Real analysis front page

a repository of mathematical know-how

Real analysis front page

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[QUICK DESCRIPTION]

This is a navigation page with links to articles about techniques that are useful in real analysis. See also the companion page to this one entitled [[I have a problem to solve in real analysis]].

[note incomplete] This page will clearly have to be substantially developed and reorganized as the Tricki grows. [/note]

[[How to use the Bolzano-Weierstrass theorem]] [cut] Quick description|| The Bolzano-Weierstrass theorem asserts that every bounded sequence of real numbers has a convergent subsequence. More generally, it states that if $X$ is a closed bounded subset of $\mathbb{R}^n$ then every sequence in $X$ has a subsequence that converges to a point in $X$. This article is not so much about the statement, or its proof, but about how to use it in applications. If you come across a statement of a certain form (explained in the article), then the Bolzano-Weierstrass theorem may well be helpful. [/cut]

[[Constructing exotic sets and functions using limiting arguments]] [cut] Quick description|| If you want to construct a set or function with a strange property (for instance, you might want a function that was continuous everywhere and differentiable nowhere) then a good way of doing so is often to define your object as a limit of a sequence of objects that exhibit the behaviour you want on smaller and smaller distance scales.[/cut]

[[I have a problem to solve in real analysis]] [cut] Quick description || This is a page that tries to understand what kind of problem you are trying to solve, so that it can take you to appropriate advice on the Tricki.[/cut]

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