| Abstract: | This paper proposes a genetic development of the concept of limit of a sequence leading to a definition, through a succession
of proofs rather than through a succession of sequences or a succession of εs. The major ideas on which it is based are historical
and depend on Euclid, Archimedes, Fermat, Wallis and Newton. Proofs of equality by means of inequalities precede the notion
of limit. For example, the determination of the volume of a pyramid precedes the definition of limit. The algebraic details
given here are anachronistically modern, and the notion of a vice between two inequalities which provides the distinctive
perspective of this paper would not have been recognized in this form by any of the named mathematicians since it presumes
the existence of negative numbers and their comparability in a modern sense with positive numbers. |
