On Mon, 30 Oct 1995 email@example.com wrote:
> Does anyone know the provenance of the following function which is > discontinuous on the rationals in [1,2] but continuous on the > irrationals? Does it have a name? Who is credited with defining > it? > > Define the function h: [1,2]-->R as follows: > > h(x) = 0 if x is irrational > h(x) = 1/n if x is rational and x = m/n, where m and n are positive > integers with no common factors. > > I came across the function in an exercise set in the book > _Real Analysis_ by Patrick Fitzpatrick, with no reference to other > source. > > Joel Lehmann > Dept. Math & CS > Valparaiso University > I don't know the provenance of this function, which has been a staple of real analysis courses for many years. However, I DO have a name for it, that I've been using for the last 30 years, and that some (who must have got it from me) put into a book, namely "Stars over Babylon". To see why the name is appropriate, draw a fairly accurate picture!