Sigh. You clearly just don't know what you're talking about. The matter is resolved... you are answering a different question of convergence. as terms are added to the series representing .999..., the function converges to 1.0, but that is not the same thing as stating .999... = 1.0 convergence is about finite limits. this is a mathematical requirement, else one could never solve a problem of distance as one object aproaches another because the distance is always halved, but obviously the distance between the two objects does approach Zero. convergence is a rule of necessity and of finite possibilities. that's not the case with .999... in this case, the number .999... will always have an infinitesimal difference with 1.0.