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# The validity of 0.99999... = 1

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Kaynex
 Voting Style: Open Point System: 7 Point Started: 12/5/2014 Category: Science Updated: 2 years ago Status: Post Voting Period Viewed: 965 times Debate No: 66412
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 Pro Well, here's a debate for fun. I am very much into math and this is how I roll. Anyway, the debate is a common one seen over the internet, 0.999... = 1. That is infinite 9's. I am arguing that the statement is valid.First round is acceptance.Report this Argument Con I am debating that .99... does not equal 1.Report this Argument Pro Thank you for accepting the debate AthiestPerson!Before I begin, I'm going to let λ = 0.99999... so it is easier to read the work.C1: They have no difference in valueSubtracting λ from 1 results in zero, showing they have no difference in value. They can be used similarily in an equation. Therefore, λ = 1C2: You cannot make it "not 1"λ to any power is still λ. This is a property that only the number 1 is capable of.a*λ is infinitessimally less than a. This is also a property that only 1 is capable of.C3: There is Mathematical proof of thisLet's begin by noting that λ can be made by just adding 9's infinitely.In summation notation: λ = Σ [9 / 10^n] --- {The sum goes from 1 to infinity}λ = 9 Σ [1 / 10^n]λ = 9 Σ [1 / 10]^nThis is just a geometric sequence, and can be solved using: Σ a^i [from i=m to n] = [a^m - a^n] / [1 - a]λ = 9[(1/10)^1 - (1/10)^infinity] / [1 - (1/10)]λ = 9[1/10] / [9/10] λ = 9[1/10][10/9]λ = 1 Report this Argument Con I have no clue how to use that symbol, so my representation will be ]{= .99999... First, let me ask you a question; Do you think that .3333333 is equal to 1/3? What about .666666 being equal to 2/3? Now I shall begin. Here is my proof: The function y=1-1/x is often used to show how the repeating decimal 0.9999... is equal to 1. When x=1, y=1; x=10, y=0.9; x=10000, y=.9999, and so on. The limit of 1-1/x as x approaches infinity equals 1. An assumption is often made, however, that if the limit of an expression as x approaches infinity is 1, then that expression must equal 1 when x equals infinity. Assumption: 1-1/x = 1 when x = infinity Subtraction: -1/x = 0 Multiplication: -1 = 0x Zero Property: -1 = 0 -1 does not equal 0, therefore 1-1/x does not equal 1 when x = infinity. You cannot treat "infinity" like a normal number, you can only think of it in terms of limits. Some things to think about: 1. Saying ]{ = 1 is like saying 9999999999 = 10000000000. The numbers are completely different. They change completely. 2. Just because someone should not wish to write down the whole decimal out every time doesn't mean that it becomes the number one. At any time, you could make a simple symbol that represents the repeating decimal./Report this Argument Pro No problem that you can't use the symbol, the work was very easily read. For future reference though, you can copy-paste the symbol.Just like division by 0, multiplication by infinity makes no sense and cannot be done.For example, 3x5 = 3 + 3 + 3 + 3 + 3 = 15But 3xinfinity = 3 + 3 + 3 + 3 + 3 + 3 +... It doesn't come to a definite answer as an operation demands.Essentially, this line: "Subtraction: -1/x = 0Multiplication: -1 = 0x" Is flawed and cannot be done. Rebuttal to 1.λ = 1 is not like saying 9999999999 = 10000000000, because this would imply a finite amount of 9's.Instead λ = 1 IS like saying 9999999999.99999... = 10000000000, and that is a statement that should be expected, since I implied that λa = a.Statement 2 is a non-issue to the claim that λ = 1.Report this Argument Con You winReport this Argument Pro How much wood could a woodchuck chuck if a woodchuck could chuck wood?Report this Argument Con If a woodchuck could chuck wood, he would chuck a good amount of wood.Report this Argument Pro Would he chuck as much wood as he could?Report this Argument Con Yes, the woodchuck would chuck as much wood as the woodchuck could if the woodchuck could chuck wood.Report this Argument
12 comments have been posted on this debate. Showing 1 through 10 records.
Posted by MettaWorldPeace 2 years ago
I don't understand how you worded it, but your job isn't to enlighten me and I 'm not debating this, still maybe some people understand it, so your words aren't wasted.
Posted by Kaynex 2 years ago
It didn't like my unicodes... But lambda ^ inf = 1
Posted by Kaynex 2 years ago
Interesting question Metta, let's figure out.
Let _5;^W34; = L

By my definition of _5;:
L = lim[nU94;inf] (]1;[1U94;n] 9/10^n)^n
That summation is still 1, regardless if I put the ^n on it or not:
L = lim[nU94;inf] 1^n
L = 1
Posted by MettaWorldPeace 2 years ago
I have a question for Pro, what would lamda to the infinite power be set to?
Posted by Surrealism 2 years ago
Another reason that -1/x=0 does not follow to -1=0 is that zero times infinity is an indeterminate form. This meaning that it could equal any real number depending on the circumstances. In this case it equals -1.
Posted by Kaynex 2 years ago
Lol, it's NBD AtheistPerson, this debate is just for fun. Give it your best shot, there are ways to make it look invalid.
Posted by AtheistPerson 2 years ago
Sh*t. I'm not big on math so... anyways I just looked at it a different way. Boy am I f*cking r*tarded. I feel so stupid.
Posted by Kaynex 2 years ago
I agree, 0.999... does not ACTUALLY exist, and has no uses in the real world.

But this is math on paper. It has nothing to do with reality. Math is governed by a different set of rules, and I followed them to get to my answer.
Posted by Vajrasattva-LeRoy 2 years ago
More Gibberish ...

As L. Ron Hubbard stated in his 1950 book on Dianetics,
Absolutes have to be considered logically unobtainable.
Albert Einstein stated that the universe itself is finite but unbounded.
"Infinity" has no actual existence.
It's Impossible to get an infinite # of 9s.
Ergo, .999 ... cannot, & does not, = 1.
As a matter of fact, if you study Quantum Physics, 1 cannot exist.
Posted by SNP1 2 years ago
Why are there people that still argue against truism on here? It is just another loss.
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