[joe_the_user]

You think that's bad? Theoretical math has "conditionally convergent series'" [1] Sum in order and it can convergence to a given value. Rearrange the terms and any real number is possible.

I have a hunch there could be a bit of relation between these things.

[1] https://en.wikipedia.org/wiki/Conditional_convergence

[StefanKarpinski]

It's an interesting connection. Any finite collection of real values (represented in floating-point or otherwise) has a definite correct sum. If you're constrained to the floating-point to represent that value, you should ideally round the true value to the closest float and return that. Computing this true sum of a sequence of floating-point values is surprisingly hard though. The state of the art seems to be Radford Neal's paper on superaccumulators from 2015:

https://arxiv.org/abs/1505.05571

Fortunately pairwise summation (Julia's default) is fast and fairly hard to trip up, although it certainly is possible to trick it.