[PDF] real analysis 1 pdf

What are the major theorems of real analysis?

Read and repeat proofs of the important theorems of Real Analysis: The Nested Interval Theorem The Bolzano-Weierstrass Theorem The Intermediate Value Theorem The Mean Value Theorem The Fundamental Theorem of Calculus Develop a library of the examples of functions, sequences and sets to help explainthe fundamental concepts of analysis.

What is open set analysis?

One of the most important concepts of analysis is the concept of open set. This makes sense in the context of the real line, or in the more general case of Euclidean space, or in the even more general setting of a metric space. Here we use notation appropriate to the real line, but little change is required to deal with the other cases.

Is there a function for a real number?

That is, for every real numbera, there is a function,sa:R!R, given by The UNIQUENESS OF ADDITION AND MULTIPLICATIONsays that these functions are indeedfunctions, i.e. there is only one value for each element in the domain.