Only Intervals Preserve the Invertibility of Arithmetic Operations

In standard arithmetic, if we, e.g., accidentally added a wrong number y to the preliminary result x, we can undo this operation by subtracting y from the result x+y. A similar possibility to invert (undo) addition holds for intervals. In this paper, we show that if we add a single non-interval set, we lose invertibility. Thus, invertibility requirement leads to a new characterization of the class of all intervals.