# 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`

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### 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`

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The $\LaTeX$ code for \(\owns\) is `\owns`

or `\ni`

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### 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`

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## 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`

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