Symbols:Epsilon

Epsilon

Element of a Set

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

See element of a set.

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

The $\LaTeX$ code for $\owns$ is \ni (that is, in backwards), or \owns.

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.

Alternative Symbol

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.