Melchoir, my logic is flawless and I know very well what you are trying to do. You might as well give up here because there is no analogy between this proof and 0.999... = 1. There is simply no way you can start off with 0.999... and end up with 1 using transitivity of equality. Why? Because 0.999... is not equal to 1. It is less than 1.