Who is Epsilon ($\epsilon$)? a binary relation?

Question

I was reading:

Transitive set ordered by epsilon

and

http://www.princeton.edu/~jburgess/PHI323S13Problems.pdf (ex. 4)

so, who is epsilon?

Thanks in advance!

Answer 1

Epsilon is the name of $\epsilon$, the fifth letter of the Greek alphabet; here it refers to the membership relation $\in$, as when we write, for instance, $3\in\Bbb Z$. When we say that a set $S$ is ordered by epsilon, we mean that $\langle S,\in\rangle$ is a strict linear order: if $x,y\in S$, then exactly one of $x\in y$, $x=y$, and $y\in x$ holds. This is analogous to $\langle\Bbb N,<\rangle$ being a strict linear order: for each $m,n\in\Bbb N$, then exactly one of $m<n$, $m=n$, and $n<m$ holds.

Answer 2

Instead of "espilon" the authors might have written "the is-an-element-of relation", but that doesn't sound cool.