Cauchy started with the definition of variables and mastered the concept of limit in the course of algebraic analysis of 182 1, pointing out that infinitesimal and infinitesimal are not fixed quantities but variables, and infinitesimal is a variable with zero as the limit. This is an epoch-making concept in the history of mathematics. The introduction of this concept makes many vague and even contradictory concepts in calculus suddenly clear.

Infinitesimal is generally a variable (including series and functions). In the process of independent variable change, this variable is infinitely close to 0 (note that it can be greater than or less than 0). Cauchy put forward a series of calculation methods of calculus on the basis of this concept, thus making his own contribution to the rigor of calculus.