Is $\{\varepsilon\}$ a conventional way to mark the empty language? I am grading an exercise in Automata and Formal Languages and see many of the students use $\{\varepsilon\}$ as the empty language. At first I thought this was an error, and I have asked the lecturer who confirmed. But I keep seeing this and I'm losing my confidence. Is this kind of thing used by anyone? Meaning, does anyone use $\{\varepsilon\}$ as the empty language (even though it would &quot;override&quot; the obvious meaning of the singleton of $\varepsilon$)?
No, that's the language containing one string: the empty string, which is very much distinct from the empty language. The finite state machine on the left accepts language $\{\}$, the finite state machine on the right accepts language $\{\varepsilon\}$. They are not the same.

If a lot of students are confused maybe explicitly show the difference in an exercise/during a lecture.

As an example, we could use the language as a password check. Anyone submitting an accepted word would be let through. Then $\{\}$ means &quot;let no one in&quot; and $\{\varepsilon\}$ means &quot;let anyone that submits a blank password in&quot;. Those are quite different indeed!