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	2013-03-22 17:56:49
Last modified on	2013-03-22 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