There's a cool math challenge about writing every number from 0 to 100 with exactly three $3$'s.
Most of the solutions use a clever way to write $50$ with only one $3$ :
$$ \left \lfloor\sqrt{\sqrt{\sqrt{\sqrt{\sqrt{\sqrt{\sqrt{\sqrt{\sqrt{\sqrt{3!!!}}}}}}}}}}\right \rfloor = 50 $$
I wonder if it's possible to write every natural number with a similar way ?
Edit : To keep the spirit of the puzzle, I think only factorials, square roots and floor functions are allowed.