Trix (technical analysis) - Revision history

en>InedibleHulk: This article about sums up him up, I'd wager. If not, someone will see to it later.

2014-10-31T06:40:28Z

This article about sums up him up, I'd wager. If not, someone will see to it later.

← Older revision		Revision as of 08:40, 31 October 2014
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	~~{{distinguish\|Ring (mathematics)}}~~		Irwin Butts at home std test is what my spouse loves to contact [http://xrambo.com/blog/191590 over the counter std test] me although I don't really like becoming known as like that. North Dakota is our birth location. One of the [http://Ehealthforum.com/health/sore-throat-after-oral-sex-t138861.html extremely] best things in the globe for him is [http://hsmlibrary.dothome.co.kr/xe/board_koQG15/407574 at home std test] over the counter std test to collect badges but he is struggling to std testing at home discover time for it. He used to be unemployed but now he is a meter reader.<br><br>Have a look at my web blog: [http://www.eyelevelfederalway.com/xe/index.php?mid=Promotions&page=1&document_srl=571267 http://www.eyelevelfederalway.com/xe/index.php?mid=Promotions&page=1&document_srl=571267]
	In [~~[mathematics]~~]~~, there are two different notions of a~~ '~~''ring of sets''', both referring to certain families of sets~~.
	~~In [[order theory]], a nonempty [[family of sets]] <math>\mathcal{R}</math>~~ is ~~called a '''ring (~~of ~~sets)''' if it is~~ [~~[closure (mathematics)\|closed]] under [[intersection (set theory)\|intersection]] and [[union (set theory)\|union]]. That is, for any <math>A,B\in\mathcal{R}<~~/~~math>,~~
	~~#<math>A \cap B \in \mathcal{R}<~~/~~math> and~~
	~~#<math>A \cup B \in \mathcal{R}~~.</~~math><ref name="b37">{{citation~~
	~~\| last = Birkhoff \| first = Garrett \| authorlink = Garrett Birkhoff~~
	~~\| doi = 10.1215~~/~~S0012~~-~~7094~~-37-~~00334~~-X
	~~\| issue = 3~~
	~~\| journal = Duke Mathematical Journal~~
	~~\| mr = 1546000~~
	~~\| pages = 443–454~~
	~~\| title = Rings of sets~~
	~~\| volume = 3~~
	~~\| year = 1937}}~~.~~</ref>~~

	~~In [[measure theory~~]~~], a ring of sets~~ is ~~instead a family closed under unions and~~ [~~[set-theoretic difference]]s~~.~~<ref>{{citation\|title=Measure Theory and Integration\|first=Gar\|last=De Barra\|publisher=Horwood Publishing\|year= 2003\|isbn=9781904275046\|page=13}}~~.~~</ref> That is, it obeys the two properties~~
	~~#<math>A \setminus B \in \mathcal{R}<~~/~~math> and~~
	~~#<math>A \cup B \in \mathcal{R}.<~~/~~math>~~
	~~This implies that it is also closed under intersections, because of the identity~~
	~~:<math>A\cap B=A\setminus(A\setminus B),<~~/~~math>~~
	~~however, a family of sets that is closed under unions and intersections might not be closed under differences.~~

	~~==Examples==~~
	~~If ''X'' is any set, then the [[power set]] of ''X'' (the family of all subsets of ''X'') forms a ring of sets in either sense.~~

	~~If (''X'',≤) is a [[partially ordered set]], then its [[upper set~~]~~]s (the subsets of ''X'' with~~ the ~~additional property that if ''x'' belongs~~ to ~~an upper set ''U'' and ''x'' ≤ ''y'', then ''y'' must also belong~~ to ~~''U'') is closed under both intersections and unions~~. ~~However, in general it will not~~ be ~~closed under differences of sets.~~

	~~The [[open set]]s and [[closed set]]s of any [[topological space]] are closed under both unions and intersections~~.<~~ref name="b37"/~~>

	~~If ''T'' is any transformation of a space, then the sets that are mapped into themselves by ''T'' are closed under both unions and intersections.~~<~~ref name="b37"/~~>

	~~If two rings of sets are both defined on the same elements, then the sets that belong to both rings themselves form~~ a ~~ring of sets~~.~~<ref name="b37"~~/>

	==~~Related structures~~==
	~~A ring of sets (in the order-theoretic sense) forms a [[distributive lattice]] in which the intersection and union operations correspond to the lattice's meet and join operations, respectively~~. Conversely, every distributive lattice is isomorphic to a ring of sets; in the case of [[finite set\|finite]] distributive lattices, this is [[Birkhoff's representation theorem]] and the sets may be taken as the lower sets of a partially ordered set.~~<ref name="b37"~~/~~> Every [[field of sets]] and so also any [[σ-algebra]] also is a ring of sets~~.

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

	~~{{DEFAULTSORT:Ring Of Sets}}~~
	~~[[Category:Set families]~~]

en>Addbot: Bot: Migrating 1 interwiki links, now provided by Wikidata on d:q4051794

2013-03-14T16:12:32Z

Bot: Migrating 1 interwiki links, now provided by Wikidata on d:q4051794

← Older revision		Revision as of 18:12, 14 March 2013
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	~~Let me first begin by at home std testing introducing myself~~. ~~My title~~ ~~home [http:~~//~~allwomenstalk~~.~~com~~/7-~~hottest~~-~~celebrities~~-~~reportedly~~-~~infected~~-~~with-stds std test~~] ~~kit~~ is ~~Boyd Butts even though~~ it ~~is not~~ the ~~name on my birth certification~~. ~~One~~ of the ~~extremely very [http~~:/~~/dateplate~~.~~com/dayzfe get redirected here~~] ~~best things~~ in the ~~globe for me is~~ to ~~do aerobics~~ and ~~now I~~'~~m attempting~~ to ~~earn money with~~ it. ~~He used~~ [~~http:~~/~~/payiz~~.az/~~index~~.~~php?do~~=/~~profile~~-~~14379/info/ over~~ the ~~counter std test~~] to be ~~unemployed but now he is~~ a ~~computer operator but his marketing by no means arrives. Years ago we moved to North Dakota~~.<br>~~<br>Here~~ is ~~my weblog ..~~. [~~http~~:~~//chorokdeul.co.kr/index.php?document_srl=454418&mid=customer21 chorokdeul.co.kr~~]		{{distinguish\|Ring (mathematics)}}
			In [[mathematics]], there are two different notions of a '''ring of sets''', both referring to certain families of sets.
			In [[order theory]], a nonempty [[family of sets]] <math>\mathcal{R}</math> is called a '''ring (of sets)''' if it is [[closure (mathematics)\|closed]] under [[intersection (set theory)\|intersection]] and [[union (set theory)\|union]]. That is, for any <math>A,B\in\mathcal{R}</math>,
			#<math>A \cap B \in \mathcal{R}</math> and
			#<math>A \cup B \in \mathcal{R}.</math><ref name="b37">{{citation
			\| last = Birkhoff \| first = Garrett \| authorlink = Garrett Birkhoff
			\| doi = 10.1215/S0012-7094-37-00334-X
			\| issue = 3
			\| journal = Duke Mathematical Journal
			\| mr = 1546000
			\| pages = 443–454
			\| title = Rings of sets
			\| volume = 3
			\| year = 1937}}.</ref>

			In [[measure theory]], a ring of sets is instead a family closed under unions and [[set-theoretic difference]]s.<ref>{{citation\|title=Measure Theory and Integration\|first=Gar\|last=De Barra\|publisher=Horwood Publishing\|year= 2003\|isbn=9781904275046\|page=13}}.</ref> That is, it obeys the two properties
			#<math>A \setminus B \in \mathcal{R}</math> and
			#<math>A \cup B \in \mathcal{R}.</math>
			This implies that it is also closed under intersections, because of the identity
			:<math>A\cap B=A\setminus(A\setminus B),</math>
			however, a family of sets that is closed under unions and intersections might not be closed under differences.

			==Examples==
			If ''X'' is any set, then the [[power set]] of ''X'' (the family of all subsets of ''X'') forms a ring of sets in either sense.

			If (''X'',≤) is a [[partially ordered set]], then its [[upper set]]s (the subsets of ''X'' with the additional property that if ''x'' belongs to an upper set ''U'' and ''x'' ≤ ''y'', then ''y'' must also belong to ''U'') is closed under both intersections and unions. However, in general it will not be closed under differences of sets.

			The [[open set]]s and [[closed set]]s of any [[topological space]] are closed under both unions and intersections.<ref name="b37"/>

			If ''T'' is any transformation of a space, then the sets that are mapped into themselves by ''T'' are closed under both unions and intersections.<ref name="b37"/>

			If two rings of sets are both defined on the same elements, then the sets that belong to both rings themselves form a ring of sets.<ref name="b37"/>

			==Related structures==
			A ring of sets (in the order-theoretic sense) forms a [[distributive lattice]] in which the intersection and union operations correspond to the lattice's meet and join operations, respectively. Conversely, every distributive lattice is isomorphic to a ring of sets; in the case of [[finite set\|finite]] distributive lattices, this is [[Birkhoff's representation theorem]] and the sets may be taken as the lower sets of a partially ordered set.<ref name="b37"/> Every [[field of sets]] and so also any [[σ-algebra]] also is a ring of sets.

			==References==
			{{reflist}}

			{{DEFAULTSORT:Ring Of Sets}}
			[[Category:Set families]]

en>Krassotkin: ru:Trix

2012-05-20T18:53:29Z

ru:Trix

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