On 14 Apr 2020 at 18:44, Adam P. Goucher wrote: Yes, also by the great late J. H. Conway:
https://en.wikipedia.org/wiki/Conway_base_13_function
It's actually stronger than what you've asked for; it takes every real value on every nontrivial interval.
how cool -- I came up with a proof using a similar idea, back as an undergraduate: the question was to prove that the algebraic numbers were countable.. I did it in base 13. with the digits 0123456789 + - ^ . With the convention that ^^N denotes the Nth solution to the polynomial. It was then , as with Conays' base 13 function it was easy to show that every algebraic number maps to an integer and so is countable. I did that a lotta years ago [as a sophomore] but I think it was a valid proof. I can't even remember what the "proper" proof was any more /Bernie\ Bernie Cosell bernie@fantasyfarm.com -- Too many people; too few sheep --