TeXipedia

llcorner

Represents a lower-left corner bracket symbol commonly used in mathematical notation and formal logic.

Overview

Primarily employed in mathematical logic, set theory, and formal reasoning to denote specific operations or delimiters.

  • Often paired with \ulcorner to create box-like notation structures
  • Frequently appears in modal logic and formal proofs
  • Used in mathematical linguistics and theoretical computer science for semantic notation
  • Common in formal specifications and mathematical foundations texts

Examples

Denoting the floor function in number theory

⌞x⌟=max⁡{n∈Z:n≤x}\llcorner x \lrcorner = \max\{n \in \mathbb{Z} : n \leq x\} 
\llcorner x \lrcorner = \max\{n \in \mathbb{Z} : n \leq x\}

Representing a boundary operator in topology

∂(A×B)=(⌞A×B)∪(A×⌞B)\partial(A \times B) = (\llcorner A \times B) \cup (A \times \llcorner B) 
\partial(A \times B) = (\llcorner A \times B) \cup (A \times \llcorner B)

Indicating the lower bound of an interval in order theory

x∈[a,b]  ⟺  ⌞x≥a and x≤bx \in [a,b] \iff \llcorner x \geq a \text{ and } x \leq b 
x \in [a,b] \iff \llcorner x \geq a \text{ and } x \leq b