Yeah, pretty much the only case I can think of when you'd want to check floating points for equality is for bug hunting e.g. if you calculate a set of disjoint probabilities you might want to verify that they add up to 1.
Eg when you want to add a list of (non-negative) numbers, it makes a difference what order you add them in. The usual recommendation is to add them in ascending order.
It's not commutative, yes, but it should still obey the property that the relative error terms add instead of multiplying, no?
(i.e. in the parent's case of "checking that, if you add a bunch of disjoint probabilities, they're at most 1", doing that with approximate equality seems fine to me?)
