Meaning of epsilon number | Babel Free

Definitions

Any (necessarily transfinite) ordinal number α such that ω^α = α; (by generalisation) any surreal number that is a fixed point of the exponential map x → ωˣ.

Equivalents

Examples

“More generally, the epsilon numbers are the ordinals #92;varepsilon for which #92;varepsilon#61;#92;omega#92;varepsilon. The smallest epsilon number is #92;varepsilon#95;0. It is a countable ordinal, being the countable union of countable sets. By the Veblen fixed-point theorem, the class of epsilon numbers is unbounded.”

“We show that the associated ordinals are the #92;varepsilon#95;0th epsilon number and the first #92;varepsilon#95;0-critical number, respectively.”

“2014, Charles C. Pinter, A Book of Set Theory, 2014, Dover, [Revision of 1971 Addison-Wesley edition], page 203, Thus there is at least one epsilon number, namely ε₀; we can easily show, in fact, that ε₀ is the least epsilon number.”

CEFR level