I am new to math and am exploring how to formally represent a sequence of events. I want to be able to say "an event sequence $E_s$ is a sequence of events $\langle e_1, e_2,\ldots, e_n\rangle$". Just basically trying to define a sequence of objects.
What is the appropriate way to do that (in set theory notation, or something better if that is what is typical)?
I have done some searches, but all the examples/definitions of "sequences in set theory" I've seen have to do with numbers, so not sure if it's different when not dealing with numbers.
First of all, in set theory, everything is generally considered to be a set. So sequences are sets, and the sequenced objects are also sets. We can give those sets meanings and call them by $1,2,3$ and so on, or $\pi,e,\sqrt{-1}$ and so forth.
In general, a sequence is a function. Finite sequences are functions whose domain is finite, so usually it's taken as some $\{1,\ldots,n\}$ for some natural number $n$. This means that we can write it as some $f(1)$ to $f(n)$. But it is common to write $\langle e_1,\ldots,e_n\rangle$ or $\langle e_i\mid 1\leq i\leq n\rangle$ as well.
As for the definition, it seems to me that you've nailed it. Writing "An event sequence $E_s$ is a sequence of events $\langle e_1,\ldots,e_n\rangle$" is very clear and to the point.