Order theory | Binary relations

Dense order

In mathematics, a partial order or total order < on a set is said to be dense if, for all and in for which , there is a in such that . That is, for any two elements, one less than the other, there is another element between them. For total orders this can be simplified to "for any two distinct elements, there is another element between them", since all elements of a total order are comparable. (Wikipedia).

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From playlist Abstract Algebra

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From playlist Orders on Sets

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From playlist Abstract algebra

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From playlist Abstract Algebra

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From playlist Set Theory

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From playlist Graph Theory

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From playlist Abstract algebra

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From playlist Abstract Algebra

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From playlist Group theory

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From playlist Mathematics

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From playlist Mathematics

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From playlist CSE373 - Analysis of Algorithms - 2012 SBU

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From playlist Talks and Tutorials

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From playlist MAST30026 Metric and Hilbert spaces

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From playlist Machine Learning

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From playlist Virtual Conference

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From playlist Advances in Applied Probability 2019

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Ex: Order Integers from Least to Greatest

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From playlist Introduction to Integers

Related pages

Composition of relations | Countable set | Euclidean relation | If and only if | Subring | Symmetric relation | Categorical theory | Dyadic rational | Archimedean property | Algebraic number | Total order | Limit ordinal | Kripke semantics | Rational number | Idempotent relation | Back-and-forth method | Binary relation | Dense-in-itself | Transitive relation | Dense set | Quadratic irrational number | Reflexive relation | Mathematics | Set (mathematics) | Integer | Real number | Comparability | Order isomorphism