Well-order as a construction principle for physical theories

Abstract

Physics has up to now missed to express in mathematical terms the fundamental idea of events of a path in time and space uniquely succeeding one another. An appropriate mathematical concept that reflects this idea is a wellordered set. In such a set every subset has a least element. Thus every element of a well-ordered set has as its definite successor the least element of the subset of all elements larger than itself. This is apparently contradictory to the densely ordered real number lines which conventionally constitute the coordinate axes in any representation of time and space and in which between any two numbers exists always another number. In this article it is shown how decomposing this disaccord in favour of well-ordered sets causes spacetime to be discontinuous.