Interesting challenge. The spec seems complete to me, but I can imagine it being easy to make an incorrect assumption because "Convert" could lead to some people assuming that $f(x)$ is expressing $x$ as a binary fraction. Would it be worth stating explicitly that this is in general impossible so people have an idea of what they are getting into before they start?

(Alternatively maybe something other than "Convert" in the title, such as "Bijection from"?)

The new title more than covers it. I like it.

Not really. Now it's even more unclear to me than before. What does it mean for a function to be "from rational numbers", for example. It would help if you explained what you wanted in plain English.

This is a very mathematical challenge. I wouldn't expect most people who write code to understand it, so its target audience will be people who enjoy both golfing code and mathematics.

The previous title sounded like a straightforward conversion challenge, which could attract people who don't have the background knowledge to attempt it. The new title sounds unapproachable to people not familiar with the mathematics, which gives a more accurate impression of the challenge.

Having said that, for people who don't yet know the terms but are interested in learning before considering trying the challenge, it might be worth making the first mention of the rational numbers a link to somewhere like Wikipedia.

I know what a rational number is. I don't understand what it means for a function to be "from" rational numbers. I also don't understand "order equivalence", what the relation in the first set of bullets is trying to tell us, and what the notation in the second set of bullets even means in the first place.

I would have no problem with this on the Math site, where many users probably do understand these things. However here on the Code Golf site, this is just math elitism. -1 and moving on.

I split the first bullet in two, and I rewrote the second with less notation. A function is "from the rational numbers" if it takes rational numbers as its inputs (domain). Sometimes you forget that something is actually jargon (xkcd), so I reworded this. Order equivalence is that the order of the inputs is the same as the order of the outputs. I tried rewording this as well.

I don't think the ideas here are complex, but solving it is definitely more mathy than the average question here. I think that's how the open-ended-function tag generally is. It might be that this isn't the kind of thing you enjoy. Thank you for taking the time to read it and give feedback.