a repository of mathematical know-how

Finding subsets front page

Quick description

This page contains links to articles that are about techniques for finding subsets with given properties of sets such as \mathbb{N}, \mathbb{R}, \mathbb{R}^2, the complete graph on n vertices, the discrete cube, or the set of all subsets of \mathbb{N}. It is not about finding structured subsets such as subgroups or subspaces, so the techniques have a combinatorial flavour.

The articles

Just-do-it proofs

How to use Zorn's lemma

Transfinite induction

How to use the continuum hypothesis

Finding small nets Quick description ( A \delta-net of a metric space X is a subset \Delta\subset X such that for every x\in X there exists y\in\Delta such that d(x,y)\leq\delta. It is often useful to have a small \delta-net for a metric space. This article discusses a few techniques for finding them, giving particular reference to an idea that can be summarized by the following slogan: a maximal separated set is a net. )

Probabilistic combinatorics front page


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