TeXipedia

llless

Represents a strict much-less-than relationship in mathematical notation, indicating a significantly smaller value or hierarchical ordering.

Overview

Primarily used in advanced mathematics and theoretical computer science to denote strong ordering relationships or nested hierarchies.

  • Common in order theory and set theory to show strict ordering relationships
  • Useful in category theory for expressing nested properties or compositions
  • Appears in formal logic and abstract algebra when describing multiple levels of comparison
  • Often employed when standard inequality symbols are insufficient to express complex ordering relationships

Examples

Representing a strictly much less than relationship in ordered sets.

AB    A<BA \llless B \implies A < B
A \llless B \implies A < B

Showing nested subset relationships with strict inequality.

X1X2X3X_1 \llless X_2 \llless X_3
X_1 \llless X_2 \llless X_3

Comparing asymptotic growth rates in complexity theory.

f(n)g(n)h(n)f(n) \llless g(n) \llless h(n)
f(n) \llless g(n) \llless h(n)