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.

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

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

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.