# Symbols:Greek/Epsilon

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## Epsilon

The $5$th letter of the Greek alphabet.

Minuscules: $\epsilon$ and $\varepsilon$
Majuscule: $\Epsilon$

The $\LaTeX$ code for $\epsilon$ is \epsilon .
The $\LaTeX$ code for $\varepsilon$ is \varepsilon .

The $\LaTeX$ code for $\Epsilon$ is \Epsilon .

### Element of Set

The notation for an object being an element of a set uses a stylized form of the letter $\epsilon$:

$x \in S$, $S \owns x$

This notation was invented by Peano, from the first letter of the Greek word είναι, meaning is.

The $\LaTeX$ code for $\in$ is \in .

The $\LaTeX$ code for $\owns$ is \owns  or \ni.

### Arbitrarily Small Positive Quantity

Many a proof in analysis will famously start:

"Let $\epsilon > 0$ ..."

where it is frequently left unstated that $\epsilon$ is a real number, arbitrarily small.

The $\LaTeX$ code for $\epsilon > 0$ is \epsilon > 0 .

### Vacuum Permittivity

$\varepsilon_0$

The vacuum permittivity is the physical constant denoted $\varepsilon_0$ defined as:

$\varepsilon_0 := \dfrac {e^2} {2 \alpha h c}$

where:

$e$ is the elementary charge
$\alpha$ is the fine-structure constant
$h$ is Planck's constant
$c$ is the speed of light defined in $\mathrm m \, \mathrm s^{-1}$

Of the above, only the fine-structure constant $\alpha$ is a measured value; the others are defined.

It can be defined as the capability of an electric field to permeate a vacuum.

From Value of Vacuum Permittivity, it has the value:

$\varepsilon_0 = 8 \cdotp 85418 \, 78128 (13) \times 10^{-12} \, \mathrm F \, \mathrm m^{-1}$ (farads per metre)

The $\LaTeX$ code for $\varepsilon_0$ is \varepsilon_0 .

## Sources

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