Automatic sequence - Revision history

2001:980:D78E:1:B053:E121:5683:B334: /* Decimation */ corrected typo

2014-11-27T20:16:16Z

Decimation: corrected typo

← Older revision		Revision as of 22:16, 27 November 2014
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	Andera ~~is what you can call her but~~ she ~~by no means truly favored that name~~. ~~Since~~ I ~~was 18~~ I'~~ve been operating as a bookkeeper but [http://kjhkkb.net/xe/notice/374835 online psychic] soon~~ my ~~wife and I will [http://www~~.~~octionx.sinfauganda.co.ug/node/22469 love psychic readings] start our own company~~. ~~I've always loved residing~~ in ~~Kentucky~~ but ~~now I'm considering other options. To climb is something I really enjoy performing~~.<br><br>my web ~~page ... real psychics (~~[http://~~gcjcteam~~.~~org~~/~~index.php?mid=etc_video&document_srl=696611&sort_index=regdate&order_type=desc click the next internet page~~])		The author's title is Andera and she thinks it sounds quite good. I am truly fond of handwriting but I can't make it my occupation truly. Office supervising is what she does for a living. Her family life in Ohio but her spouse desires them to transfer.<br><br>My web blog: [http://chungmuroresidence.com/xe/reservation_branch2/152663 real psychics]

Salix alba: /* Properties */fix tags, replaced: ^{∗ → ^∗ (2) using AWB}

2014-02-28T19:24:41Z

Properties: fix tags, replaced: ∗ → ∗ (2) using AWB

← Older revision		Revision as of 21:24, 28 February 2014
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	~~{{Other uses\|Closure (disambiguation){{!}}Closure}}~~		Andera is what you can call her but she by no means truly favored that name. Since I was 18 I've been operating as a bookkeeper but [http://kjhkkb.net/xe/notice/374835 online psychic] soon my wife and I will [http://www.octionx.sinfauganda.co.ug/node/22469 love psychic readings] start our own company. I've always loved residing in Kentucky but now I'm considering other options. To climb is something I really enjoy performing.<br><br>my web page ... real psychics ([http://gcjcteam.org/index.php?mid=etc_video&document_srl=696611&sort_index=regdate&order_type=desc click the next internet page])

	~~'''Deductive closure'''~~ is ~~a [[property (philosophy)\|property]] of a [[set (mathematics)\|set]] of [[object (philosophy)\|objects]] (usually the objects in question are [[statement (logic)\|statement]]s)~~. ~~A [[set (mathematics)\|set]] of objects, <var>O</var>, is said to exhibit ''closure'' or to be~~ '~~'closed'' under~~ a ~~given~~ [~~[closure operator\|operation]], <var>R<~~/~~var>, provided that for every object, <var>x<~~/~~var>, if <var>x<~~/~~var> is a member of <var>O<~~/~~var>~~ and ~~<var>x<~~/~~var> is <var>R<~~/~~var>-related to any object, <var>y</var>, then <var>y</var> is a member of <var>O</var>~~.~~<ref>[[Peter D~~. ~~Klein]], ''Closure'', ''[[The Cambridge Dictionary of Philosophy]] (second edition)<~~/~~ref> In the context of statements, a deductive closure is the set of all the statements that can be [[Deductive reasoning\|deduced~~]~~] from a given set of statements~~.

	~~In [[propositional calculus\|propositional logic]], the set of all true propositions exhibits~~ ''~~'deductive closure''': if set <var>O</var>~~ is ~~the set of true propositions, and operation~~ <~~var~~>R<~~/var~~> is [~~[logical consequence]] (“<math>\vdash<~~/~~math>”), then provided that proposition <var>p</var> is a member of <var>O</var> and <var>p</var> is <var>R</var>-related to <var>q<~~/~~var> (i~~.~~e., p <math>\vdash<~~/~~math> q), <var>q</var> is also a member of <var>O</var>~~.

	== ~~Epistemic closure~~ ==
	~~{{main\|Epistemic closure}}~~

	In [[epistemology]], many philosophers have and continue to debate whether particular subsets of [[proposition]]s—especially ones ascribing [[knowledge]] or [[Theory of justification\|justification]] of a [[belief]] to a subject—are closed under deduction.

	~~==References==~~
	~~{{reflist}}~~

	~~[[Category:Concepts in logic]]~~
	~~[[Category:Deductive reasoning\|Closure]]~~
	~~[[Category:Logical consequence]]~~
	~~[[Category:Propositional calculus]]~~
	~~[[Category:Set theory]~~]

en>Gandalf61: /* Substitution point of view */ k is used as base in rest of article

2013-04-22T09:32:45Z

Substitution point of view: k is used as base in rest of article

← Older revision		Revision as of 11:32, 22 April 2013
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	~~Nice to satisfy you~~, ~~my title~~ is ~~Numbers Held though I don~~'~~t truly like becoming known as like~~ that~~. Hiring~~ is ~~his profession. One~~ of ~~the issues she loves most~~ is to ~~do aerobics and now she~~ is ~~trying to make money with it~~. ~~North Dakota~~ is ~~our beginning location~~.<br><br>~~Visit my blog post ::~~ [~~http:~~//~~www~~.~~youporn-nederlandse~~.~~com~~/~~user~~/~~CMidgett www~~.~~youporn-nederlandse~~.~~com~~]		{{Other uses\|Closure (disambiguation){{!}}Closure}}

			'''Deductive closure''' is a [[property (philosophy)\|property]] of a [[set (mathematics)\|set]] of [[object (philosophy)\|objects]] (usually the objects in question are [[statement (logic)\|statement]]s). A [[set (mathematics)\|set]] of objects, <var>O</var>, is said to exhibit ''closure'' or to be ''closed'' under a given [[closure operator\|operation]], <var>R</var>, provided that for every object, <var>x</var>, if <var>x</var> is a member of <var>O</var> and <var>x</var> is <var>R</var>-related to any object, <var>y</var>, then <var>y</var> is a member of <var>O</var>.<ref>[[Peter D. Klein]], ''Closure'', ''[[The Cambridge Dictionary of Philosophy]] (second edition)</ref> In the context of statements, a deductive closure is the set of all the statements that can be [[Deductive reasoning\|deduced]] from a given set of statements.

			In [[propositional calculus\|propositional logic]], the set of all true propositions exhibits '''deductive closure''': if set <var>O</var> is the set of true propositions, and operation <var>R</var> is [[logical consequence]] (“<math>\vdash</math>”), then provided that proposition <var>p</var> is a member of <var>O</var> and <var>p</var> is <var>R</var>-related to <var>q</var> (i.e., p <math>\vdash</math> q), <var>q</var> is also a member of <var>O</var>.

			== Epistemic closure ==
			{{main\|Epistemic closure}}

			In [[epistemology]], many philosophers have and continue to debate whether particular subsets of [[proposition]]s—especially ones ascribing [[knowledge]] or [[Theory of justification\|justification]] of a [[belief]] to a subject—are closed under deduction.

			==References==
			{{reflist}}

			[[Category:Concepts in logic]]
			[[Category:Deductive reasoning\|Closure]]
			[[Category:Logical consequence]]
			[[Category:Propositional calculus]]
			[[Category:Set theory]]

en>Braincricket: /* Examples */Typo fixing, typos fixed: , → , using AWB (8062)

2012-07-22T10:22:57Z

Examples: Typo fixing, typos fixed: , → , using AWB (8062)

New page

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Automatic sequence - Revision history

2001:980:D78E:1:B053:E121:5683:B334: /* Decimation */ corrected typo

Salix alba: /* Properties */fix tags, replaced: ∗ → ∗ (2) using AWB

en>Gandalf61: /* Substitution point of view */ k is used as base in rest of article

en>Braincricket: /* Examples */Typo fixing, typos fixed: , → , using AWB (8062)

Salix alba: /* Properties */fix tags, replaced: ^{∗ → ^∗ (2) using AWB}