Thank you John.
A question, if I may.

Why cannot g be just
$$g(x) = \frac{x}{10}$$

That is, without the floor?

is that because the pure less-than \$$<\$$ part of the relation, must work as well?
Or is it because, we are allowed to start our 'checks' with any b (say b=44) ?
(because in that scenario, the \$$g=x/10\$$ does not work, but
\$$g(x) = \lfloor \frac{x}{10} \rfloor \$$ does)