Assume there is no mathematical difference between 0.(9) and 1.
Our first problem is that if A = B, then B does not exist, there is only A. But simply by bringing it up, you claim it exists.
Our second problem is that if you can assume that an infinite string of the maximum-digit-value numbers brings it up to the next value, then one could say that 9999999 repeating is equal to infinity. If by simply repeating numbers of maximum-digit-value you can get infinity, then all numbers are infinity as long as the system is based on them+1. With a base 2 system 11111111 repeating is infinity. With an extremely odd number system, Pi could be infinity.
In order for 0.(9) to equal 1, all numbers (no matter how small) must be equal to infinity when repeated (including 0.9), and 0.(9) cannot exist.
Totally works.
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