# Real Analysis/Introduction

The subject of real analysis is concerned with studying the behavior and properties of functions, sequences, and sets on the Real number line, which we denote ${\displaystyle \mathbb {R} }$. Concepts that we wish to examine through real analysis include properties like Limits, Continuity, Derivatives (rates of change), Integration (amount of change over time). Many of these ideas that, on a conceptual or practical level, are dealt with at lower levels of mathematics, including a regular First-Year Calculus course, and so to the uninitiated reader the subject of Real Analysis may seem rather shallow and trivial. However, the depth and complexity (and arguably the beauty) of Real Analysis is that we wish to generalize these properties away from the "nice" functions and sets dealt with in everyday mathematics, and rigorously prove these properties for all objects in the universe of the Real numbers. Thus real analysis can to some degree be viewed as a development of a rigorous, well-proven framework to support spatial and conceptual ideas that we frequently take for granted.