alt Hacker NewsI'm going to agree with the downvoted people and say that this sort of approach is largely meaningless if you allow arbitrary mappings. IMO the most reasonable mathematical formulation given the structure of the integers (in the sense of e.g. Peano) is that to truly represent an integer you have to represent zero and each other representable number has a representable predecessor, i.e. to say you can represent 5 you need 0,1,2,3,4, and 5 to be representable. By a straightforward counting argument, 2^64-1 is then the largest representable number, in other words the obvious thing is right.
Replies
In the spirit of floating points, I'd say posits offer an excellent insight into the trade-offs between precision and accuracy, while being meaningfully representative of a number system rather than some arbitrary functions.
Your idea can't even represent 1/2. What good is that?
You're imposing an abitrary set of preferred numbers, which is boring and useless for measuring large things.
As I've replies several times before, we don't allow arbitrary mappings. We allow computable mappings but consider only obviously non-cheating languages like Turing machines or lambda calculus or Linux's bc or any existing programming language, that are not geared toward outputting insanely large numbers.