TeXipedia

rfloor

Represents the right floor bracket, used to denote the closing delimiter in mathematical floor functions and set notation.

Overview

Essential in mathematical notation where values need to be rounded down to the nearest integer or for specific set constructions.

  • Pairs with \lfloor to create complete floor function notation
  • Common in number theory and discrete mathematics
  • Used in programming-related mathematics to denote rounding operations
  • Appears frequently in algorithmic complexity analysis and set theory expressions
  • Often employed in formal mathematical proofs and definitions where precise integer bounds are needed

Examples

Defining the floor function for a real number x.

⌊x⌋=max⁡{n∈Z:n≤x}\lfloor x \rfloor = \max\{n \in \mathbb{Z} : n \leq x\} 
\lfloor x \rfloor = \max\{n \in \mathbb{Z} : n \leq x\}

Showing the ceiling-floor inequality for real numbers.

⌊x⌋≤x<⌊x⌋+1\lfloor x \rfloor \leq x < \lfloor x \rfloor + 1 
\lfloor x \rfloor \leq x < \lfloor x \rfloor + 1

Expressing the fractional part of a number using floor notation.

x−⌊x⌋∈[0,1)x - \lfloor x \rfloor \in [0,1) 
x - \lfloor x \rfloor \in [0,1)