Publication Date
8-2012
Abstract
From a purely mathematical viewpoint, once a statement is rigorously proven, it should be accepted as true. Surprisingly, in applications, users are often reluctant to accept a rigorously proven statement until the proof is supplemented by its intuitive explanation. In this paper, we show that this seemingly unreasonable reluctance makes perfect sense: the proven statement is about the mathematical model which is an approximation to the actual system; an intuitive explanation provides some confidence that the statement holds not only for the model, but also for systems approximately equal to this model -- in particular, for the actual system of interest.
Comments
Technical Report: UTEP-CS-12-15
Published in Applied Mathematical Sciences, 2012, Vol. 6, No. 125, pp. 6215-6219.