Word Pronunciation & Dictionary

epsilon number

Word Rarity Rare

Frequency: Zipf frequency 2.88 in modern English

Syllables: ep-silon num-ber
IPA

19

Scrabble Score

13

Letters

3

Syllables

11

Unique Chars

Meaning

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.

Example Sentences

"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."

Etymology

From the Greek letter ε (“epsilon”), used to denote the numbers.

Inflected Forms

epsilon numbers (plural)

Phrases

delta number gamma number epsilon-induction

Frequently Paired Words

delta number gamma number epsilon-induction

Questions

What does epsilon number mean?: 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.
Where does epsilon number come from?: From the Greek letter ε (“epsilon”), used to denote the numbers.

How to pronounce epsilon number

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