Define a real valued function on the reals by [tex] f(x):=\begin{cases} 0, & x \not\in \mathbb{Q} \\

\frac{1}{q}, & x = \frac{p}{q}, \gcd(p,q)=1, q >0 \end{cases}[/tex].

Where is this function continuous?

The problem appeared in Hyman Bass’s article in the June 2015 issue of the notices of AMS. I casually dismissed it as another standard problem, having “seen it somewhere before” but it caught the eye of one colleague and another colleague, an analyst, said it was non-routine. Given the interest, I thought about where I could have seen it and my first instinct was to check baby Rudin. There it was in chapter 4, problem 18. Although I have to admit, if I had seen it before, it was probably not from Rudin.

Fact check: Bass mentioned he learnt about real numbers in 1951 at Princeton while Rudin wrote his textbook when he teaching at MIT in the early 1950s. The first edition appeared in 1953. So the source might have pre-dated Rudin.