[AnimalMuppet]

But what you would actually get is something like this:

   x---0.1 + 0.2 ---x
      x---0.3---x

That is, the range of 0.1 + 0.2 would be wider than the range of 0.3. And now what do you do? There is overlap, so are they equal? But there are parts that don't overlap, so are they different?

[Nullabillity]

Make equality checks illegal, and instead define specific operations for contains and overlaps.

[crazygringo]

Well right now you basically can't ever check for equality with floating-point arithmetic and trust that two numbers that should intuitively be equal are reported as equal.

For me, floating-point equality would be if there are any parts that overlap. Basically "=" would mean "to the extent of the floating-point accuracy of this system, these values could be equal".

If you're doing a reasonably limited number of operations with values reasonably larger than the error range, then it would meet a lot of purposes -- you can add 0.5 somewhere in your code, subtract 0.5 elsewhere, and still rely on the value being equal to the original.