The Wikipedia article says how, you need a definition of real numbers that includes nonzero infinitesimals (IOW does not satisfy the Archimedian property). So

The Wikipedia article says how, you need a definition of real numbers that includes nonzero infinitesimals (IOW does not satisfy the Archimedian property). So let there be an ω with 0.999... = 1 - 1/ω. Then a number between 0.999... and 1 would be 1 - 0.5/ω.