# ceiling

The *ceiling* of a real number is the smallest integer greater than or equal to the number. The ceiling of $x$ is usually denoted by $\lceil x\rceil $.

Some examples: $\lceil 6.2\rceil =7$, $\lceil 0.4\rceil =1$, $\lceil 7\rceil =7$, $\lceil -5.1\rceil =-5$, $\lceil \pi \rceil =4$, $\lceil -4\rceil =-4$.

Note that this function is not the integer part ($[x]$), since $\lceil 3.5\rceil =4$ and $[3.5]=3$.

The notation for floor and ceiling was introduced by Iverson in 1962[1].

## References

- 1 N. Higham, Handbook of writing for the mathematical sciences, Society for Industrial and Applied Mathematics, 1998.

Title | ceiling |

Canonical name | Ceiling |

Date of creation | 2013-03-22 11:48:21 |

Last modified on | 2013-03-22 11:48:21 |

Owner | yark (2760) |

Last modified by | yark (2760) |

Numerical id | 17 |

Author | yark (2760) |

Entry type | Definition |

Classification | msc 26A09 |

Classification | msc 11-00 |

Synonym | ceiling function |

Synonym | smallest integer function |

Synonym | smallest integer greater than or equal to |

Related topic | BeattysTheorem |

Related topic | Floor |