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 as the mathematically familiar R.
Concepts that we wish to examine through real analysis include properties like Limits, Continuity, Derivatives (rates of change), and Integration (amount of change over time). Many of these ideas are, on a conceptual or practical level, 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 senseless and trivial.
However, Real Analysis is at a depth, complexity, and arguably beauty, that it is because under the surface of everyday mathematics, there is an assurance of correctness, that we call rigor, that permeates the whole of mathematics. Thus, Real Analysis can, to some degree, be viewed as a development of a rigorous, well proven framework to support the intuitive ideas that we frequently take for granted.
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