[Cthulhu_]

A variant I've seen was "We've sent you a recovery code to your email at gmail.com". I think it's useful for login name based authentication, since people will have multiple email addresses and may forget which one they used for that account.

(we have a 15 year old who's made at least four, probably more different gmail addresses for different purposes. Ironically, the one he used to sign up for porn includes his real first/lastname)