epsilon

IPA/ˈepsɪlɒn/
KK[ˈɛpsəlˌɑn]IPA/ˈepsɪlɑːn/

epsilon — noun

  • epsilonsingular
  • epsilonsplural

1. In the Greek writing system, the character that appears fifth in the set is epsi

1.nounB1
Definition

In the Greek writing system, the character that appears fifth in the set is epsilon, written as Ε (uppercase) or ε (lowercase) and widely used as a symbol in mathematics and science.

Example

Professor Andrei wrote a lowercase epsilon on the board during the calculus lecture.

lowercase/uppercase epsilon

The symbol ε often appears in formulas for limits and series in advanced math textbooks.

Common collocations
  • lowercase epsilon
  • uppercase epsilon
  • epsilon value
  • epsilon symbol
  • the letter epsilon
  • epsilon-delta proof
Synonyms
  • ε

    the actual Greek letter symbol, used in place of the word in mathematical writing

  • fifth letter

    descriptive phrase naming its position in the Greek alphabet

Grammar Patterns

an epsilon

lowercase/uppercase epsilon

epsilon + noun (epsilon-delta proof)

Usage Note

Countable noun; the plural is 'epsilons'. In mathematical writing, the lowercase form ε is far more common than the uppercase Ε. Learners in STEM fields will encounter epsilon most often as a symbol for an arbitrarily small positive quantity, especially in limit proofs (epsilon-delta definition). Outside technical contexts, epsilon appears in the names of fraternities, sororities, and academic honour societies.

Common Mistakes

The value of epsilon is equal to 5%.
The value of ε is equal to 5%.
In mathematical writing the Greek letter symbol is preferred over spelling out the word.
Write a capital epsilon at the start of the equation.
Write a lowercase epsilon for the small quantity.
The uppercase Ε looks like a capital E and is rarely used in formulas; lowercase ε is the symbol for small values.

Word family

  • epsilonic
    adjectiveC2
  • epsilon-delta
    adjectiveC2

Synonym discussion

Sense: noun/1

Epsilon is the English name for the fifth letter of the Greek alphabet, roughly equivalent to a short 'e' sound. Unlike most Latin letters, epsilon has no everyday English counterpart — it is first and foremost the name of a letter from another writing system. 'Varepsilon' (or 'ϵ') is a typographical variant of the lowercase form, distinguished by a different stroke shape and used in some math textbooks for readability. 'Greek alphabet' names the entire set of 24 letters, of which epsilon is one member. 'Letter name' is a broader category referring to any system of names for alphabet letters (e.g. 'A', 'bee', 'cee', 'epsilon'). So while epsilon names a specific character, varepsilon names a calligraphic style of the same character, and Greek alphabet refers to the whole writing system it belongs to.

epsilon ↗varepsilonGreek alphabetletter name

Common collocations

Nouns

  • epsilon symbol
  • epsilon value
  • epsilon-delta proof

Phrases

  • the letter epsilon
  • lowercase epsilon
  • uppercase epsilon
  • epsilon of the Greek alphabet

Prepositions

  • epsilon in [word/name]
  • epsilon of [value]
  • written as epsilon

Etymology

GreekLatinEnglish

The English name comes from the Greek phrase 'ἒ ψιλόν' (e psilon), meaning 'plain e' or 'bare e'. Ancient Greek had two ways of writing the 'e' sound: the diphthong αι (ai) had come to be pronounced like an 'e', so speakers needed a way to distinguish the simple letter ε from that sound. They called ε 'psilon' (plain/naked) — hence 'e-psilon'. The word travelled into Latin and then into English as 'epsilon', first recorded in English in the 1600s.