Can you make all natural number from 3 with only four function that
$$x!,\; \sqrt{x},\;\lceil x\rceil,\;\lfloor x \rfloor $$
?
ex) $1=\lfloor \sqrt3 \rfloor$
$\;\;\;\;\;2= \lceil \sqrt3 \rceil$
$\;\;\;\;\;3=3$
$\;\;\;\;\;4=\lceil\left(\sqrt{3!}\right)!\rceil$
$\;\;\;\;\;5=\lfloor \sqrt{\sqrt{(3!)!}} \rfloor$
I know that all natural number s.t. $n \geq 3$ can make 3.