Symbols:Greek/Epsilon
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, $\varepsilon_0$ 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
- 2014: Christopher Clapham and James Nicholson: The Concise Oxford Dictionary of Mathematics (5th ed.) ... (previous) ... (next): epsilon