Lomer-Cottrell junction - Revision history

131.151.111.44 at 22:16, 21 February 2014

2014-02-21T22:16:08Z

← Older revision		Revision as of 00:16, 22 February 2014
Line 1:		Line 1:
	~~{{Other uses\|hierarchy (disambiguation)}}~~		Andrew Simcox is the title his mothers and fathers gave him and he totally [http://www.010-5260-5333.com/index.php?document_srl=1880&mid=board_ALMP66 certified psychics] enjoys this title. Office supervising is where my primary earnings comes from but I've usually wanted my psychic solutions by lynne ([http://myoceancounty.net/groups/apply-these-guidelines-when-gardening-and-grow/ myoceancounty.net]) personal company. For years she's been living in Kentucky but her spouse desires them to move. To play lacross is some thing I really enjoy performing.<br><br>Here is my blog post: psychics online - [http://alles-herunterladen.de/excellent-advice-for-picking-the-ideal-hobby/ alles-herunterladen.de],
	~~{{Unreferenced\|date=December 2007}}~~

	~~In [[mathematics]], a '''hierarchy'''~~ is ~~a set-theoretical object, consisting of a~~ [~~[preorder]] defined on a set~~. This is often referred to as an [[ordered set]], though that is an ambiguous term, which many authors reserve for [[partially ordered set \| partially ordered sets]] or [[totally ordered set \| totally ordered sets]]. ~~The term ''pre-ordered set'' is unambiguous, and is always synonymous with a mathematical hierarchy~~. ~~The term ''hierarchy'' is used to stress a ''[[hierarchical~~]~~]'' relation among the elements.~~

	~~Sometimes, a set comes equipped with a natural hierarchical structure~~. ~~For example, the set of natural numbers ''N''~~ is ~~equipped with a natural pre-order structure,~~ where ~~<math>n \le n~~'</~~math> whenever we can find some other number <math>m</math> so that <math>n + m = n'<~~/~~math>~~. ~~That is, <math>n'<~~/~~math> is bigger than <math>n<~~/~~math> only because we can get to <math>n'<~~/~~math> from <math>n</math>~~ '~~'using'' <math>m</math>~~. ~~This~~ is ~~true for any commutative monoid~~. ~~On the other hand, the set of integers ''Z'' requires a more sophisticated argument for its hierarchical structure, since we can always solve the equation~~ <~~math~~>~~n + m = n'</math> by writing <math>m = (n'-n)~~<~~/math~~>~~.{{Citation needed\|date=January 2013 \| text="The argument should be provided here in the text."}}~~

	~~A mathematical hierarchy (a pre-ordered set) should not be confused with the more general concept of a [[hierarchy]] in the social realm, particularly when one~~ is ~~constructing computational models which are used to describe real~~-~~world social, economic or political systems. These hierarchies, or [[complex networks]], are much too rich to be described in the category~~ [http://~~ncatlab~~.~~org~~/nlab/show/Set Set] of sets.<ref>We may need a bigger [[topos]].</ref> This is not just a pedantic claim; there are also mathematical hierarchies which are not describable using set theory.{{Citation needed\|date=January 2013}}

	Another natural hierarchy arises in [[computer science]], where the word refers to [[poset \|partially ordered sets]]s whose elements are [[class (set theory)\|classes]] of objects of increasing [[complexity]]. In that case, the preorder defining the hierarchy is the class-~~containment relation. [[Containment hierarchy\|Containment hierarchies]] are thus special cases of hierarchies.~~

	~~==Related terminology==~~
	Individual elements of a hierarchy are often called '''levels''' and a hierarchy is said to be infinite if it has infinitely many distinct levels but said to '''collapse''' if it has only finitely many distinct levels.

	~~==Example==~~
	~~In [[theoretical computer science]], the [[time hierarchy]] is a classification of [[decision problem]]s according to the amount of time required to solve them.~~

	~~==See also==~~
	~~{{col~~-~~begin}}~~
	~~{{col~~-~~break}}~~
	*[[Order theory]]
	*[[Tree structure]]
	*[[Lattice (mathematics)\|Lattice]]{{dn\|date=May 2012}}
	*[[Polynomial hierarchy]]
	*[[Chomsky hierarchy]]
	*[[Analytical hierarchy]]
	*[[Arithmetical hierarchy]]
	*[[Hyperarithmetical hierarchy]]

	~~{{col~~-~~break}}~~
	* [[Abstract algebraic hierarchy]]
	*[[Borel hierarchy]]
	*[[Wadge hierarchy]]
	*[[Difference hierarchy]]
	* [[Tree (data structure)]]
	* [[Tree (graph theory)]]
	* [[Tree network]]
	* [[Tree (descriptive set theory)]]
	* [[Tree (set theory)]]
	~~{{col~~-~~end}}~~

	~~== References ==~~
	~~<references~~ />

	~~[[Category:Hierarchy~~]]


	~~{{math-stub}}~~

en>Magioladitis: clean up, removed underlinked tag using AWB (9814)

2013-12-23T08:42:00Z

clean up, removed underlinked tag using AWB (9814)

← Older revision		Revision as of 10:42, 23 December 2013
Line 1:		Line 1:
	~~Hello~~, ~~my title~~ is ~~Andrew and my spouse doesn't like it at all~~. ~~Office supervising~~ is ~~exactly where her main earnings comes from but she's already applied~~ for ~~an additional one~~. ~~To play lacross~~ is ~~some thing he would by no means give up~~. ~~Her~~ [~~http:~~//~~myoceancounty~~.~~net~~/~~groups~~/~~apply-these-guidelines-when-gardening-and-grow~~/ ~~psychic phone] family clairvoyants ([http:~~//~~Www~~.~~Indosfriends~~.~~com~~/~~profile~~-~~253/info~~/ http://~~Www~~.~~Indosfriends.com~~/~~profile-253~~/~~info~~/]~~) members lives in Ohio but her spouse desires them to transfer~~.<br><br>~~Review my web site - tarot card readings~~ - [~~http://findyourflirt~~.~~net/index~~.~~php?m~~=~~member_profile&p~~=~~profile&id~~=~~117823 click~~ the ~~up coming post~~],		{{Other uses\|hierarchy (disambiguation)}}
			{{Unreferenced\|date=December 2007}}

			In [[mathematics]], a '''hierarchy''' is a set-theoretical object, consisting of a [[preorder]] defined on a set. This is often referred to as an [[ordered set]], though that is an ambiguous term, which many authors reserve for [[partially ordered set \| partially ordered sets]] or [[totally ordered set \| totally ordered sets]]. The term ''pre-ordered set'' is unambiguous, and is always synonymous with a mathematical hierarchy. The term ''hierarchy'' is used to stress a ''[[hierarchical]]'' relation among the elements.

			Sometimes, a set comes equipped with a natural hierarchical structure. For example, the set of natural numbers ''N'' is equipped with a natural pre-order structure, where <math>n \le n'</math> whenever we can find some other number <math>m</math> so that <math>n + m = n'</math>. That is, <math>n'</math> is bigger than <math>n</math> only because we can get to <math>n'</math> from <math>n</math> ''using'' <math>m</math>. This is true for any commutative monoid. On the other hand, the set of integers ''Z'' requires a more sophisticated argument for its hierarchical structure, since we can always solve the equation <math>n + m = n'</math> by writing <math>m = (n'-n)</math>.{{Citation needed\|date=January 2013 \| text="The argument should be provided here in the text."}}

			A mathematical hierarchy (a pre-ordered set) should not be confused with the more general concept of a [[hierarchy]] in the social realm, particularly when one is constructing computational models which are used to describe real-world social, economic or political systems. These hierarchies, or [[complex networks]], are much too rich to be described in the category [http://ncatlab.org/nlab/show/Set Set] of sets.<ref>We may need a bigger [[topos]].</ref> This is not just a pedantic claim; there are also mathematical hierarchies which are not describable using set theory.{{Citation needed\|date=January 2013}}

			Another natural hierarchy arises in [[computer science]], where the word refers to [[poset \|partially ordered sets]]s whose elements are [[class (set theory)\|classes]] of objects of increasing [[complexity]]. In that case, the preorder defining the hierarchy is the class-containment relation. [[Containment hierarchy\|Containment hierarchies]] are thus special cases of hierarchies.

			==Related terminology==
			Individual elements of a hierarchy are often called '''levels''' and a hierarchy is said to be infinite if it has infinitely many distinct levels but said to '''collapse''' if it has only finitely many distinct levels.

			==Example==
			In [[theoretical computer science]], the [[time hierarchy]] is a classification of [[decision problem]]s according to the amount of time required to solve them.

			==See also==
			{{col-begin}}
			{{col-break}}
			*[[Order theory]]
			*[[Tree structure]]
			*[[Lattice (mathematics)\|Lattice]]{{dn\|date=May 2012}}
			*[[Polynomial hierarchy]]
			*[[Chomsky hierarchy]]
			*[[Analytical hierarchy]]
			*[[Arithmetical hierarchy]]
			*[[Hyperarithmetical hierarchy]]

			{{col-break}}
			* [[Abstract algebraic hierarchy]]
			*[[Borel hierarchy]]
			*[[Wadge hierarchy]]
			*[[Difference hierarchy]]
			* [[Tree (data structure)]]
			* [[Tree (graph theory)]]
			* [[Tree network]]
			* [[Tree (descriptive set theory)]]
			* [[Tree (set theory)]]
			{{col-end}}

			== References ==
			<references />

			[[Category:Hierarchy]]


			{{math-stub}}

106.190.49.104 at 07:47, 26 June 2012

2012-06-26T07:47:25Z

New page

Hello, my title is Andrew and my spouse doesn't like it at all. Office supervising is exactly where her main earnings comes from but she's already applied for an additional one. To play lacross is some thing he would by no means give up. Her [http://myoceancounty.net/groups/apply-these-guidelines-when-gardening-and-grow/ psychic phone] family clairvoyants ([http://Www.Indosfriends.com/profile-253/info/ http://Www.Indosfriends.com/profile-253/info/]) members lives in Ohio but her spouse desires them to transfer.<br><br>Review my web site - tarot card readings - [http://findyourflirt.net/index.php?m=member_profile&p=profile&id=117823 click the up coming post],