You havent given an upper estimate because I just constructed a list larger than yours which isnt nearly complete  The step where you say that you have an upper bound is unjustified and where the argument goes wrong  As for Do you claim that not every certainly I agree that every real number has a binary expansion and a decimal expansion  in fact each has either  or  such expansions  There are three possibilities for the two one decimal expansion and one binary expansion eg sqrt two decimal expansions and one binary expansion eg  and two decimal expansions and two binary expansions eg   But I dont claim that each one has a finite binary expansion which is essentially what youre claiming