well-ordering
Least-element property ordering
Well-ordering is a mathematical property of a set: every nonempty subset has a least element.
The natural numbers are well-ordered under their usual ordering—any collection of them contains a smallest.
The real numbers are not well-ordered, since an interval like (0,1) has no minimum.
The well-ordering principle states that any set can be well-ordered, a claim equivalent to the axiom of choice.
Self-evident starting principle
- choiceAct of selecting
- cardinalitySize of a set
- CantorSet theory founder
- successorOne who replaces another
totality · comparability · subset · chain · enumeration · trichotomy · foundation · countable
Ranked authority structure
- latticeOpenwork of crossed strips
- transitivityRelation that chains through
- reflexivityQuality of self-reference
- chainLinked segments forming length
embedding · isomorphism · monotone · bounded
Formal admission process
- recursionProcess invoking itself
- descentDownward slope or lineage
- terminationAct of ending something
axiom
Self-evident starting principle
- choiceAct of selecting
- cardinalitySize of a set
- CantorSet theory founder
successor · totality · comparability · subset · chain · enumeration · trichotomy · foundation · countable
hierarchy
Ranked authority structure
- latticeOpenwork of crossed strips
- transitivityRelation that chains through
- reflexivityQuality of self-reference
chain · embedding · isomorphism · monotone · bounded
induction
Formal admission process
- recursionProcess invoking itself
- descentDownward slope or lineage
- terminationAct of ending something
- relationsrelation, relationship, equivalence relation, connection, link
- set theorysets, set, subset, superset, empty set
- order theorylattice, upper bound, lower bound, comparable, incomparable
- orderingsranking
- Math RulesPythagorean theorem, distributive property, commutative property, associative property, product rule
- ordinalsfirst, second, third, fourth, fifth