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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?

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$\lfloor \log_{10} n \rfloor$ 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
up vote 3 down vote accepted

The floor and ceiling functions map a real number to the largest previous or the smallest following integer, respectively.

More precisely, $\lfloor x\rfloor$ is the largest integer not greater than $x$ and $ \lceil x \rceil$ is the smallest integer not less than $x$.

$$\lfloor x\rfloor=\max \{ n \in \mathbb{Z}: n \leq x\}$$

$$\lceil x \rceil=\min \{ n \in \mathbb{Z}: n \geq x \}$$

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thank you for answer ! – Titi Kokov Aug 24 '14 at 14:50

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