I saw a comment by Asaf Karagila a while back that remarked on the elements of $\pi$. I'm aware of how natural numbers get said to have elements in set theory, such as $3$ having the elements $\{\}, \{\{\}\}, \{\{\}, \{\{\}\}\} \}$. This doesn't quite make it clear to me how rational numbers have elements also, but I'll forego that here.
It seems even less clear to me that a number like $\pi$ or $e$ would have elements. I thought for a moment that using the terms of an infinite series used to compute $e$ might work, but on further reflection this seems suspicious, since it seems that different non-terminating series could get used to compute $e$, as holds for $\pi$.
What are the elements of $e$?
