Rounding number

I have the formula: r(n) = (9t(1+n)-10^t+1)/9 where t = lowerboundof(log10(n))

What's the math symbol describing lower and upper bound of a non-integer positive number?

-
$\lfloor \log_{10} n \rfloor$ gives greatest integer less than $\log_{10} n$ – rsadhvika Aug 24 '14 at 14:48
isn't that rounding the number to the nearest integer? – Titi Kokov Aug 24 '14 at 14:49
yes you can round it to either floor or ceiling : $\lfloor \log_{10} n \rfloor \le \log_{10} n \le \lceil \log_{10} n \rceil$ – rsadhvika Aug 24 '14 at 14:52

More precisely, $\lfloor x\rfloor$ is the largest integer not greater than $x$ and $\lceil x \rceil$ is the smallest integer not less than $x$.
$$\lfloor x\rfloor=\max \{ n \in \mathbb{Z}: n \leq x\}$$
$$\lceil x \rceil=\min \{ n \in \mathbb{Z}: n \geq x \}$$