TeXipedia

ngtr

Represents the 'not greater than' relation, indicating that one value is not strictly larger than another.

Overview

Serves as a negation symbol in mathematical logic and set theory, particularly useful when expressing inequalities or constraints.

  • Common in formal proofs and mathematical reasoning where exclusion of the greater than relationship needs to be explicitly stated.
  • Often used alongside other comparison operators in complex mathematical statements.
  • Appears frequently in advanced algebra, analysis, and theoretical computer science when defining bounds or constraints.
  • Provides a more formal alternative to crossing out the greater than symbol manually.

Examples

Expressing that one value is not greater than another in a mathematical inequality.

x≯y  ⟹  x≤yx \ngtr y \implies x \leq y 
x \ngtr y \implies x \leq y

Showing multiple non-greater-than relationships in a sequence.

a≯b≯c  ⟹  a≤b≤ca \ngtr b \ngtr c \implies a \leq b \leq c 
a \ngtr b \ngtr c \implies a \leq b \leq c

Using the not-greater-than symbol in a set definition.

S={x∈R:x≯0}S = \{x \in \mathbb{R} : x \ngtr 0\} 
S = \{x \in \mathbb{R} : x \ngtr 0\}