.9999 repeating = 1

Lets get down to business. And to make it easier I will number the arguments 1. Is infinity a number? Infinity is a finite number. All it is the largest number that you can have most people don't conceder it to be a number because you can never count to it because as soon as you the next number would become infinity, but this still means that even if you can't count to infinity it is a number and is finite. To use an example of how infinity can be a finite number, there are infinite number of decimals, fractions, and ratios that are in between the numbers 4 and 5. Now in this example 5 would act as infinity because if you counted each individual value in between these numbers you would never be able to count to 5 because the values would only get closer and close but never becoming 5. Now I hoped that most people got that example but it proves how infinity can exist even if you cannot reach it. a. My opponent's first is attack is against my statement "The first thing that we have to understand that infinity is (despite its name) is a finite number. .. ". Now first I would like to clarify that is statement was meant to ironic and funny not to be a real point. But I can still defend it, the reason that it is called infinity is because we think of it a something that can't be reached even though it is a real number. b. Next my opponent tries to argue that my source doesn't support my claim but I think this quote should work just fine "In mathematics, "infinity" is often used in contexts where it is treated as if it were a number". Also you can cross apply my example from my overview that infinity can be represented as a number in sets. Next he try to say that my sources is so I decided to find some more sources that support what I am saying . http://www.youtube.com... this also explains the example I give in the overview . http://www.c3.lanl.gov... . http://www.mathacademy.com... 2. Right hand side left hand side is flawed. With the fact that infinity is a finite number as I explained above this proves that the rhs lhs theory is flawed because when the decimals reach infinity they would stop and by multiplying it by 10 would cause it to have one less decimal causing it not to be equal to 1. And even if you don't believe that infinity is finite I can still prove that the same problem would happen in the rhs lhs theory with an infinite infinity. a. Power of infinity- when it comes to infinity there are different values of infinity. Go back to the example I gave in the first overview about how there a infinite number of values in between 4 and 5, now there is also a infinite values between 4 and 6. But how can there be the same number of values between 4 and 5 and 4 and 6 if the second set contains the first set and should be bigger, that because it is the set of values between 4 and 6 is a higher power of infinity and is bigger the first set. Now when you apply this to the rhs lhs theory he you multiply the .999999… you will still have an infinite number of 9's after the decimal but it still is 1 less the what you originally had because it is a lower power of infinity 3. Why my opponent's math is wrong In this part we have to understand one quick fact and that is that 1/3 does not = .333333…. repeating. This is because in our base 10 system we have no why to represent a 3rd thus when we try to divide 1 by 3 we get a repeating series of 3 but because it is never can divide evenly it will never = 1/3. Now with that said I will attack my opponent's theory, because as I stated above the 1/3 does not = .3333… it cannot be apply in the equation that my opponent uses, instead we have to look at from the only why that we calculate this equation is to use the only way to evenly divide 1 by 3 and that is by using remainders. (for the people who have forgotten how remainders work here is the wiki to remand you . http://en.wikipedia.org...) When we do the same equation with remainders this is what happens 1/3= .3333 remainder 1 1/3 x 3= .3333 remainder 1 x3 1= 1 Because when you multiply the remainder 1 by 3 it allows you to evenly divide it and would cause the last 9 in the sequence to become a 10 because of the added remainder which cause the next 9 to become a 10 because you would carry the one and so on and so on till you get one. This proves that not only is my opponent's flawed it only further proves that 9999… doesn't equal 1 4. More reasons that 9999… doesn't equal 1 a. The number line paradox- if you where to graph both 1 and .9999… they would not be in the same place even if you had the .9999's go to the infinite place it would never be in the same place as one there would always be an infinitely small gap between them that would prevent them from being equal b. The law of the function- a function is a equation that has one value of y for each x. now if .9999… was to equal 1 it would cause 1 value of x being 1 to have 2 y values the first at .9999… and the second at 1 this would cause a problem because that would mean that our number system is not a function. This would prevent .9999… from being 1 because it violates the fact. 5. The burden of proof- earlier my opponent claimed that I have failed to meet my burden of proof this has one major problem and that is that I'm con I don't have a burden of proof the pro does all the con has is the burden of refutation.