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The fifth Greek letter, conventionally a very small positive quantity.
Also known as: Greek letter epsilon, Epsilon symbol, ε, Small quantity symbol
Epsilon is the conventional name for something arbitrarily small but not zero — the letter mathematicians reach for when they need a margin that can be made as tight as required. It also names permittivity in electromagnetism and strain in engineering.
Is a letter of the Greek alphabet before it is a symbol: what it denotes is fixed by the field it appears in, not by the character itself. The uses below are the documented conventions, not competing definitions.
Contexts: Mathematics
In mathematical analysis, denotes an arbitrarily small positive quantity, as in epsilon–delta proofs of limits.
Contexts: Mathematics
In electromagnetism, denotes permittivity, the measure of how a material responds to an electric field.
Contexts: Mathematics
In engineering, denotes strain — deformation relative to original length.
Contexts: Mathematics
In computing, denotes machine epsilon, the smallest difference a floating-point format can represent.
Contexts: Mathematics
Is easily mistaken for the set-membership sign ∈, which is a different character with a fixed meaning — 'is an element of' — rather than a variable.
The two are drawn very similarly and the distinction matters: one names a quantity, the other asserts a relation.
Contexts: Mathematics
A rounded shape open to the right, formed of two stacked curves, like a backwards 3.
The set-membership sign is a distinct character from this letter, and the resemblance is close enough that the two are routinely substituted for one another.
Paired in the epsilon–delta definition of a limit, where epsilon is the tolerance demanded and delta the closeness that achieves it.