0. 999. . . Is not equal to 1

Algebraic proof: When refuting this you assume that there is an end to 0. 9999. . . , But there isn't. When you move the decimal point to the right of 0. 999. . . You don't eliminate any 9's because it is infinity. Thus, Infinity-1 equals infinity. This proof was already mentioned on round one as well as the counter for it stating it again does not help the case in any way, You have also failed to answer the question for this proof which was:how you get 0. 9 * 1000 = 90. 0 purely by moving the decimal point without considering those 'invisible' zeros? The movement of the decimal point relies on the zeros being there if not please show proof on how moving the decimal point not just for any multiple of 10, Without considering those 'INVISIBLE ZEROS' and without changing the question. When refuting this you assume that there is an end to 0. 9999. . . When I wrote 0. 999. . . 9 the 9 after the dots is based on the same pattern we assume the 9 goes on forever. The zero still has to exist otherwise the movement of the decimal place can NOT occur (if not please answer the question above with those requirements set). Which is why I mention the function f(x)=2x. The function has an infinite set of outputs however the function can still be transformed, In reference to this the zeros exist both on the left and right side otherwise you can not just move the decimal point as it relies on the zeros being there. In reference to infinity-1=infinity has caused twice as many paradox as it has solved because we are oversimplifying and using operation on concepts that are not numbers. Similar to the fact we are walking using over brain even if we feel the body is doing it by themselves in other words we can not oversimplify things and forget about the basic requirement otherwise we get results like this. Proof 2 ignored: reason debate rule also remember fractions have different values for different bases. Proof 3:If 0. 9999. . . . Does not equal 1, We should be able to find a number between them. Let's subtract 0. 9999. . . . From 1. 1-0. 99999. . . . =0. 0000. . . . . The dot dot dot means infinitely many 0's. So1-0. 999999=0. 00000. . . . OR1-0. 999. . . . =0I'm going to assume you are not going to count epsilon as an answer between 0. 999. . . And 1 because it is not a real number if that is indeed your answer then you answered your own proof. If you restrict which class of numbers can be used to compare the difference does not automatically suggest that the answer is valid for all cases. Also when you are subtracting you got zero for all the remaining numbers this is only possible if there was a first carry over where the 0 was a 10 and not 9. It is easier to convince people that, As no real number exist between the two hence they are equal. This is because people will just think about rounding and the fact that they are extreamly close (not many people know or think about infinitesimal numbers). However, This argument should also make the following statement valid. There exist no integer between 1 and 2 therefore 1 = 2. According to your proof, This should be valid as I restricted the numbers used hence I got this result. Tell me how many people would be convinced by this proof and what is the main difference between this and your proof? Also in your proof, You are only looking at a precession of 5(changes per line) and ignoring the rest because of the pattern so you get this answer in the integer proof the FULL numbers are used and are not constructed from a pattern.