So I was browsing Wikipedia, and I stumbled across this article: http://en.wikipedia.org/wiki/Conway_base_13_function
The article claims that the Conway base 13 function, as a function from (0,1) to the reals is a counter example to the converse of the Intermediate Value Theorem (i.e., that for any a, b in (0,1) if f(a) < f(b), then for any c between f(a) and f(b), there is an x between a and b such that f(x) = c, but the function is not continuous)
The function sounds like it is very interesting; however, the article as written is very sparse and the definition of the function is not very clear to me. Maybe I'm misunderstanding the definition, but as it's written, it doesn't even seem to be a surjection to (0,1) though the article claims that it is.
Unfortunately, a google search of the function didn't bring anything up other than the wikipedia article. Is there anyone who understands this function who could give clear definition of it?