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# Integer part

(Redirected from Truncation)

The integer part (or truncation) of a real number corresponds to rounding towards zero. Thus, the integer part of a positive number is its floor, and the integer part of a negative number is its ceiling.

${\displaystyle [x]={\begin{cases}\lfloor x\rfloor {\text{ if }}x>0,\\0{\text{ if }}x=0,\\\lceil x\rceil {\text{ if }}x<0.\end{cases}}={\begin{cases}\lfloor x\rfloor {\text{ if }}x\geq 0,\\\lceil x\rceil {\text{ if }}x<0.\end{cases}}\,}$

For example, the integer part of ${\displaystyle \scriptstyle \pi \,}$ is 3. The integer part of ${\displaystyle \scriptstyle {\sqrt[{3}]{1729}}\,}$ is ${\displaystyle \scriptstyle \left\lfloor {\sqrt[{3}]{1729}}\right\rfloor \,=\,12\,}$. Likewise, the integer part of the (real) cubic root of –1729 is ${\displaystyle \scriptstyle \left\lceil {\sqrt[{3}]{-1729}}\right\rceil \,=\,-12.\,}$

In the OEIS, sequences of nonintegers are sometimes given by their integer parts. For example, EXAMPLE GOES HERE. (Provide examples)[1]