Chuck Lindsey's story on the origins of analytic set theory is true. Aleksandrov (in Luzin's seminar in 1915) was proving that every uncountable Borel set contains a non-empty perfect subset (so that the continuum hypothesis is true for Borel sets) when he noticed the mistake. Suslin noticed that Aleksandrov's proof actually applied to a larger class of sets than the Borel sets, which he called A-sets because they were produced by a transfinite inductive process called the A-operation. (The A was supposed to be for "analytic", but Aleksandrov said it was for "Aleksandrov".) I mentioned this story in my 1994 article on "Descriptive set theory and uniqueness of trigonometric series" in the Archive for History of Exact Sciences. The basic facts are given in Lebesgue's preface to Luzin's book "Ensembles analytiques".