Classifying Topics of Discontinuity (removable vs. non-removable)

In the realm of mathematical analysis, the classification of discontinuities plays a pivotal role in understanding the behavior of functions. Specifically, this investigation delves into the categorization of discontinuities, distinguishing between removable and non-removable instances. By scrutinizing the characteristics and implications of these distinct types, we aim to unravel the nuances that govern the nature of disruptions in a function's continuity. This exploration is fundamental for mathematicians and researchers seeking a precise comprehension of discontinuity patterns within the broader context of mathematical functions.