zlacker

>>tromp+(OP)
The problem, as stated, provably has no answer. Assume such a number exists. Call it n. Now define a new 64-bit numbering scheme such that each number x is interpreted as n+x. n+x > n, which invalidates the hypothesis. There needs to be more constraints for this to be interesting. Like largest number representable where the representation is closed under addition and multiplication, or something like that.

>>4death+ay6
Posits formerly unums, these are amazing. The best solution I've seen. Look up John Gustafson. This article doesn't mention him or posits. They can expand with inaccuracy but retain precision. Or sacrifice precision for accuracy. Making the best use of the bits depending on the application.