 Point  
Started:  1/19/2011  Category:  Education  
Updated:  7 years ago  Status:  Post Voting Period  
Viewed:  7,592 times  Debate No:  14439 
Intro
.999... is not a whole number, it is infinite. You cannot subtract two infinite numbers and get a whole number, which is what you are doing. Saying [9.999...  .999 = 9] is flawed logic. You are at some point rounding .999... to 1. In calculus we are taught that an infinite number minus an infinite number will equal an infinite number. [9.999...  .999] is the same as saying [Infinity  Infinity] 

Intro
It probably doesn't help that I haven't done calculus, but I can still spy multiple flaws in my opponents logic. Furthermore my bottom argument conforms to the top argument, so by not attacking the top argument (proof if anyone wishes) , my opponent concedes that point, and the bottom is merely an application of the top, rendering it correct. Nevertheless... My case 1. If we take the opposite method in proving this case 10.9999... we see that there is a difference of 0.000... we will never see the one, resulting in a difference of 0. 2. On refuting my opponent the idea of 9.99...  0.999.. being infinity  infinity is quite wrong. There is clearly a difference of 9. Indeed we times one number by 10 to get the second no. 3. How about adding a negative infinity to positive infinity, that should be 0. There's a list of other points, but you never need to round  0.99...  0.99... is 0, the are the same number. 4. Of course 0.999... isn't a whole number in that form, whole numbers are essentially integers (not quite accurate of course) What my opponent probably means is something like 0.888...  0.777... = 0.111... and being unable to simplify 0.111... Con's case is refuted. Vote Pro.
If 1 = 0.999... then since 1  1/infinity = 0.999..., 1/infinity must be proven to equal zero. Zero, when multiplied by anything, must equal itself (that is, zero). though 22 multiplied by 1/infinity equals 1/infinity (because 22/infinity equals 1/infinity), infinity multiplied by 1/infinity yields one. Zero multiplied by infinity yields zero, not one, so 0 does not equal 1/infinity so 1 does not equal 0.999... 

Intro
Con still hasn't attacked my main proof, granting it valid. And since the second try is based on the first, attacking the second is pointless. Also, I'm not sure if layout comes under any category of voting, but I'd like voters to realise the incoherence of my opponent's arguments. Without ado, let's proceed. My Case 1. The point is still unaddressed. To ever assume a difference is to assume a finite number of 9s, but there are an infinite number of 9s. 24  Not countered, not will to waste time on them. New points: 1. If two numbers are different it should be possible to find another number in between the 2 numbers, but as I'm sure voters can deduce, this is not the case. 2. The number 0.9999.... can be expanded as: 0.9999... = 0.9+0.09.... ie. = 9/10 + 9/100.... = 9/10 + 9/10(1/10).... =9/10 + 9/10(1/10)^1 +9/10(1/10)^2.... In other words: 0.9999... = (9/10)(1/(11/10)) ie. = (9/10)(1/(9/10)) = (9/10)(10/9) =1 Voters, the resolution has been adequately proven in multiple ways and through multiple proofs. I strongly urge a Pro vote.
I apologize for the vague second round, I wasn't near a computer for a while so I rushed something out when I saw I was near the time limit. .999... is an infinitesimally small number. This is part of the reason of why limits exist. If you were to draw this on a graph, the .999... would approach the number 1, but never intersect it. It would just get infinitely closer to it. The proofs that Pro has provided are correct under his interpretation of infinity. But to me 9.999... .999... cannot compute, its like trying to divide an apple by an orange. To me they are just words now, since infinity cannot be expressed by any simple numerical means like this. It almost seems too easy, if you catch my drift. For example, if I wanted to subtract .999... from 9.999... I would have to perform subtraction for every number in 9.999... This process would continue into infinity, since the amount of 9's I would have to take into consideration are infinite. For Pro's proof to work means you have to stop subtracting at some point to get an answer of 1, which to me is not possible. What this debate has come down to is just an interpretation of infinity, which if I am correct, makes Pro's evidence and proofs null and void. 
Logic_on_rails  DrStrangeLuv  Tied  

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Logic_on_rails  DrStrangeLuv  Tied  

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Logic_on_rails  DrStrangeLuv  Tied  

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Logic_on_rails  DrStrangeLuv  Tied  

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Logic_on_rails  DrStrangeLuv  Tied  

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Logic_on_rails  DrStrangeLuv  Tied  

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http://thenewcalculus.weebly.com...
And when debating mathamatics, by giving your own standpoint you are in the same breath refuting the other's case
i.e.  opponent says 2+2=5 so i say 2+2=4, i don't have to add on that 2+2 doesn't = 5, because my preface automatically does that. a simple 2+2=4 will suffice, even if my opponent takes a page and a half to say 2+2=5, my 2+2=4 will still suffice
I cannot find anywhere a rational fraction that when pluged into a scientific calculator and told not round. gives us .99999999.... or 9.999999999999. thus it debunks your argument
Arguments  Pros argument had a more solid basis in Mathematical logic than Con. Pros assertion were not adequately refuted by Con and Con did not present an adequate argument of his own.
http://en.wikipedia.org...
Please don't run tautological topics. Some things are objective true and debating them is absolutely pointless.
RFD: I want to punish Logic for running dumb things... but conversely want to punish Strangelove for accepting this debate. I couldn't decide who deserved to lose more, so I gave a straight ballot.