Epsilon (Ε, ε)
Quick Info
- Pronunciation: EP-si-lon
- English: e
- Common Use: Small quantity
Historical Background
Fifth letter of the Greek alphabet, derived from Phoenician letter "he". The name comes from the Phoenician word for window, reflecting its original pictographic representation of a window or doorway.
Scientific Applications
Mathematics
Small positive number
Physics
Electric permittivity
Economics
Price elasticity
Quantum Mechanics
Energy levels
Symbol Codes
Unicode
Uppercase
- Code: U+0395
- Hex: Ε
- Decimal: Ε
Lowercase
- Code: U+03B5
- Hex: ε
- Decimal: ε
HTML
Uppercase
Ε
HTML entity for uppercase Epsilon
Lowercase
ε
HTML entity for lowercase epsilon
LaTeX
Uppercase
\Epsilon
LaTeX command for uppercase Epsilon
Lowercase
\epsilon
LaTeX command for lowercase epsilon
Common Usage
Mathematics
Analysis
Arbitrarily small positive number
Limits
Error bounds and approximations
Optimization
Tolerance levels
Physics
Electromagnetism
Electric permittivity
Optics
Dielectric constant
Mechanics
Strain measurement
Economics
Microeconomics
Elasticity of demand
Market Analysis
Price sensitivity
Econometrics
Error terms
Common Applications
Analysis
Limit definition
Error bounds
Neighborhood
Physics
Relative permittivity
Stefan-Boltzmann law
Levi-Civita symbol
Special Applications
Electromagnetic Theory
Electric displacement
Permittivity
Speed of light
Mathematical Analysis
Limit process
Epsilon ball
Convergence criterion
Field Applications
Mathematics
- • Limit theory
- • Numerical analysis
- • Error bounds
- • Topology
Physics
- • Dielectric constants
- • Field theory
- • Quantum mechanics
- • Material properties
Engineering
- • Signal processing
- • Error tolerance
- • Circuit analysis
- • System design
Writing Guidelines
Uppercase resembles the Latin E, lowercase has a distinctive curved shape. Note that there are two common variants of lowercase epsilon: ε (lunate) and ϵ (straight). In handwriting, ensure the lowercase ε is clearly distinguished from the Latin e and the Greek sigma (σ).
How to Type Epsilon
Windows
Alt Code
- Hold Alt
- Type 238 for ε
- Release Alt
Character Map
- Open Character Map
- Select Greek
- Find and copy Epsilon
Unicode
- Hold Alt + X
- Type 03B5
- Release Alt + X
macOS
Option Key
- Press Option + e for ε
Character Viewer
- Press Control + Command + Space
- Select Greek
- Click Epsilon
Linux
Compose Key
- Press Compose + e + e for ε
Unicode
- Press Ctrl + Shift + U
- Type 03B5
- Press Enter
Frequently Asked Questions
What is the difference between Epsilon (Ε) and Latin E?
While they look identical in uppercase form, Epsilon and Latin E have different historical origins and uses. Epsilon is primarily used in Greek text and scientific notation, particularly for small quantities and error terms.
Why are there two forms of lowercase epsilon (ε and ϵ)?
The two forms are the lunate epsilon (ε) and the straight epsilon (ϵ). The lunate form is more common in mathematical and scientific contexts, while the straight form appears in some typographic traditions.
How is epsilon used in mathematics?
In mathematics, epsilon typically represents a very small positive number, often used in limit definitions, error bounds, and approximations. The phrase "for any ε > 0" is common in mathematical proofs.
What's the difference between ε₀ and εᵣ in physics?
ε₀ (epsilon-zero) represents the permittivity of free space, a fundamental physical constant, while εᵣ (epsilon-relative) represents the relative permittivity or dielectric constant of a material.