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. In some academic articles and textbooks these terms are instead written as wellorder, wellordered, and wellordering or well order, well ordered, and well ordering.

Well-order - Wikipedia Jump to content From Wikipedia, the free encyclopedia Class of mathematical orderings Transitive binary relations v t e Symmetric Antisymmetric Connected Well-founded Has joins Has meets Reflexive Irreflexive Asymmetric Total, Semiconnex Anti- reflexive Equivalence relation Y ✗ ✗ ✗ ✗ ✗ Y ✗ ✗ Preorder (Quasiorder) ✗ ✗ ✗ ✗ ✗ ✗ Y ✗ ✗ Partial order ✗ Y ✗ ✗ ✗ ✗ Y ✗ ✗ Total preorder ✗ ✗ Y ✗ ✗ ✗ Y ✗ ✗ Total order ✗ Y Y ✗ ✗ ✗ Y ✗ ✗ Prewellordering ✗ ✗ Y Y ✗ ✗ Y ✗ ✗ Well-quasi-ordering ✗ ✗ ✗ Y ✗ ✗ Y ✗ ✗ Well-ordering ✗ Y Y Y ✗ ✗ Y ✗ ✗ Lattice ✗ Y ✗ ✗ Y Y Y ✗ ✗ Join-semilattice ✗

related reading

• Partially ordered seten.wikipedia.org
• Well-ordering theorem - Wikipediaen.wikipedia.org
• Ordinal number - Wikipediaen.wikipedia.org
• Set Theory > Basic Set Theory (Stanford Encyclopedia of Philosophy)plato.stanford.edu
• Zorn's lemma - Wikipediaen.wikipedia.org
• Schröder–Bernstein theorem - Wikipediaen.wikipedia.org
• First-order logic - Wikipediaen.wikipedia.org
• Ergodicity - Wikipediaen.wikipedia.org
• Arithmetical hierarchy - Wikipediaen.wikipedia.org
• Set Theory (Stanford Encyclopedia of Philosophy)plato.stanford.edu
• Type theory - Wikipediaen.wikipedia.org
• Well-defined expression - Wikipediaen.wikipedia.org