epsilon number
epsilon number noun: 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.
Noun
epsilon number (plural epsilon numbers)
- 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.
- 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...1977, Herbert B. Enderton, Elements of Set Theory, Elsevier (Academic Press), page 240
- We show that the associated ordinals are the #92;varepsilon#95;0th epsilon number and the first #92;varepsilon#95;0-critical number, respectively.1981, The Journal of Symbolic Logic, Association for Symbolic Logic, page 17
Forms of epsilon number
| plural | epsilon numbers |
|---|
Origin of epsilon number
From the Greek letter ε (“epsilon”), used to denote the numbers.
Questions about epsilon number
- What does epsilon number mean?
- Epsilon number means 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.
- What part of speech is epsilon number?
- Epsilon number is a noun.
- What is the plural of epsilon number?
- The plural of epsilon number is epsilon numbers.
Words near epsilon number in the dictionary
Source and license
Adapted from Wiktionary: epsilon number (page history and authors). Text available under the Creative Commons Attribution-ShareAlike 4.0 license. Word.ws reformatted the entry and added links. Wiktionary data of 2026-09-02.
Last updated:
Cite this entry: “epsilon number.” Word.ws, https://word.ws/epsilon_number. Based on Wiktionary, CC BY-SA 4.0.