---
tag: PQSHBKCE7V
kind: concept
name: Epsilon number
aliases: [epsilon-nought-mathematics, epsilon-number-mathematics, epsilon-numbers, epsilon-numbers-mathematics, epsilon-zero-mathematics]
sources:
  - wikipedia: en:3981747@r1353053180
    locator: Epsilon number
    note: adopted
    mention: wikipedia://en/3981747
    sections: [Summary]
same_as:
  wikidata: Q1403155
  wikipedia: Epsilon number
inventory: [90QV9H74EK]
---

## Summary

In mathematics, the **epsilon numbers** are a collection of transfinite numbers whose defining property is that they are fixed points of an **exponential map**. Consequently, they are not reachable from 0 via a finite series of applications of the chosen exponential map and of "weaker" operations like addition and multiplication. The original epsilon numbers were introduced by Georg Cantor in the context of ordinal arithmetic; they are the [[ordinal numbers|0RDJK7EQYY]] *ε* that satisfy the equation

$$\varepsilon = \omega^\varepsilon,$$

in which $\omega$ is the smallest infinite ordinal.