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lll

Represents a strict less-than relationship between three elements, indicating a triple ordering in mathematical expressions.

Overview

Primarily used in advanced mathematics and set theory to denote strict ordering relationships between multiple elements or sets.

  • Common in order theory and abstract algebra for expressing multiple strict inequalities.
  • Useful in formal logic and mathematical proofs where sequential ordering needs to be shown.
  • Often appears alongside other relational operators in theoretical mathematics and computer science contexts.

Examples

Comparing three variables using the much less than relation.

x⋘y⋘zx \lll y \lll z 
x \lll y \lll z

Expressing a rapidly decreasing sequence of positive numbers.

a1⋘a2⋘a3⋘⋯a_1 \lll a_2 \lll a_3 \lll \cdots 
a_1 \lll a_2 \lll a_3 \lll \cdots

Showing relative orders of magnitude in asymptotic analysis.

f(n)⋘g(n)⋘h(n)as n→∞f(n) \lll g(n) \lll h(n) \quad \text{as } n \to \infty 
f(n) \lll g(n) \lll h(n) \quad \text{as } n \to \infty