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)