Epsilon
Epsilon (Ε, ε) is the fifth letter of the Greek alphabet. In maths ε is an arbitrarily small positive number; in physics ε₀ is the permittivity of free space; in machine learning ε is the chance of exploring in an ε-greedy policy and a tiny constant added to a denominator for numerical stability.
How to read it
Epsilon is said ep-SY-lon in Britain and EP-suh-lahn in America (Cambridge Dictionary: /epˈsaɪ.lɒn/ and /ˈep.sə.lɑːn/). In Modern Greek έψιλον stands for an “eh” sound (University of Arizona). The name means “simple e”, from the Greek psīlos, simple (American Heritage Dictionary).
Also searched as: epsilon letter, epsilon symbol, ε, Ε, ε meaning.
Capital, small and look-alike forms
| Form | Character | Code point | Unicode name |
|---|---|---|---|
| Capital | Ε | U+0395 | Greek capital letter epsilon |
| Small | ε | U+03B5 | Greek small letter epsilon |
| Straight (lunate) epsilon | ϵ | U+03F5 | Greek lunate epsilon symbol |
The capital Ε looks like the Latin E. The small letter has two shapes in maths, the rounded ε and the straight ϵ, which Unicode encodes separately. Unicode cross-refers ε to the Latin small letter open e ɛ (U+025B), and ϵ to the small element-of sign ∊ (U+220A). The element-of sign ∈ (U+2208) grew out of an epsilon: Jeff Miller’s history of mathematical symbols says Giuseppe Peano used an epsilon for set membership in 1889, as an abbreviation of the Latin est. Miller adds that Peano’s symbol looks like a lunate epsilon, not the stylised one used now, and Unicode notes that ∊ is not the straight epsilon.
Epsilon in maths
ε is a small positive number. OpenStax’s Calculus Volume 1 defines a limit with it: the limit of f(x) as x approaches a is L if for every ε > 0 there is a δ > 0 such that f(x) is within ε of L whenever x is within δ of a. Miller traces ε to Augustin-Louis Cauchy in 1821, who wrote “denote by ε a number as small as one may wish”; he cites Finney and Thomas that ε stood for erreur, error. In statistics ε is also the vector of errors when a regression model is written in matrix form (Miller).
In AI and machine learning
An ε-greedy policy is one that, in Google’s Machine Learning Glossary, follows a random policy with probability ε and a greedy policy otherwise. ε is also a small constant added to a denominator: PyTorch’s Adam optimiser adds ϵ (default 10⁻⁸) to the denominator of its update, and its batch normalisation layers add eps (default 10⁻⁵) “for numerical stability”.
Other uses of epsilon
In physics ε₀ is the vacuum electric permittivity. NIST’s 2022 CODATA value is 8.854 187 8188 × 10⁻¹² farads per metre.
More greek letters
Browse symbols drawn with letters and numbers.
Sources
- Greek and Coptic: Range 0370–03FF (code chart), The Unicode Standard, Version 18.0, Unicode Consortium, Greek and Coptic, pp. 39–41
- Mathematical Operators: Range 2200–22FF (code chart), The Unicode Standard, Version 18.0, Unicode Consortium, Mathematical Operators, set membership
- epsilon (Cambridge Dictionary entry), Cambridge Advanced Learner’s Dictionary & Thesaurus, Cambridge University Press, epsilon, noun
- epsilon (American Heritage Dictionary entry), The American Heritage Dictionary of the English Language, Fifth Edition, HarperCollins Publishers, epsilon, n.
- Modern Greek Alphabet And Phonetics, University of Arizona, Center for Middle Eastern Studies, Letter table
- Calculus Volume 1, 2.5 The Precise Definition of a Limit, OpenStax (Rice University), Definition (epsilon-delta definition of the limit)
- Earliest Uses of Symbols of Calculus, Jeff Miller, Earliest Uses of Various Mathematical Symbols, MacTutor History of Mathematics, University of St Andrews, Delta and epsilon
- Earliest Uses of Symbols of Set Theory and Logic, Jeff Miller, Earliest Uses of Various Mathematical Symbols, MacTutor History of Mathematics, University of St Andrews, Membership
- Earliest Uses of Symbols for Matrices and Vectors, Jeff Miller, Earliest Uses of Various Mathematical Symbols, MacTutor History of Mathematics, University of St Andrews, Matrix notation in regression
- Machine Learning Glossary, Google for Developers, epsilon greedy policy
- torch.optim.Adam, PyTorch 2.14 documentation, PyTorch Foundation, Signature and algorithm
- torch.nn.BatchNorm1d, PyTorch 2.14 documentation, PyTorch Foundation, Parameters
- CODATA Value: vacuum electric permittivity, 2022 CODATA recommended values, U.S. National Institute of Standards and Technology, Value
Last reviewed September 30, 2026 by Rory Hansen. How we research