The ambiguity in digit representations only comes from numbers ending in 1's (in base 2, or ending in 9's in base 10). If you do the argument in a different bas

The ambiguity in digit representations only comes from numbers ending in 1's (in base 2, or ending in 9's in base 10). If you do the argument in a different base than 2 you can avoid the problem: you can construct a number whose base 10 representation consists only of 5's and 6's and which is different from any number in the list.