Cauchy’s definition of limit experiences actual infinite to potential infinity in the leap. Weierstrass’s definition, in turn, reflects the transition from a static to a dynamic concept idea. The definition of limit has great abstract difficulty, and its multi-level structure has increased the difficulty of teaching. In this paper,as the mathematical methodology a guide, the difficulty of teaching the definition of the limit can effectively be overcome.

the definition of the limit, abstract difficulty, mathematical methodology.