Integer part

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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.

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

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

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

See also

• Fractional part
• Round

External links

• Weisstein, Eric W., Integer Part, from MathWorld—A Wolfram Web Resource.
• Weisstein, Eric W., Floor Function, from MathWorld—A Wolfram Web Resource.
• Weisstein, Eric W., Ceiling Function, from MathWorld—A Wolfram Web Resource.
• Floor and ceiling functions—Wikipedia.org.
• Fractional part—Wikipedia.org.