TeXipedia

lesseqqgtr

Represents a combination of less than or equal to and greater than relations, used in mathematical comparisons and inequalities.

Overview

Serves as a specialized mathematical relation symbol that combines both less-than-or-equal-to and greater-than relationships in a single notation, primarily used in advanced mathematics and formal logic.

  • Common in order theory and abstract algebra when describing complex relationships between elements
  • Useful in mathematical proofs and formal specifications where multiple comparative relations need to be expressed
  • Often appears alongside other inequality symbols in academic papers and advanced mathematical texts
  • Particularly valuable in situations requiring precise expression of bidirectional comparisons

Examples

Comparing two sequences using the less-equal-greater relation.

{an}⪋{bn}\{a_n\} \lesseqqgtr \{b_n\} 
\{a_n\} \lesseqqgtr \{b_n\}

Expressing a non-strict ordering relationship between variables.

x⪋y  ⟺  x≤y or x≥yx \lesseqqgtr y \iff x \leq y \text{ or } x \geq y 
x \lesseqqgtr y \iff x \leq y \text{ or } x \geq y

Showing possible relationships between statistical measures.

Xˉ1⪋Xˉ2\bar{X}_1 \lesseqqgtr \bar{X}_2 
\bar{X}_1 \lesseqqgtr \bar{X}_2