It's not a total (heh) disaster, since many intervals are comparable with many other intervals. Floating point implicitly "solves" this problem by truncating the implicit interval onto a member of a fixed discrete set. It does so quite cleverly, but ultimately it still silently loses information; sometimes (admittedly rarely) you might want the correct result "I was unable to compute an answer due to lack of input precision" that happens when you try and work out whether [0,2] is less than [1,3].

Forget ordering. The useful equals relation becomes ternary.