Tricki

## Real analysis front page

### 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.

How to use the Bolzano-Weierstrass theorem Quick description ( The Bolzano-Weierstrass theorem asserts that every bounded sequence of real numbers has a convergent subsequence. More generally, it states that if is a closed bounded subset of then every sequence in has a subsequence that converges to a point in . 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. )

Constructing exotic sets and functions using limiting arguments 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.)

I have a problem to solve in real analysis 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.)