Tricki
a repository of mathematical know-how

I have a problem to solve in real analysis

Quick description

This is an experimental page that is designed to provide automatic assistance to anybody who wants to solve a problem in real analysis. The idea is that by choosing appropriate answers to questions that will be put to you, you will be led to a Tricki page that will help you with your particular analysis problem (if a helpful page exists). The article is not by any means complete, but the hope is that it will eventually be able to provide assistance with a wide range of problems that might be set as not too difficult exercises on a first course in real analysis.

Note iconIncomplete This article is incomplete. There is some way to go before this article will be complete.

How to solve your problem

Some problems in real analysis can be solved by means of what one might call "axiomatics": you perform a sequence of operations such as replacing a wordy definition with a quantifier version, looking at the contrapositive of a statement, negating statements that involve strings of quantifiers, and so on, until the proof drops out. It is clear that proofs of this kind could be carried out by a computer (and I think probably there are systems out there that can already do this). If you think that your problem might be "semi-automatic" in this way, but would still like some help, then have a look at the following article.

I have a problem to solve in real analysis and I do not believe that a fundamental idea is needed

If your problem is not of this "easy" kind, then it will be helpful to narrow down the subject matter a little. Most first courses in real analysis begin with a discussion of the real numbers and limits of sequences and sums, then they move to continuous functions, then they discuss differentiability, and then Riemann integration. Further topics may include pointwise and uniform convergence of sequences of functions, and differentiability of functions from \mathbb{R}^n to \mathbb{R}^m. While there are some techniques that work for more than one of these subareas, it will be convenient to discuss them on separate pages. So the first question is this: which of the following descriptions best fits the area that your problem is about?

I need to find a real number with a certain property

I have a problem about the convergence of a sequence

I have a problem about a supremum or an infimum

I have a problem about an infinite sum

I have a problem about a continuous function

I have a problem about open or closed sets

I have a problem about differentiation

I have a problem about integration

I have a problem about uniform convergence

I have a problem about differentiation in higher dimensions