# 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 a 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.

### A 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 .

## Also denoted as

While $\epsilon$ is common, so is $\varepsilon$. The symbols are, in general, interchangeable.

Some writers prefer $\epsilon$ and some prefer $\varepsilon$.

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

On $\mathsf{Pr} \infty \mathsf{fWiki}$ the preferred symbol is $\epsilon$.