.9999 repeating = 1

Sorry about the grammar in the last few rounds I have had a lot of work to do and not much time to look over my arguments. So in this last round for the sanity of the people reading this I am going to be short and sweet. 1.1/3 There is one critical reason that you are not going to buy my opponent's argument and this he makes no response to my attack that .333… only approximately equals 1/3, thus they only way to find what 1/3 actually equals is to use remainders which when multiplied by the cause one to be added in on the 9's causing them to become 10's and carrying the 1 to the next 9 repeats the cycle to equal 1. This proves that multiplying 1/3 doesn't .999… it will equal 1. This argument goes dropped in my opponent's last speech meaning that there is no way that my opponent can hope to win this argument. The only argument that my opponent even attempts to extend is the example of the hotel, but this doesn't matter for 2 reasons 1 even if there were an % number of rooms there is always one left over meaning that you will never get an exact answer, and 2 you should prefer my example because it take into account for this flaw and is the only way to get an exact answer to the problem. 2.Rhs lhs My opponent drops too many of my arguments in the last speech for him to have a hope to win this point. First my opponent seem to ignore all of the arguments I make, what I am saying is that even if % is not finite and is constantly increasing then when it is used in a math equation you change the rate that % is increasing, this is supported my example ,that my opponent miss interprets, that if % theoretically for the purpose of easy math equaled to 1 and if you added 1 to that % you would get 2 which acts as a higher power of infinity now even if infinity were to increase without bounds the answer to the equation would always be one above infinity. To explains further in the same situation if % increase to 2 adding one to % would equal 3 they same would happen for 4,5,6,7,8,9 even if infinity was constantly increasing the %+1 will always be bigger. This proves the flaws of the rhs lhs equation because it shows that even if there % number of nines behind the decimal when you multiple it by ten it acts as if there are %-1 9's behind the decimal but it will always be on less than the original .999… thus proving my point. The only other thing my opponent has to support his claim is that there couldn't be a 9 at the end of repeating 0's, but my opponent gives nothing to support his own claim I have proof of how we never able to reach infinity yet we know it is there and the numbers between 0 and % infinity as we attempt to reach it this proves how we could have a 9 at the end of the sequence of 0's because even if we can never reach it we know it is there. All my opponent's attacks are based on nothing he gives you no examples no base for his arguments all he says is that he is right yet I am wrong but I am the only one giving examples and proof to back my claims meaning you are going to prefer my arguments over his. Because these critical failures by my opponent he has no proof backing his rhs lhs theory meaning that there is no way that he can win. 3.His limit equation On this argument my opponent drops one critical argument and that is that 1/% ~0 this shows that this equation could only prove that .999… can only be approximately equal to 1. Because in the final step of his equation where he takes 1-1/10 the % power, the 1/10to the % will be approximately equal to 0 and when you subtract this from 1 you get approximately equal to 1. This argument goes completely dropped by my opponent meaning that this completely disproves his attempt to prove his point 4.Number line paradox This is going to be critical in this round because my opponent make no arguments against it. It disproves that .999… could equal 1 because they are located on different position on a number line even though they are very close together they are not in the same place meaning that they can't be equal. Because of the fact that my opponent drops this argument it proves that .999… doesn't equal 1 and is going to be this finishing blow because there is nothing from my opponent that attempts to disprove this meaning it is going to win me this debate. 5.Closing statements Because this is the last speech I feel that I should reinforce the fact that when as judges vote on this round base your vote only on what has been presented in the round. Weigh the evidence that both sides present and look at the arguments and how each one proves or disproves the topic. Don't base your vote on what you know, but only the information given to you in the round.