TeXipedia

lesseqgtr

Represents a mathematical relation combining less than, equal to, and greater than in a single symbol, used for comparing quantities that may have any of these relationships.

Overview

Serves as a specialized mathematical comparison operator primarily found in advanced mathematical notation and formal logic contexts.

  • Common in set theory and abstract algebra when describing complex relationships between elements
  • Useful in mathematical proofs where multiple possible relationships need to be expressed concisely
  • Often appears alongside similar relational operators in formal mathematical writing
  • Particularly valuable in situations where the relationship between quantities may vary or is being analyzed

Examples

Comparing two sequences that alternate in their relative ordering.

{an}⋚{bn}\{a_n\} \lesseqgtr \{b_n\} 
\{a_n\} \lesseqgtr \{b_n\}

Expressing a non-transitive relationship between three variables.

x⋚y and y⋚z but x⋚̸zx \lesseqgtr y \text{ and } y \lesseqgtr z \text{ but } x \not\lesseqgtr z 
x \lesseqgtr y \text{ and } y \lesseqgtr z \text{ but } x \not\lesseqgtr z

Describing oscillating behavior in a numerical analysis context.

f(xn)⋚f(x∗) as n→∞f(x_n) \lesseqgtr f(x^*) \text{ as } n \to \infty 
f(x_n) \lesseqgtr f(x^*) \text{ as } n \to \infty