TeXipedia

lessdot

Represents a less-than relation with a centered dot, used in mathematical comparisons and ordered sets.

Overview

Serves as a specialized relational operator in advanced mathematics, particularly useful in order theory and abstract algebra.

  • Common in formal mathematical proofs and theoretical computer science.
  • Often appears alongside other dotted comparison operators for expressing complex ordering relationships.
  • Helpful when standard inequalities need additional semantic distinction.
  • Frequently used in academic papers and mathematical publications where precise relation notation is essential.

Examples

Comparing sequences where one sequence dominates another term by term.

{an}⋖{bn}  ⟹  an<bn for all n\{a_n\} \lessdot \{b_n\} \implies a_n < b_n \text{ for all } n 
\{a_n\} \lessdot \{b_n\} \implies a_n < b_n \text{ for all } n

Expressing strict dominance in a partial ordering relation.

x⋖y  ⟹  x<y and x≺yx \lessdot y \implies x < y \text{ and } x \prec y 
x \lessdot y \implies x < y \text{ and } x \prec y