It is suggested that limits to the variation of physical variables are
themselves unattainable, though they can be approached as closely as
desired. This general unattainability principle is illustrated in vari
ous ways. It leads on to a study of how to remove infinities in physic
s when they cause conceptual problems, and how to introduce infinities
or zeros for those boundary points in physics which are in some sense
unattainable. An analogy between temperature in thermodynamics and ti
me in cosmology is pointed out for the case when boundary points are i
nvolved. (C) 1998 Academic Press Limited.