---
tag: 08GR54CKEA
kind: concept
name: Floor function
aliases: [greatest-integer-function, integer-part]
msc: [26A09]
sources:
  - url: https://en.wikipedia.org/wiki/Floor_and_ceiling_functions
    locator: lead section
---

## Summary

The floor function sends a real number $x$ to the greatest integer that is less than or equal to $x$. We write $\lfloor x \rfloor$ for it.
For example, $\lfloor 2.7 \rfloor = 2$ and $\lfloor -2.7 \rfloor = -3$.