Ontology:Q819 - Revision history

Reversedragon: "not my president"

2025-06-05T05:29:20Z

"not my president"

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	== Usage notes ==		== Usage notes ==

	Set theory axioms have much more wide-ranging implications than anybody would immediately think of. For instance, the axiom of choice: what happens if we apply the axiom of choice to people? We get something that looks roughly like [[redlink - Q?? Liberalism\|Liberal-republicanism]]. But centuries of history have shown there to be problems with this concept. For one, if a group of people is relatively stable, it is still possible for somebody to be sent as a representative that a lot of people feel doesn't represent them. For another, if the boundaries of groups of people are rapidly changing due to changing ideologies or any other reason, there will be arguments over where voting districts should be drawn — whether people who are sorting into different groups should be in the same district or different districts, how many parties votes should be potentially nominating, how many parties should be represented in parliament, how many parties should be competing for president if applicable. Any debate about gerrymandering ultimately comes down to an argument about what sets accurately contain what people and what sets of people can safely apply the axiom of choice in order to treat broad groups of people as one person.		Set theory axioms have much more wide-ranging implications than anybody would immediately think of. For instance, the axiom of choice: what happens if we apply the axiom of choice to people? We get something that looks roughly like [[redlink - Q?? Liberalism\|Liberal-republicanism]]. But centuries of history have shown there to be problems with this concept. For one, if a group of people is relatively stable, it is still possible for somebody to be sent as a representative that a lot of people feel [[redlink - Q?? not my president\|doesn't represent them]]. For another, if the boundaries of groups of people are rapidly changing due to changing ideologies or any other reason, there will be arguments over where voting districts should be drawn — whether people who are sorting into different groups should be in the same district or different districts, how many parties votes should be potentially nominating, how many parties should be represented in parliament, how many parties should be competing for president if applicable. Any debate about gerrymandering ultimately comes down to an argument about what sets accurately contain what people and what sets of people can safely apply the axiom of choice in order to treat broad groups of people as one person.

	Studying the axioms of ZFC set theory and which axioms truly make sense in the physical world has very important implications for reforming or replacing Liberal-republicanism.		Studying the axioms of ZFC set theory and which axioms truly make sense in the physical world has very important implications for reforming or replacing Liberal-republicanism.

Reversedragon: implications of set theory in real life

2025-06-05T05:28:13Z

implications of set theory in real life

← Older revision		Revision as of 05:28, 5 June 2025
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	</dl>		</dl>

	=== Wavebuilder combinations ===		== Wavebuilder combinations ==

	<dl class="wikitable hue data_wavebuild">		<dl class="wikitable hue data_wavebuild">
	{{WaveBuildNone\| -- \| -- }} <!-- en: WITH ?? PRODUCES ?? -->		{{WaveBuildNone\| -- \| -- }} <!-- en: WITH ?? PRODUCES ?? -->
	</dl>		</dl>

			== Usage notes ==

			Set theory axioms have much more wide-ranging implications than anybody would immediately think of. For instance, the axiom of choice: what happens if we apply the axiom of choice to people? We get something that looks roughly like [[redlink - Q?? Liberalism\|Liberal-republicanism]]. But centuries of history have shown there to be problems with this concept. For one, if a group of people is relatively stable, it is still possible for somebody to be sent as a representative that a lot of people feel doesn't represent them. For another, if the boundaries of groups of people are rapidly changing due to changing ideologies or any other reason, there will be arguments over where voting districts should be drawn — whether people who are sorting into different groups should be in the same district or different districts, how many parties votes should be potentially nominating, how many parties should be represented in parliament, how many parties should be competing for president if applicable. Any debate about gerrymandering ultimately comes down to an argument about what sets accurately contain what people and what sets of people can safely apply the axiom of choice in order to treat broad groups of people as one person.

			Studying the axioms of ZFC set theory and which axioms truly make sense in the physical world has very important implications for reforming or replacing Liberal-republicanism.


	[[Category:Set theory ontology]]		[[Category:Set theory ontology]]

Reversedragon: link

2025-06-05T04:58:36Z

link

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	{{HueCSS}}<ol class="hue clean compound"><li>		{{HueCSS}}<ol class="hue clean compound"><li>
	<onlyinclude><dfn class="field_geo" data-dimension="Z" data-qid="819" data-field="set theory" data-object="ZFC set theory" data-note="" data-lexeme="">[[Ontology:~~Q800~~\|ZFC set theory]]<ins class="field"></ins>{{WaveScore\|sum=1\|quilt=1\|ply=1}}</dfn></onlyinclude>		<onlyinclude><dfn class="field_geo" data-dimension="Z" data-qid="819" data-field="set theory" data-object="ZFC set theory" data-note="" data-lexeme="">[[Ontology:Q819\|ZFC set theory]]<ins class="field"></ins>{{WaveScore\|sum=1\|quilt=1\|ply=1}}</dfn></onlyinclude>
	</li></ol><!-- change summary: copy fake Item from [[Special:PermanentLink/NNNN\|Ontology:Q800]] --> __NOTOC__		</li></ol><!-- change summary: copy fake Item from [[Special:PermanentLink/NNNN\|Ontology:Q800]] --> __NOTOC__

Reversedragon: ZFC set theory axioms

2025-06-05T04:28:57Z

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>

Reversedragon: copy fake Item from Ontology:Q800

2025-06-05T02:44:11Z

copy fake Item from Ontology:Q800

New page

{{HueCSS}}<ol class="hue clean compound"><li>
<onlyinclude><dfn class="field_geo" data-dimension="Z" data-qid="819" data-field="set theory" data-object="ZFC set theory" data-note="" data-lexeme="">[[Ontology:Q800|ZFC set theory]]<ins class="field"></ins>{{WaveScore|sum=1|quilt=1|ply=1}}</dfn></onlyinclude>
</li></ol> __NOTOC__

== Characteristics in draft ==

=== Properties ===

<dl class="wikitable hue">
{{HueClaim|P=item type| {{Template:Z1}} }}
{{HueRoster|P=label (en)| {{Ontology:Q819}} }}
{{HueClaim|P=alias (en)| Zermelo-Fraenkel Choice-axiom set theory (ZFC) | ZFC (set theory) }}
{{HueClaim|P=external identifier| -- }}
{{HueRoster|P={{Ontology:P3}}| {{Ontology:Q800}} }} 
{{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 }}
</dl>

=== Wavebuilder combinations ===

<dl class="wikitable hue data_wavebuild">
{{WaveBuildNone| -- | -- }} 
</dl>

[[Category:Set theory ontology]]