What does the letter epsilon signify in mathematics? This letter "$\varepsilon$" is called epsilon right ? What does it signify in mathematics ?

Hilbert's epsilon-calculus used the letter $\varepsilon$ to denote a value satisfying a predicate. If $\phi(x)$ is any property, then $\varepsilon x. \phi(x)$ is a term $t$ such that $\phi(t)$ is true, if such $t$ exists. One can define the usual existential and universal quantifiers $\exists$ and $\forall$ in terms of the $\varepsilon$ quantifier:
$$\begin{eqnarray}
\def\hil#1{#1(\varepsilon x. #1(x))}
\exists x.\phi(x) & \equiv  & \hil{\phi}\\
\forall x.\phi(x) & \equiv  & \phi(\varepsilon x.\lnot\phi(x))
\end{eqnarray}
$$
