You are here
Homediscrete
Primary tabs
discrete
This entry aims at highlighting the fact that all uses of the word discrete in mathematics are directly related to the core concept of discrete space:

A discrete set is a set that, endowed with the topology implied by the context, is a \PMlinkescaptetextdiscrete space. For instance for a subset of $\mathbb{R}^{n}$ and without information suggesting otherwise, the topology on the set would be assumed the usual topology induced by norms on $\mathbb{R}^{n}$.

A random variable $X$ is discrete if and only if its image space is a discrete set (which by what’s just been said means that the image is a discrete topological space for some topology specified by the context). The most common example by far is a random variable taking its values in a enumerated set (e.g. the values of a die, or a set of possible answers to a question in a survey).

Discretization of ODEs and PDEs is the process of converting equations on functions on open sets of $\mathbb{R}^{n}$ (with boundary conditions) into equations on functions on discrete subsets of $\mathbb{R}^{n}$.
Mathematics Subject Classification
54A05 no label found Forums
 Planetary Bugs
 HS/Secondary
 University/Tertiary
 Graduate/Advanced
 Industry/Practice
 Research Topics
 LaTeX help
 Math Comptetitions
 Math History
 Math Humor
 PlanetMath Comments
 PlanetMath System Updates and News
 PlanetMath help
 PlanetMath.ORG
 Strategic Communications Development
 The Math Pub
 Testing messages (ignore)
 Other useful stuff
 Corrections