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 topologyMathworldPlanetmath implied by the context, is a \PMlinkescaptetextdiscrete space. For instance for a subset of n and without information suggesting otherwise, the topology on the set would be assumed the usual topology induced by norms on 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 n (with boundary conditionsMathworldPlanetmath) into equations on functions on discrete subsets of 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