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Well-order

In mathematics, a well-order (or well-ordering or well-order relation) on a set S is a total ordering on S with the property that every non-empty subset of S has a least element in this ordering. The set S together with the ordering is then called a well-ordered set (or woset). In some academic articles and textbooks these terms are instead written as…

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Overview

Examples and counterexamples

Equivalent formulations

Initial segments

Order topology

Ordinal numbers

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Map overview Semantic statistics

Well-order

Nodes61
Edges60
Triples48
Avg. degree1.97
Density0.032787
Components1

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Well-order

Top relations

related to References · 21
Well-order → Cambridge University Press, Halmos, ISBN, January, Mathematics, May, Naive, New York, NJ, Notes, Paul, Practical Foundations, Princeton, Reprinted, Springer-Verlag, Tao, Taylor, Van Nostrand Company, Well-ordered, What's
related to Reals · 10
Well-order → All, An, And, For, However, In, Since, Suppose, The, ZFC
related to Ordinal numbers · 8
Well-order → Counting, Every, For, In, Natural, Note, The, Thus
related to Rational numbers · 4
Well-order → However, Other, The, There
related to Initial segments · 3
Well-order → An, By, For
related to Order topology · 2
Well-order → Every, With

Important terminology Word statistics

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Important terminology

set well ordering well-ordered order element every numbers initial subset displaystyle least ordinal number natural type elements ordered also example

Entity relationships Subject–Predicate–Object triples

SubjectPredicateObjectConfidenceSrc
Well-orderrelated to Initial segmentsAn0.60section
Well-orderrelated to Initial segmentsBy0.60section
Well-orderrelated to Initial segmentsFor0.60section
Well-orderrelated to Order topologyEvery0.60section
Well-orderrelated to Order topologyWith0.60section
Well-orderrelated to Ordinal numbersEvery0.60section
Well-orderrelated to Ordinal numbersThe0.60section
Well-orderrelated to Ordinal numbersIn0.60section
Well-orderrelated to Ordinal numbersCounting0.60section
Well-orderrelated to Ordinal numbersNote0.60section
Well-orderrelated to Ordinal numbersThus0.60section
Well-orderrelated to Ordinal numbersFor0.60section

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    Min side: 3
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