TeXipedia

boxdot

Represents a binary operator displaying a dot centered within a square box, commonly used in mathematical logic and set theory.

Overview

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

  • Often employed in modal logic and algebraic specifications
  • Used to denote specialized operations or relations in mathematical proofs
  • Appears in formal mathematical texts and academic papers where precise symbolic notation is required
  • Particularly useful in contexts where both containment (represented by the box) and central focus (represented by the dot) need to be conveyed simultaneously

Examples

Expressing a binary operation with boxed dot notation in abstract algebra.

a⊡b=ca \boxdot b = c 
a \boxdot b = c

Defining a custom binary relation between sets using boxed dot.

A⊡B={x:x∈A and x∈B}A \boxdot B = \{x : x \in A \text{ and } x \in B\} 
A \boxdot B = \{x : x \in A \text{ and } x \in B\}

Using boxed dot to denote a special composition of functions.

(f⊡g)(x)=f(x)⋅g(x)(f \boxdot g)(x) = f(x) \cdot g(x) 
(f \boxdot g)(x) = f(x) \cdot g(x)