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

单词	Discrete
释义	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 $\\mathbb{R}^{n}$ .
随便看	ExampleOfTraceOfAMatrix example of trace of a matrix ExampleOfTranscendentalNumber example of transcendental number ExampleOfTransfiniteInduction example of transfinite induction ExampleOfTreesetTheoretic example of tree (set theoretic) ExampleOfUncountableFamilyOfSubsetsOfACountableSetWithFiniteIntersections example of uncountable family of subsets of a countable set with finite intersections ExampleOfUnderdeterminedPolynomialInterpolation example of under-determined polynomial interpolation ExampleOfUseOfTaylorsTheorem example of use of Taylor’s theorem ExampleOfUsingEisensteinCriterion example of using Eisenstein criterion ExampleOfUsingLagrangeMultipliers example of using Lagrange multipliers ExampleOfUsingResidueTheorem example of using residue theorem ExampleOfVectorPotential example of vector potential ExampleOfWellfoundedInduction example of well-founded induction ExamplesForHenselsLemma