Epsilon Symbol (ε): Meaning, Why It Is Not ∈, and LaTeX
July 10, 2026
The epsilon symbol is ε, the fifth letter of the Greek alphabet. It nearly always stands for something arbitrarily small — the ε in an epsilon-delta proof, a tolerance, an error term. Copy it below, or jump to how to type it.
| Character | Unicode | HTML entity | LaTeX | Windows alt code |
|---|---|---|---|---|
| ε lowercase epsilon | U+03B5 | ε | \varepsilon | Alt + 238 |
| ϵ lunate epsilon | U+03F5 | ϵ | \epsilon | — |
What the symbol means
| Where | Meaning |
|---|---|
| Analysis | An arbitrarily small positive number, as in epsilon-delta |
| Numerics | Machine epsilon — the smallest relative rounding step |
| Mechanics | Strain, the fractional change in length |
| Electromagnetism | Permittivity, with ε₀ the permittivity of free space |
| Statistics | The error or residual term in a regression model |
| Reinforcement learning | Exploration rate in an epsilon-greedy policy |
ε is not ∈
This is the mix-up worth knowing about. The Greek letter ε and the set-membership sign ∈ (U+2208) look similar in some fonts but are entirely different characters with entirely different meanings — one is a small quantity, the other reads “is an element of”. Pasting one where you meant the other produces a statement that is not just wrong but meaningless.
In LaTeX the commands are \varepsilon for the letter and \in for membership. If you find yourself typing \epsilon for “belongs to”, that is the bug.
ε in the definition of a limit
The epsilon-delta definition is where most people first meet the letter. It says: however small a tolerance ε you demand around the limit, there is some distance δ within which the function stays inside it. The order of the quantifiers is the whole content of the definition.
ε as strain and as error
In mechanics, strain is the fractional change in length — a dimensionless ratio, which is why it pairs with stress through Young’s modulus. In regression, ε is the part of the response the model does not explain.
How to type it
Windows
- ε: hold
Altand type238on the numeric keypad - In Word, type
03B5and pressAlt + X - For the set-membership sign ∈, use
2208withAlt + X— not the Greek letter
Mac
- Open Character Viewer with
Control + Command + Spaceand search “epsilon” - Or enable the Greek keyboard, where ε sits on the
ekey
HTML
εorεfor ε∈or∈for ∈
In LaTeX
LaTeX has two shapes, and the naming is the opposite of what most people expect. \epsilon gives the lunate ϵ, while \varepsilon gives the curly ε that maths texts normally use. If your epsilons look unfamiliar, this is why.
Frequently asked questions
What does ε mean in maths?
An arbitrarily small positive quantity. In analysis it is the tolerance in a limit proof; more loosely it means 'a tiny amount'.
Is ε the same as ∈?
No. ε is the Greek letter epsilon; ∈ is the set-membership sign meaning “is an element of”. They are different characters with unrelated meanings.
Why are there two epsilon shapes in LaTeX?
Historical typesetting. \epsilon is the lunate ϵ and \varepsilon is the curly ε — most maths texts use the curly one, so \varepsilon is usually what you want.
See also the delta symbol it is always paired with, the real numbers symbol, and the sigma symbol.
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