What does epsilon mean?
Epsilon is the fifth letter of the Greek alphabet, written Ε in uppercase and ε in lowercase, and it corresponds to the short 'e' sound in English. Beyond its role as a letter, epsilon has become one of the most recognizable symbols in mathematics, where it conventionally stands for an arbitrarily small positive quantity — a number greater than zero but as tiny as one likes. This usage is central to analysis and calculus, particularly in the famous epsilon-delta definitions of limits and continuity devised by mathematicians such as Cauchy and Weierstrass in the nineteenth century. In physics and computer science, epsilon similarly denotes small tolerances or margins of error. By extension, the word occasionally appears in ordinary language to mean a vanishingly small amount, as in "not an epsilon of difference." Its Greek name derives from the phrase e psilon, meaning "simple e," distinguishing it from the digraph αι.
The fifth letter of the Greek alphabet (Ε, ε), corresponding to the English short 'e'.
"The lowercase epsilon resembles a curved 'e' with a horizontal bar."
Also used in mathematics to represent an arbitrarily small positive quantity.
A very small or negligible amount of something.
"The two candidates differed by an epsilon on nearly every issue."
Figurative extension of the mathematical sense; relatively rare outside technical contexts.
Standard plural, used mainly when referring to multiple instances of the letter or multiple small quantities in mathematics.
"The proof holds for all epsilons greater than zero."
Mathematicians use epsilon to name quantities so small they're essentially zero — yet without it, calculus's rigorous foundations would fall apart.
Reviewed by Deb Chak, Editor. AI-assisted content curated by RJS Tech Solutions LLP.
Etymology of epsilon
The word epsilon comes from Ancient Greek ἒ ψιλόν (e psilon), literally "simple e," a name coined in the medieval period to distinguish the plain vowel sound from the diphthong written αι, which had come to be pronounced identically. It entered European scholarly vocabulary through the transmission of Greek learning and has been used in English since at least the early modern period. As a Greek letter name, it shares its origin with siblings such as alpha, beta, gamma, and delta, which likewise denote letters of the Greek alphabet and, by convention, key constants and variables across mathematics and science.
How epsilon is actually used
Primarily a technical term used in mathematics, physics, computer science, and engineering; figurative use for a tiny amount is comparatively rare but understood. The plural is epsilons.
Easily confused with epsilon
An eponym is a person after whom something is named, whereas epsilon is a Greek letter or a symbol for a tiny quantity.