Is the function 1/x continuous at 0?

TL;DR

This paper discusses the concept of continuity in functions, emphasizing the importance of correct definitions and clarifying common misconceptions, especially regarding the continuity of 1/x at 0.

Contribution

It clarifies the proper notion of continuity and its distinction from related concepts, highlighting the importance of precise definitions in mathematical analysis.

Findings

Continuity is often misunderstood and confused with other notions.

The paper emphasizes the importance of using correct definitions of continuity.

It discusses the specific case of the function 1/x at 0 and the issues surrounding its continuity.

Abstract

Brief development of the idea of the very important notion of continuity is given. Continuity is often confused with contiguity, "drawing the graph in one go," "no gaps," etc. The author argues in support of using correct notions of continuity as well as that of function, where continuity is not to be considered in vacuous situations, such as when the function does not exist.