Epsilon number

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 ε that satisfy the equation

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

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