Dealing with the concept of infinity.

Early Greek attempts to understand infinite processes involved the so-called Method of Exhaustion which enabled one to construct areas of non polygonal figures by a summation process.

Archimedes Quadrature of a Parabola, circa 200 B.C.E.

They were aware of the paradoxes involved in performing a process an infinite number of times (e.g. Xeno's paradox)

Making Limits Precise

The concept of an infinitesimal (a positive quantity, smaller than 1, 1/2, 1/3, 1/4, 1/5, etc.) Calculus, based on infinitesimals and Non-standard Analysis

Readings on the history of Infinitesimal Calculus

Concise summary of the development of the Calculus

Teaching Limits

How to Teach Limits [Stanford web site]

Teaching limits with a computer algebra system