TeXipedia

between

Denotes a binary relation indicating that one value lies between two others in mathematical expressions.

Overview

Commonly employed in mathematical logic, set theory, and formal proofs to express ordering relationships and intervals.

  • Essential in defining ranges and bounded sets in mathematics
  • Useful in expressing constraints and conditions in formal specifications
  • Often appears alongside inequalities and order relations
  • Particularly valuable in abstract algebra and real analysis when describing element relationships

Examples

Expressing a value lying between two numbers in a mathematical inequality.

3≬1 and 53 \between 1 \text{ and } 5 
3 \between 1 \text{ and } 5

Describing a range of values in a set notation.

x≬a and b  ⟹  x∈(a,b)x \between a \text{ and } b \implies x \in (a,b) 
x \between a \text{ and } b \implies x \in (a,b)

Representing an intermediate value in a sequence.

a1<x≬a2 and a3<a4a_1 < x \between a_2 \text{ and } a_3 < a_4 
a_1 < x \between a_2 \text{ and } a_3 < a_4