TABLE OF CONTENTS The last 350 years of continuum modelling has resulted in exceptional scientific understanding and achievement. Unfortunately, it has also lulled many of us into the belief that continuum models are the best models one can use and that these are immune from defects. Our limited world view too often has overlooked deficiencies of continuum models, a few of which will be discussed, for completeness, in this chapter.
The basis of all continuum modelling is the concept of infinity, to which we turn our attention first.
There are basically two concepts of infinity. The first is characterized by the symbol ? and denotes a process, that is, the process of growing beyond all bound. It is not a number. Thus, for example we have
which means that as x approaches zero, the value of 
is increasing beyond all bounds.
The second concept of infinity is characterized by the number of elements in a given set. For example, the number of points on the X axis in the interval 0 ? x ? 1 is denoted by C (for Cantor (1955)). C is the cardinality of the infinite number of points in the given interval. It is called a transfinite cardinal. It is a number quite unlike numbers like 1, -27, ?, 3 + 4 i. Nevertheless, it is a number and it is intimately associated with continuum modelling, so...
