TeXipedia

ulcorner

Displays a specialized bracket character showing the upper-left corner of a box or enclosure, commonly used in mathematical and logical notation.

Overview

Primarily employed in formal logic, set theory, and advanced mathematics to create specialized notation and visual groupings.

  • Often paired with \urcorner, \llcorner, and \lrcorner to form complete box-like enclosures
  • Frequently used in modal logic and formal proofs to denote specific operators or delimiters
  • Appears in mathematical linguistics and computer science notation for marking syntactic structures
  • Requires the amssymb package for proper rendering

Examples

Denoting the ceiling function in number theory

⌈x⌉=⌜x⌝\lceil x \rceil = \ulcorner x \urcorner 
\lceil x \rceil = \ulcorner x \urcorner

Representing a syntactic corner in formal logic

⌜ϕ⌝\ulcorner \phi \urcorner 
\ulcorner \phi \urcorner

Indicating Gödel numbers in mathematical logic

⌜P(x)⌝=n\ulcorner P(x) \urcorner = n 
\ulcorner P(x) \urcorner = n