[ainoobler]

How can you tell the difference between (r,r) and (r+ε,r+ε)? The argument in the article assumes that there is an ε such that it is impossible to tell the difference between r and r+ε. So this means that the entire square can be covered by squares of side length ε and since the unit square is compact this means that there are only finitely many ε squares required to cover the entire unit square. Variation within the ε squares is imperceptible so this means there are only finitely many symbols that can be perceived to be different.