During class, we were introduced to a proof that used the ceiling function. We assumed (without proof) that:
$$ \left\lceil{\frac{n}{2^i}}\right \rceil= \left\lceil{\frac{\lceil{\frac{n}{2}}\rceil}{2^{i-1}}}\right\rceil,$$
for $i \geq 1$, where $d$ is a positive integer.
I am interested in seeing how this can be proved. I don't know much about the ceiling function, other than its basic properties. I found a general result here , which says for positive integers $m$, $n$ and arbitrary real number $x$.
$$ \left\lceil{\frac{x}{mn}}\right \rceil= \left\lceil{\frac{\lceil{\frac{x}{m}}\rceil}{n}}\right\rceil,$$