TeXipedia

backepsilon

Represents a reversed epsilon symbol commonly used in mathematical logic and set theory.

Overview

Serves as a specialized mathematical notation primarily found in advanced mathematical contexts, particularly in formal logic and theoretical set theory.

  • Often used to denote specific relations or operations in mathematical proofs
  • Appears in academic papers and textbooks discussing formal mathematical systems
  • Provides a distinct alternative to the standard epsilon when a reversed orientation is needed for specific mathematical concepts

Examples

Used in mathematical logic to denote the inverse membership relation.

A∍B  ⟺  B∈AA \backepsilon B \iff B \in A 
A \backepsilon B \iff B \in A

Expressing a reverse epsilon relation in set theory.

∀x(x∍S→P(x))\forall x (x \backepsilon S \rightarrow P(x)) 
\forall x (x \backepsilon S \rightarrow P(x))

Demonstrating the relationship between standard epsilon and backepsilon.

x∈y  ⟺  y∍xx \in y \iff y \backepsilon x 
x \in y \iff y \backepsilon x