TeXipedia

lfloor

Represents the left floor bracket used for denoting the floor function in mathematics, indicating rounding down to the nearest integer.

Overview

Essential in number theory, computer science, and discrete mathematics for expressing the largest integer less than or equal to a given number.

  • Commonly paired with \rfloor to enclose expressions in floor function notation
  • Frequently used in algorithmic complexity analysis and mathematical proofs
  • Appears in contexts involving integer division, rounding, and discrete optimization
  • Important in programming-related mathematical notation where integer operations are discussed

Examples

Floor function notation showing the largest integer less than or equal to x.

⌊x⌋=3 for 3≤x<4\lfloor x \rfloor = 3 \text{ for } 3 \leq x < 4 
\lfloor x \rfloor = 3 \text{ for } 3 \leq x < 4

Floor division in mathematical expressions.

⌊n2⌋\lfloor \frac{n}{2} \rfloor 
\lfloor \frac{n}{2} \rfloor

Integer part of a logarithm calculation.

⌊log⁡2(n)⌋\lfloor \log_2(n) \rfloor 
\lfloor \log_2(n) \rfloor