This tag is for questions involving the greatest integer function (or the floor function) and the least integer function (or the ceiling function).
The greatest integer function, or the floor function, is usually denoted by $\lfloor\_\rfloor$ (although some authors prefer $[\_]$). For a real number $x$, $\lfloor x\rfloor$ is the largest integer that is less than or equal to $x$. For example, $\lfloor 2^{1000}\rfloor=2^{1000}$, $\lfloor\sqrt{105}\rfloor=10$, and $\lfloor -\pi\rfloor =-4$.
The least integer function, or the ceiling function, is usually denoted by $\lceil\_\rceil$. For a real number $x$, $\lceil x\rceil$ is the smallest integer that is greater than or equal to $x$. For example, $\lceil 2^{1000}\rceil=2^{1000}$, $\lceil\sqrt{105}\rceil=11$, and $\lceil -\pi\rceil =-3$.
