Statements (18)
| Predicate | Object |
|---|---|
| gptkbp:instanceOf |
Mathematical axiom
|
| gptkbp:category |
Axiom of set theory
|
| gptkbp:compatibleWith |
gptkb:Constructivist_mathematicians
|
| gptkbp:controversy |
Non-constructive nature
|
| gptkbp:equivalentTo |
gptkb:Well-ordering_theorem
gptkb:Zorn's_lemma |
| gptkbp:field |
gptkb:Set_theory
|
| https://www.w3.org/2000/01/rdf-schema#label |
Axiom of choice
|
| gptkbp:includedIn |
gptkb:Zermelo–Fraenkel_set_theory_with_choice_(ZFC)
|
| gptkbp:introduced |
gptkb:Ernst_Zermelo
|
| gptkbp:introducedIn |
1904
|
| gptkbp:state |
Given any collection of nonempty sets, there exists a choice function selecting one element from each set
|
| gptkbp:symbol |
gptkb:AC
|
| gptkbp:usedIn |
gptkb:Banach–Tarski_paradox
gptkb:Hahn–Banach_theorem gptkb:Tychonoff's_theorem |
| gptkbp:bfsParent |
gptkb:logic
|
| gptkbp:bfsLayer |
4
|