Ontology:Q819: Difference between revisions
copy fake Item from Ontology:Q800 |
ZFC set theory axioms |
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{{HueRoster|P=label (en)| {{Ontology:Q819}} }} | {{HueRoster|P=label (en)| {{Ontology:Q819}} }} | ||
{{HueClaim|P=alias (en)| Zermelo-Fraenkel Choice-axiom set theory (ZFC) | ZFC (set theory) }} | {{HueClaim|P=alias (en)| Zermelo-Fraenkel Choice-axiom set theory (ZFC) | ZFC (set theory) }} | ||
{{HueClaim|P=external identifier| - | {{HueClaim|P=external identifier| [https://en.wikipedia.org/wiki/Zermelo%E2%80%93Fraenkel_set_theory Zermelo-Fraenkel set theory] }} | ||
{{HueRoster|P={{Ontology:P3}}| {{Ontology:Q800}} }} <!-- en: sub-case of set theory --> | {{HueRoster|P={{Ontology:P3}}| {{Ontology:Q800}} }} <!-- en: sub-case of set theory --> | ||
{{HueRoster|P=case of| field of mathematics }} | {{HueRoster|P=case of| field of mathematics }} | ||
{{HueClaim|P=[[User:Reversedragon/FirstNineThousand|prototype]] notes| set theory where sets are "computational" and pointers into the set cause a kind of infinite loop bug in the logic }} | {{HueClaim|P=[[User:Reversedragon/FirstNineThousand|prototype]] notes| set theory where sets are "computational" and pointers into the set cause a kind of infinite loop bug in the logic }} | ||
</dl> | |||
=== Components === | |||
<dl class="wikitable hue"> | |||
{{HueRoster|P=model combines claims| [S2] Sets are collections of unique objects / Set cardinality measures a set's number of elements which are unique and partly defines the set }} | |||
{{HueRoster|P=model combines claims| [Z2] Sets are equal if they contain all of the same unique elements / axiom of extensionality }} | |||
{{HueRoster|P=model combines claims| [S2] Sets can contain other sets }} | |||
{{HueRoster|P=model combines claims| [S2] Sets cannot contain themselves / Every non-empty set contains a member which makes it not equivalent to itself / axiom of regularity }} | |||
{{HueRoster|P=model combines claims| [Z2] Every element in a set is a set / No element in a set is an atom (atomic data structure) }} | |||
{{HueRoster|P=model combines claims| [Z2] Any two sets can join into a greater set / For any two sets there can be a set containing them / axiom of pairing }} | |||
{{HueRoster|P=model combines claims| [S2] Any element in a set can represent the whole set / When constructing a new set out of one element from each set it does not matter which one is used / AC (axiom of choice) }} | |||
</dl> | </dl> | ||
Revision as of 04:28, 5 June 2025
Characteristics in draft
Properties
- item type
- Z (wiki feature; pronounced C) 1-1-1
- label (en)
- alias (en)
- Zermelo-Fraenkel Choice-axiom set theory (ZFC)
- ZFC (set theory)
- external identifier
- sub-case of [Item]
- set theory (top-level category) 1-1-1
- case of
- field of mathematics
- prototype notes
- set theory where sets are "computational" and pointers into the set cause a kind of infinite loop bug in the logic
Components
- model combines claims
- [S2] Sets are collections of unique objects / Set cardinality measures a set's number of elements which are unique and partly defines the set
- model combines claims
- [Z2] Sets are equal if they contain all of the same unique elements / axiom of extensionality
- model combines claims
- [S2] Sets can contain other sets
- model combines claims
- [S2] Sets cannot contain themselves / Every non-empty set contains a member which makes it not equivalent to itself / axiom of regularity
- model combines claims
- [Z2] Every element in a set is a set / No element in a set is an atom (atomic data structure)
- model combines claims
- [Z2] Any two sets can join into a greater set / For any two sets there can be a set containing them / axiom of pairing
- model combines claims
- [S2] Any element in a set can represent the whole set / When constructing a new set out of one element from each set it does not matter which one is used / AC (axiom of choice)
Wavebuilder combinations
- pronounced [P] pronounced Wavebuilder: forms result [Item]
- --
- along with [Item]
- --