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:

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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 ${\mathbb{R}}^{n}$.

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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).

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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 ${\mathbb{R}}^{n}$.
Title  discrete 

Canonical name  Discrete 
Date of creation  20130322 17:56:49 
Last modified on  20130322 17:56:49 
Owner  lalberti (18937) 
Last modified by  lalberti (18937) 
Numerical id  8 
Author  lalberti (18937) 
Entry type  Definition 
Classification  msc 54A05 
Related topic  Discrete 