>we are limited to the unit square (0<=x<=1 and 0<=y<=1). Now I map every real number in [0,1] to a symbol by simply defining the symbol for the number r as x=r

>we are limited to the unit square (0<=x<=1 and 0<=y<=1). Now I map every real number in [0,1] to a symbol by simply defining the symbol for the number r as x=r and y=r. Every symbol has measure zero and so every symbol is identical.