Wave power - Revision history

en>Rfassbind: /* List of devices */ added company website to table entry "Sea Power (company)"

2015-01-03T23:11:12Z

List of devices: added company website to table entry "Sea Power (company)"

← Older revision		Revision as of 01:11, 4 January 2015
Line 1:		Line 1:
	~~Let me first start by introducing myself~~. ~~My name is Boyd Butts even though~~ it is not the ~~name~~ on ~~my beginning certificate~~. ~~South Dakota~~ is ~~her beginning place but she requirements~~ to ~~move simply because~~ of ~~her family~~. ~~Body developing~~ is ~~what my~~ family ~~members and I appreciate~~. ~~Hiring is his occupation~~.<br><br>~~My webpage; healthy food delivery;~~ [http://~~nnx~~.~~me/weightlossfoodprograms67803 why not look here~~],

			Games can give you a trustworthy universe of experience, calmness and exhilaration. You may learn, get a good sense of success or since enjoy beating down this bad-guy. No matter form of video gaming you are into, are often the helpful tips in such post to give for yourself more fun whenever you and your family play your next sport Website.<br><br>Beginning nearly enough gems to get another local building company. Don''t waste plenty of of the gems throughout any way on rush-building anything, as if it can save you them you are going to actually eventually obtain enough for free extra gems to generate that extra builder not having cost. Particularly, customers can get free stones for clearing obstructions for example , rocks and trees, after you clear them outside they come back in addition to you may re-clear the parties to get more gems.<br><br>Lots of people which play clash of clans are seeking ways of getting 100 percent free gems. The gems are very important because they give the player the features and the power increase their gaming experience. As opposed to added equivalent games in mobile phones websites, especially those where individuals use various cracks in buy to achieve these practical information on free, the nature involved with [http://Mondediplo.com/spip.php?page=recherche&recherche=farmville farmville] and its layout does not enable any varieties of hacks that you can put to the mission. Everyone is always looking for ways for you to get free gems at clash of clans nevertheless the most important thing carry out is to employ a great venue to earn these males for free, save these kind of suitably and use they will where necessary.<br><br>In the first instance clash of clans hack into tool no survey encourages believe in among the people. Society is almost certainly definitely powered by look pressure, one of the type of most powerful forces on a the planet. Whenever long as [https://Www.Gov.uk/search?q=peer+demands peer demands] utilizes its power to gain good, clash of clans hack tool no survey will have its space in community.<br><br>Whether you're looking Conflict of The entire family Jewels Free, or may well just buying a Skimp Conflict of Tribes, currently has the smartest choice on your internet, absolutely free as well as only takes a matter of minutes to get all many.<br><br>So that you can access it into excel, copy-paste this continued medicine into corpuscle B1. If you again access an majority of energy in abnormal in corpuscle A1, the bulk in treasures will arise in B1.<br><br>Bide time until game of the yr versions of major title of the article. These often come out a spring or maybe more at the original title, but are made lots of the down loadable and extra content this was released in stages had been first title. If you have any concerns with regards to where and how to use [http://circuspartypanama.com clash of clans hack no survey or password], you can speak to us at our own website. Some games offer a much more bang for the dollar.

en>E8: Reverted good faith edits by 82.230.144.140 (talk): Restoring - discuss changes (TALK already has lengthy discussion of this formula). (TW)

2014-02-12T02:23:03Z

Reverted good faith edits by 82.230.144.140 (talk): Restoring - discuss changes (TALK already has lengthy discussion of this formula). (TW)

← Older revision		Revision as of 04:23, 12 February 2014
Line 1:		Line 1:
	~~In [[order theory\|mathematical order theory]], an '''order-embedding'''~~ is ~~a special kind of [[monotone function]], which provides a way to include one [[partially ordered set]] into another. Like [[Galois connection]]s, order-embeddings constitute a notion which~~ is ~~strictly weaker than~~ the ~~concept of an [[order isomorphism]]~~. ~~Both~~ of ~~these weakenings may be understood in terms of [[category theory]]~~.		Let me first start by introducing myself. My name is Boyd Butts even though it is not the name on my beginning certificate. South Dakota is her beginning place but she requirements to move simply because of her family. Body developing is what my family members and I appreciate. Hiring is his occupation.<br><br>My webpage; healthy food delivery; [http://nnx.me/weightlossfoodprograms67803 why not look here],

	~~== Formal definition ==~~
	~~Formally, given two partially ordered sets (''S'', ≤) and (''T'', ≤), a function ''f'': ''S'' → ''T'' is an ''order-embedding'' if ''f''~~ is ~~both [[order-preserving]] and [[order-reflecting]], i.e. for all ''x'' and ''y'' in ''S'', one has~~

	~~: <math>x\leq y \text{ if~~ and ~~only if } f(x)\leq f(y).</math><ref name="dp02">{{citation~~
	~~\| last1 = Davey \| first1 = B. A.~~
	~~\| last2 = Priestley \| first2 = H~~. A.
	~~\| contribution = Maps between ordered sets~~
	~~\| edition = 2nd~~
	~~\| isbn = 0-521-78451-4~~
	~~\| location = New York~~
	~~\| mr = 1902334~~
	~~\| pages = 23–24~~
	~~\| publisher = Cambridge University Press~~
	~~\| title = Introduction to Lattices and Order~~
	~~\| url = http://books.google.com/books?id=vVVTxeuiyvQC&pg=PA23~~
	~~\| year = 2002}}.</ref>~~

	~~Note that such a function~~ is ~~necessarily [[injective]], since ''f''(''x'') = ''f''(''y'') implies ''x'' ≤ ''y'' and ''y'' ≤ ''x''~~.<~~ref name="dp02"/~~> ~~If an order-embedding between two posets ''S'' and ''T'' exists, one says that ''S'' can be embedded into ''T''.~~

	~~== Properties ==~~

	An order isomorphism can be characterized as a [[surjective]] order-embedding. As a consequence, any order-embedding ''f'' restricts to an isomorphism between its [[domain (mathematics)\|domain]] ''S'' and its [[range (mathematics)\|range]] ''f''(''S''), which justifies the term "embedding".<~~ref name="dp02"/~~> On the other hand, it might well be that two (necessarily infinite) posets are mutually embeddable into each other without being isomorphic. An example is provided by the set of [[real number]]s and its [[interval (mathematics)\|interval]] [−~~1,1]. Ordering both sets in the natural way, one clearly finds that [&minus~~;~~1,1] can be embedded into the reals. On the other hand, one can define a function ''e'' from the real numbers to~~ [−1,1] as<ref>For a very similar example using arctan to order-embed the real numbers into an interval, see {{citation\|title=Discovering Modern Set Theory: The basics\|volume=8\|series=Fields Institute Monographs\|first1=Winfried\|last1=Just\|first2=Martin\|last2=Weese\|publisher=American Mathematical Society\|year=1996\|isbn=9780821872475\|page=21\|url=http://~~books.google.com/books?id=TPvHr7fcvHoC&pg=PA21}}.</ref>~~

	~~: <math>e(x) = \frac{2}{\pi}\arctan x</math>~~

	This is the projection of the real number line to (half of) the circle with circumference 4 (see [[trigonometric function]]s for details) and embeds the reals into [−1,1]. Yet, the two posets are not isomorphic: [−1,1] has both a [[least element\|least]] and a [[greatest element]], which are not present in the case of the real numbers. This shows that an isomorphism cannot exist.

	~~In a retract (a pair of order-preserving maps whose composition is the identity), the first of the two maps (called a coretraction) must be an order-embedding.<ref>{{citation~~
	~~\| last1 = Duffus \| first1 = Dwight~~
	~~\| last2 = Laflamme \| first2 = Claude~~
	~~\| last3 = Pouzet \| first3 = Maurice~~
	~~\| arxiv = math/0612458~~
	~~\| doi = 10.1007/s00012-008-2125-6~~
	~~\| issue = 1-2~~
	~~\| journal = Algebra Universalis~~
	~~\| mr = 2453498~~
	~~\| pages = 243–255~~
	~~\| title = Retracts of posets: the chain-gap property and the selection property are independent~~
	~~\| volume = 59~~
	~~\| year = 2008}}~~.</~~ref> However,~~ not every order-embedding is a coretraction. As a trivial example of this phenomenon, the unique order embedding from the empty poset to a nonempty poset ''P'' has no retract, because there is no order-preserving map from ''P'' to the empty poset. More illustratively, consider the "diamond poset" with elements {00, 01, 10, 11} with 00 < 01 < 11, 00 < 10 < 11 and 01 incomparable to 10. Consider the embedded sub-poset "V" consisting of {00, 01, 10} (with 00 < 01 and 00 < 10 and 01 incomparable to 10). A retract of the embedding V -> diamond would need to send 11 to somewhere in "V" above both 01 and 10, but there is no such place.

	~~== Additional Perspectives ==~~
	~~{{unreferenced section\|date=October 2013}}~~
	~~Posets can straightforwardly be viewed from many perspectives, and order embeddings are basic enough that they tend to be visible from everywhere. For example:~~
	* (Model theoretically) A poset is a set equipped with a (reflexive, antisymmetric, transitive) binary relation. An order embedding A -> B is an isomorphism from A to an [[elementary substructure]~~] of B.~~
	* (Graph theoretically) A poset is a (transitive, ~~acyclic, directed, reflexive) graph. An order embedding A -> B is a [[graph isomorphism]] from A to an [[induced subgraph]] of B.~~
	* (Category theoretically) A poset is a (small, skeletal) category such that each homset has at most one element. An order embedding A -> B is a full and faithful functor from A to B which is injective on objects, or equivalently an isomorphism from A to a [[full subcategory]] of B.

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

	~~[[Category:Order theory]]~~

en>Crowsnest: "Wave energy is the transport of energy ..." makes no sense and does not reflect the title of the article

2014-02-03T15:33:59Z

"Wave energy is the transport of energy ..." makes no sense and does not reflect the title of the article

← Older revision		Revision as of 17:33, 3 February 2014
Line 1:		Line 1:
	~~Today I am sharing~~ a ~~dark experience with we as I am from this darkness now~~. ~~Whoa! Google Chrome has crashed was~~ the ~~disaster that struck on me early this morning~~. ~~My blood flow appeared to stop for a few minutes. Then I regained my senses plus decided to fix Chrome crash.<br><br>Another solution will~~ be ~~to provide the computer system with a new msvcr71 file~~. ~~Frequently~~, ~~once the file has been corrupted or damaged~~, ~~it might no longer be able to~~ function ~~like it did before so it~~'~~s only natural to substitute the file~~. ~~Simply download another msvcr71~~.~~dll file from the internet. Frequently~~, ~~the file comes in a zip formatting. Extract the files within the zip folder plus place them accordingly inside this location: C~~:\~~Windows~~\~~System32~~. ~~Afterward, re-register the file. Click Start plus then choose Run. When the Run window appears, type~~ "~~cmd~~". ~~Press Enter and then type "regsvr32 -u msvcr71~~.~~dll" followed by "regsvr32 msvcr71~~.~~dll"~~. Press ~~Enter again plus the file ought~~ to ~~be registered accordingly~~.<br><br>So, ~~this advanced dual scan is not merely among the greater, yet it is additionally freeware~~. ~~And~~ as ~~of all of this that numerous regard CCleaner one of~~ the ~~greater registry products inside the market now~~. ~~I would add that I personally prefer Regcure for~~ the ~~simple reason which~~ it ~~has a better interface plus I learn for a truth~~ that ~~it is ad-ware~~ without ~~charge~~.~~<br><br>Check a Windows taskbar, which~~ is ~~found on~~ the ~~lower proper hand corner~~ of ~~the computer screen~~. ~~This taskbar consist of programs you have running~~ in the ~~background~~. ~~If you have too numerous of them~~, ~~they usually take~~ a ~~computer~~'~~s resources.~~<br>~~<br>So to fix this, we simply have~~ to ~~be able to create all registry files non~~-~~corrupted again. This can dramatically speed up~~ the ~~loading time of your computer and will allow you to do a big amount of details on it again. And fixing these files couldn't be simpler - we really should employ a tool called a [~~http://~~bestregistrycleanerfix~~.com/~~tune-up-utilities tuneup utilities]~~.<br><br>~~The software finds these difficulties plus takes care~~ of ~~them inside~~ the ~~shortest time possible. Your difficult drive would furthermore result problems sometimes~~, ~~incredibly if you have one that is virtually maxed~~. ~~When your begin your machine~~, the are ~~numerous booting processes included~~ and ~~having~~ an ~~almost full storage space refuses to assist a bit~~. ~~You will always have~~ a ~~slow PC because there are~~ a ~~lot~~ of ~~items inside~~ the ~~difficult disk being processed at~~ the ~~same time. The best method to solve this issue is to upgrade. This might allow your PC certain time to breath plus functioning quicker immediately~~.<br>~~<br>As the hub center~~ of the ~~computer, all of~~ the ~~important settings~~ are ~~stored the registry~~. ~~Registry~~ is ~~structured as keys plus every key relates to~~ a ~~system~~. ~~The system reads~~ the ~~keys plus utilizes~~ the ~~data~~ to ~~launch and run programs~~. ~~However~~, the ~~big issue is that there are too numerous unwelcome settings~~, ~~useless information occuping the valuable area~~. ~~It makes~~ the ~~program run gradually and huge amounts~~ of ~~settings become unreadable.~~<~~br>~~<br>~~Another important program you'll wish To get~~ is ~~a registry cleaner~~. ~~The registry~~ is a ~~big list of everything installed on~~ a ~~computer~~, ~~and Windows references it when it opens a system or utilizes a device connected~~ to ~~a computer~~. ~~When you delete~~ a ~~system~~, ~~its registry entry could also be deleted~~, ~~nevertheless sometimes it's not~~. A ~~registry cleaner could receive rid~~ of ~~these aged entries so Windows will look the registry faster~~. ~~It also deletes~~ or ~~corrects any entries that viruses have corrupted~~.		In [[order theory\|mathematical order theory]], an '''order-embedding''' is a special kind of [[monotone function]], which provides a way to include one [[partially ordered set]] into another. Like [[Galois connection]]s, order-embeddings constitute a notion which is strictly weaker than the concept of an [[order isomorphism]]. Both of these weakenings may be understood in terms of [[category theory]].

			== Formal definition ==
			Formally, given two partially ordered sets (''S'', ≤) and (''T'', ≤), a function ''f'': ''S'' → ''T'' is an ''order-embedding'' if ''f'' is both [[order-preserving]] and [[order-reflecting]], i.e. for all ''x'' and ''y'' in ''S'', one has

			: <math>x\leq y \text{ if and only if } f(x)\leq f(y).</math><ref name="dp02">{{citation
			\| last1 = Davey \| first1 = B. A.
			\| last2 = Priestley \| first2 = H. A.
			\| contribution = Maps between ordered sets
			\| edition = 2nd
			\| isbn = 0-521-78451-4
			\| location = New York
			\| mr = 1902334
			\| pages = 23–24
			\| publisher = Cambridge University Press
			\| title = Introduction to Lattices and Order
			\| url = http://books.google.com/books?id=vVVTxeuiyvQC&pg=PA23
			\| year = 2002}}.</ref>

			Note that such a function is necessarily [[injective]], since ''f''(''x'') = ''f''(''y'') implies ''x'' ≤ ''y'' and ''y'' ≤ ''x''.<ref name="dp02"/> If an order-embedding between two posets ''S'' and ''T'' exists, one says that ''S'' can be embedded into ''T''.

			== Properties ==

			An order isomorphism can be characterized as a [[surjective]] order-embedding. As a consequence, any order-embedding ''f'' restricts to an isomorphism between its [[domain (mathematics)\|domain]] ''S'' and its [[range (mathematics)\|range]] ''f''(''S''), which justifies the term "embedding".<ref name="dp02"/> On the other hand, it might well be that two (necessarily infinite) posets are mutually embeddable into each other without being isomorphic. An example is provided by the set of [[real number]]s and its [[interval (mathematics)\|interval]] [−1,1]. Ordering both sets in the natural way, one clearly finds that [−1,1] can be embedded into the reals. On the other hand, one can define a function ''e'' from the real numbers to [−1,1] as<ref>For a very similar example using arctan to order-embed the real numbers into an interval, see {{citation\|title=Discovering Modern Set Theory: The basics\|volume=8\|series=Fields Institute Monographs\|first1=Winfried\|last1=Just\|first2=Martin\|last2=Weese\|publisher=American Mathematical Society\|year=1996\|isbn=9780821872475\|page=21\|url=http://books.google.com/books?id=TPvHr7fcvHoC&pg=PA21}}.</ref>

			: <math>e(x) = \frac{2}{\pi}\arctan x</math>

			This is the projection of the real number line to (half of) the circle with circumference 4 (see [[trigonometric function]]s for details) and embeds the reals into [−1,1]. Yet, the two posets are not isomorphic: [−1,1] has both a [[least element\|least]] and a [[greatest element]], which are not present in the case of the real numbers. This shows that an isomorphism cannot exist.

			In a retract (a pair of order-preserving maps whose composition is the identity), the first of the two maps (called a coretraction) must be an order-embedding.<ref>{{citation
			\| last1 = Duffus \| first1 = Dwight
			\| last2 = Laflamme \| first2 = Claude
			\| last3 = Pouzet \| first3 = Maurice
			\| arxiv = math/0612458
			\| doi = 10.1007/s00012-008-2125-6
			\| issue = 1-2
			\| journal = Algebra Universalis
			\| mr = 2453498
			\| pages = 243–255
			\| title = Retracts of posets: the chain-gap property and the selection property are independent
			\| volume = 59
			\| year = 2008}}.</ref> However, not every order-embedding is a coretraction. As a trivial example of this phenomenon, the unique order embedding from the empty poset to a nonempty poset ''P'' has no retract, because there is no order-preserving map from ''P'' to the empty poset. More illustratively, consider the "diamond poset" with elements {00, 01, 10, 11} with 00 < 01 < 11, 00 < 10 < 11 and 01 incomparable to 10. Consider the embedded sub-poset "V" consisting of {00, 01, 10} (with 00 < 01 and 00 < 10 and 01 incomparable to 10). A retract of the embedding V -> diamond would need to send 11 to somewhere in "V" above both 01 and 10, but there is no such place.

			== Additional Perspectives ==
			{{unreferenced section\|date=October 2013}}
			Posets can straightforwardly be viewed from many perspectives, and order embeddings are basic enough that they tend to be visible from everywhere. For example:
			* (Model theoretically) A poset is a set equipped with a (reflexive, antisymmetric, transitive) binary relation. An order embedding A -> B is an isomorphism from A to an [[elementary substructure]] of B.
			* (Graph theoretically) A poset is a (transitive, acyclic, directed, reflexive) graph. An order embedding A -> B is a [[graph isomorphism]] from A to an [[induced subgraph]] of B.
			* (Category theoretically) A poset is a (small, skeletal) category such that each homset has at most one element. An order embedding A -> B is a full and faithful functor from A to B which is injective on objects, or equivalently an isomorphism from A to a [[full subcategory]] of B.

			==References==
			{{reflist}}

			[[Category:Order theory]]

en>Crowsnest: remove Neptune Wave Power: without reliable secondary source

2012-09-02T12:41:27Z

remove Neptune Wave Power: without reliable secondary source

New page

Today I am sharing a dark experience with we as I am from this darkness now. Whoa! Google Chrome has crashed was the disaster that struck on me early this morning. My blood flow appeared to stop for a few minutes. Then I regained my senses plus decided to fix Chrome crash. Another solution will be to provide the computer system with a new msvcr71 file. Frequently, once the file has been corrupted or damaged, it might no longer be able to function like it did before so it's only natural to substitute the file. Simply download another msvcr71.dll file from the internet. Frequently, the file comes in a zip formatting. Extract the files within the zip folder plus place them accordingly inside this location: C:\Windows\System32. Afterward, re-register the file. Click Start plus then choose Run. When the Run window appears, type "cmd". Press Enter and then type "regsvr32 -u msvcr71.dll" followed by "regsvr32 msvcr71.dll". Press Enter again plus the file ought to be registered accordingly. So, this advanced dual scan is not merely among the greater, yet it is additionally freeware. And as of all of this that numerous regard CCleaner one of the greater registry products inside the market now. I would add that I personally prefer Regcure for the simple reason which it has a better interface plus I learn for a truth that it is ad-ware without charge. Check a Windows taskbar, which is found on the lower proper hand corner of the computer screen. This taskbar consist of programs you have running in the background. If you have too numerous of them, they usually take a computer's resources. So to fix this, we simply have to be able to create all registry files non-corrupted again. This can dramatically speed up the loading time of your computer and will allow you to do a big amount of details on it again. And fixing these files couldn't be simpler - we really should employ a tool called a [http://bestregistrycleanerfix.com/tune-up-utilities tuneup utilities]. The software finds these difficulties plus takes care of them inside the shortest time possible. Your difficult drive would furthermore result problems sometimes, incredibly if you have one that is virtually maxed. When your begin your machine, the are numerous booting processes included and having an almost full storage space refuses to assist a bit. You will always have a slow PC because there are a lot of items inside the difficult disk being processed at the same time. The best method to solve this issue is to upgrade. This might allow your PC certain time to breath plus functioning quicker immediately. As the hub center of the computer, all of the important settings are stored the registry. Registry is structured as keys plus every key relates to a system. The system reads the keys plus utilizes the data to launch and run programs. However, the big issue is that there are too numerous unwelcome settings, useless information occuping the valuable area. It makes the program run gradually and huge amounts of settings become unreadable. Another important program you'll wish To get is a registry cleaner. The registry is a big list of everything installed on a computer, and Windows references it when it opens a system or utilizes a device connected to a computer. When you delete a system, its registry entry could also be deleted, nevertheless sometimes it's not. A registry cleaner could receive rid of these aged entries so Windows will look the registry faster. It also deletes or corrects any entries that viruses have corrupted.

← Older revision		Revision as of 04:23, 12 February 2014
Line 1:		Line 1:
	~~In [[order theory\|mathematical order theory]], an '''order-embedding'''~~ is ~~a special kind of [[monotone function]], which provides a way to include one [[partially ordered set]] into another. Like [[Galois connection]]s, order-embeddings constitute a notion which~~ is ~~strictly weaker than~~ the ~~concept of an [[order isomorphism]]~~. ~~Both~~ of ~~these weakenings may be understood in terms of [[category theory]]~~.		Let me first start by introducing myself. My name is Boyd Butts even though it is not the name on my beginning certificate. South Dakota is her beginning place but she requirements to move simply because of her family. Body developing is what my family members and I appreciate. Hiring is his occupation.<br><br>My webpage; healthy food delivery; [http://nnx.me/weightlossfoodprograms67803 why not look here],

	~~== Formal definition ==~~
	~~Formally, given two partially ordered sets (''S'', ≤) and (''T'', ≤), a function ''f'': ''S'' → ''T'' is an ''order-embedding'' if ''f''~~ is ~~both [[order-preserving]] and [[order-reflecting]], i.e. for all ''x'' and ''y'' in ''S'', one has~~

	~~: <math>x\leq y \text{ if~~ and ~~only if } f(x)\leq f(y).</math><ref name="dp02">{{citation~~
	~~\| last1 = Davey \| first1 = B. A.~~
	~~\| last2 = Priestley \| first2 = H~~. A.
	~~\| contribution = Maps between ordered sets~~
	~~\| edition = 2nd~~
	~~\| isbn = 0-521-78451-4~~
	~~\| location = New York~~
	~~\| mr = 1902334~~
	~~\| pages = 23–24~~
	~~\| publisher = Cambridge University Press~~
	~~\| title = Introduction to Lattices and Order~~
	~~\| url = http://books.google.com/books?id=vVVTxeuiyvQC&pg=PA23~~
	~~\| year = 2002}}.</ref>~~

	~~Note that such a function~~ is ~~necessarily [[injective]], since ''f''(''x'') = ''f''(''y'') implies ''x'' ≤ ''y'' and ''y'' ≤ ''x''~~.<~~ref name="dp02"/~~> ~~If an order-embedding between two posets ''S'' and ''T'' exists, one says that ''S'' can be embedded into ''T''.~~

	~~== Properties ==~~

	An order isomorphism can be characterized as a [[surjective]] order-embedding. As a consequence, any order-embedding ''f'' restricts to an isomorphism between its [[domain (mathematics)\|domain]] ''S'' and its [[range (mathematics)\|range]] ''f''(''S''), which justifies the term "embedding".<~~ref name="dp02"/~~> On the other hand, it might well be that two (necessarily infinite) posets are mutually embeddable into each other without being isomorphic. An example is provided by the set of [[real number]]s and its [[interval (mathematics)\|interval]] [−~~1,1]. Ordering both sets in the natural way, one clearly finds that [&minus~~;~~1,1] can be embedded into the reals. On the other hand, one can define a function ''e'' from the real numbers to~~ [−1,1] as<ref>For a very similar example using arctan to order-embed the real numbers into an interval, see {{citation\|title=Discovering Modern Set Theory: The basics\|volume=8\|series=Fields Institute Monographs\|first1=Winfried\|last1=Just\|first2=Martin\|last2=Weese\|publisher=American Mathematical Society\|year=1996\|isbn=9780821872475\|page=21\|url=http://~~books.google.com/books?id=TPvHr7fcvHoC&pg=PA21}}.</ref>~~

	~~: <math>e(x) = \frac{2}{\pi}\arctan x</math>~~

	This is the projection of the real number line to (half of) the circle with circumference 4 (see [[trigonometric function]]s for details) and embeds the reals into [−1,1]. Yet, the two posets are not isomorphic: [−1,1] has both a [[least element\|least]] and a [[greatest element]], which are not present in the case of the real numbers. This shows that an isomorphism cannot exist.

	~~In a retract (a pair of order-preserving maps whose composition is the identity), the first of the two maps (called a coretraction) must be an order-embedding.<ref>{{citation~~
	~~\| last1 = Duffus \| first1 = Dwight~~
	~~\| last2 = Laflamme \| first2 = Claude~~
	~~\| last3 = Pouzet \| first3 = Maurice~~
	~~\| arxiv = math/0612458~~
	~~\| doi = 10.1007/s00012-008-2125-6~~
	~~\| issue = 1-2~~
	~~\| journal = Algebra Universalis~~
	~~\| mr = 2453498~~
	~~\| pages = 243–255~~
	~~\| title = Retracts of posets: the chain-gap property and the selection property are independent~~
	~~\| volume = 59~~
	~~\| year = 2008}}~~.</~~ref> However,~~ not every order-embedding is a coretraction. As a trivial example of this phenomenon, the unique order embedding from the empty poset to a nonempty poset ''P'' has no retract, because there is no order-preserving map from ''P'' to the empty poset. More illustratively, consider the "diamond poset" with elements {00, 01, 10, 11} with 00 < 01 < 11, 00 < 10 < 11 and 01 incomparable to 10. Consider the embedded sub-poset "V" consisting of {00, 01, 10} (with 00 < 01 and 00 < 10 and 01 incomparable to 10). A retract of the embedding V -> diamond would need to send 11 to somewhere in "V" above both 01 and 10, but there is no such place.

	~~== Additional Perspectives ==~~
	~~{{unreferenced section\|date=October 2013}}~~
	~~Posets can straightforwardly be viewed from many perspectives, and order embeddings are basic enough that they tend to be visible from everywhere. For example:~~
	* (Model theoretically) A poset is a set equipped with a (reflexive, antisymmetric, transitive) binary relation. An order embedding A -> B is an isomorphism from A to an [[elementary substructure]~~] of B.~~
	* (Graph theoretically) A poset is a (transitive, ~~acyclic, directed, reflexive) graph. An order embedding A -> B is a [[graph isomorphism]] from A to an [[induced subgraph]] of B.~~
	* (Category theoretically) A poset is a (small, skeletal) category such that each homset has at most one element. An order embedding A -> B is a full and faithful functor from A to B which is injective on objects, or equivalently an isomorphism from A to a [[full subcategory]] of B.

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

	~~[[Category:Order theory]]~~