“Interval rational = algebraic” revisited
Anatoly V. Lakeyev, Владик Крейнович · ACM SIGNUM Newsletter · 1996
In [1], it is shown that if we add "interval computations" operation to the list of arithmetic operations that define rational functions, then the resulting class of "interval-rational" functions practically coincides with the class of all algebraic functions. By "practically coincides", we mean that first, every interval-rational function is algebraic, and that second, for every algebraic function A(x), there exists an interval-rational function that coincides with A(x) for almost all x. In [1], "almost all" was understood in terms of Lebesgue measure; this result is therefore, not very computer realistic, because all the numbers representable in a computer are rational and therefore, form a set of Lebesgue measure 0. In this article, we formulate a more computer-realistic version of the result that interval + rational = algebraic.