A formal language is autodense if any word can be modified by a prefix and a suffix to become a member. It is anti-autodense if adjoining a prefix and a suffix to a member always removes it from the language.

Fan et al. have studied similar properties of languages for many years. This short note, of interest almost exclusively to specialists, collects various properties of autodense and anti-autodense languages, with proofs. The proofs are mostly straightforward set-theoretic arguments. No big theorem is presented, but many propositions are stated and proved.