Symbols:Greek/Epsilon

Epsilon
The fifth letter of the Greek alphabet.

Minuscules: $\epsilon$ and $\varepsilon$

Majuscule: $\Epsilon$

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.

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.

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

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

On the preferred symbol is $\epsilon$.