Your view has been repeatedly refuted by Kahan and others. See page 25 of [1], page 1 of [2], page 22 of [3] for just a few examples. Conceptually, the reason t

Your view has been repeatedly refuted by Kahan and others. See page 25 of [1], page 1 of [2], page 22 of [3] for just a few examples. Conceptually, the reason the interval view is wrong is that if floating point values represented intervals, then their arithmetic would be incorrect. For example, the sum of an interval of width w1 and an interval of width w2 should be an interval of width w1 + w2. That, of course, is not how floats work at all. The correct view is that floats represent exact rational values and operations on them, instead of being the true mathematical ones – under which floats are not closed – compute the closest float to the true result of each operation. [1] https://www.cs.berkeley.edu/~wkahan/JAVAhurt.pdf https://www.cs.berkeley.edu/~wkahan/JAVAhurt.pdf [2] https://math.mit.edu/~stevenj/18.335/fp-myths.pdf https://math.mit.edu/~stevenj/18.335/fp-myths.pdf [3] http://lyoncalcul.univ-lyon1.fr/IMG/pdf/FloatingPoint.pdf http://lyoncalcul.univ-lyon1.fr/IMG/pdf/FloatingPoint.pdf