en>Woohookitty: Disambiguate Limiting case to Limiting case (mathematics) using popups

2014-07-04T09:57:26Z

Disambiguate Limiting case to Limiting case (mathematics) using popups

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	~~{{for\|the concept in set theory\|Tree (set theory)}}~~		It is very common to have a dental emergency -- a fractured tooth, an abscess, or severe pain when chewing. Over-the-counter pain medication is just masking the problem. Seeing an emergency dentist is critical to getting the source of the problem diagnosed and corrected as soon as possible.<br><br>Here are some common dental emergencies:<br>Toothache: The most common dental emergency. This generally means a badly decayed tooth. As the pain affects the tooth's nerve, treatment involves gently removing any debris lodged in the cavity being careful not to poke deep as this will cause severe pain if the nerve is touched. Next rinse vigorously with warm water. Then soak a small piece of cotton in oil of cloves and insert it in the cavity. This will give temporary relief until a dentist can be reached.<br><br>At times the pain may have a more obscure location such as decay under an old filling. As this can be only corrected by a dentist there are two things you can do to help the pain. Administer a pain pill (aspirin or some other analgesic) internally or dissolve a tablet in a half glass (4 oz) of warm water holding it in the mouth for several minutes before spitting it out. DO NOT PLACE A WHOLE TABLET OR ANY PART OF IT IN THE TOOTH OR AGAINST THE SOFT GUM TISSUE AS IT WILL RESULT IN A NASTY BURN.<br><br>Swollen Jaw: This may be caused by several conditions the most probable being an abscessed tooth. In any case the treatment should be to reduce pain and swelling. An ice pack held on the outside of the jaw, (ten minutes on and ten minutes off) will take care of both. If this does not control the pain, an analgesic tablet can be given every four hours.<br><br>Other Oral Injuries: Broken teeth, cut lips, bitten tongue or lips if severe means a trip to a dentist as soon as possible. In the mean time rinse the mouth with warm water and place cold compression the face opposite the injury. If there is a lot of bleeding, apply direct pressure to the bleeding area. If bleeding does not stop get patient to the emergency room of a hospital as stitches may be necessary.<br><br>Prolonged Bleeding Following Extraction: Place a gauze pad or better still a moistened tea bag over the socket and have the patient bite down gently on it for 30 to 45 minutes. The tannic acid in the tea seeps into the tissues and often helps stop the bleeding. If bleeding continues after two hours, call the dentist or take patient to the emergency room of the nearest hospital.<br><br>Broken Jaw: If you suspect the patient's jaw is broken, bring the upper and lower teeth together. Put a necktie, handkerchief or towel under the chin, tying it over the head to immobilize the jaw until you can get the patient to a dentist or the emergency room of a hospital.<br><br>Painful Erupting Tooth: In young children teething pain can come from a loose baby tooth or from an erupting permanent tooth. Some relief can be given by crushing a little ice and wrapping it in gauze or a clean piece of cloth and putting it directly on the tooth or gum tissue where it hurts. The numbing effect of the cold, along with an appropriate dose of aspirin, usually provides temporary relief.<br><br>In young adults, an erupting 3rd molar (Wisdom tooth), especially if it is impacted, can cause the jaw to swell and be quite painful. Often the gum around the tooth will show signs of infection. Temporary relief can be had by giving aspirin or some other painkiller and by dissolving an aspirin in half a glass of warm water and holding this solution in the mouth over the sore gum. AGAIN DO NOT PLACE A TABLET DIRECTLY OVER THE GUM OR CHEEK OR USE THE ASPIRIN SOLUTION ANY STRONGER THAN RECOMMENDED TO PREVENT BURNING THE TISSUE. The swelling of the jaw can be reduced by using an ice pack on the outside of the face at intervals of ten minutes on and ten minutes off.<br><br>If you have any kind of inquiries relating to exactly where along with the way to make use of [http://www.youtube.com/watch?v=90z1mmiwNS8 dentist DC], you'll be able to call us on our internet site.
	~~{{technical\|date=November 2013}}~~
	~~In [[descriptive set theory]],~~ a ~~'''tree''' on~~ a ~~set <math>X</math>~~ is ~~a set of finite sequences of elements of <math>X</math> that is closed under initial segments~~.

	~~More formally, it~~ is ~~a subset <math>T</math>~~ of <~~math~~>~~X^{~~<~~\omega}</math~~>~~, such that if~~

	:<~~math~~>~~\langle x_0~~,~~x_1,\ldots,x_{n-1}\rangle \~~in ~~T</math>~~

	and ~~<math>0\le m<n</math>,~~

	~~then~~

	~~:<math>\langle x_0,x_1,\ldots,x_{m-1}\rangle \~~in ~~T</math>~~.

	~~In particular, every nonempty tree contains the empty sequence~~.

	~~A '''branch''' through~~ <~~math~~>T<~~/math~~> is an ~~infinite sequence~~

	~~:<math>\vec x\~~in ~~X^{\omega}</math>~~ of ~~elements of <math>X</math>~~

	~~such that,~~ for ~~every natural number~~ <~~math~~>n<~~/math~~>,

	:~~<math>\vec x\|n\in T</math>,~~

	~~where <math>\vec x\|n</math> denotes~~ the ~~sequence of~~ the ~~first <math>n</math> elements of <math>\vec x</math>~~. ~~The set of all branches through <math>T</math> is denoted <math>[T]</math> and called~~ the ~~'''''body'''''~~ of the ~~tree <math>T</math>.~~

	~~A tree that has no branches is called '''''[[wellfounded]]'''''; a tree with at least one branch is '''''illfounded'''''.~~

	~~A node~~ (~~that is, element~~) of <~~math~~>T<~~/math~~> ~~is '''terminal''' if there is no node of <math>T</math> properly extending it; that is, <math>\langle x_0,x_1~~,~~\ldots~~,~~x_{n-1}\rangle \in T</math> is terminal~~ if there is ~~no element <math>x</math>~~ of ~~<math>X</math> such that that <math>\langle x_0~~,~~x_1,\ldots,x_{n-1},x\rangle \in T</math>. A tree with no terminal nodes is called '''pruned'''~~.

	If ~~we equip <math>X^\omega</math> with~~ the ~~[[product topology]] (treating ''X''~~ as ~~a [[discrete space]]), then every closed subset~~ <~~math~~>C<~~/math~~> ~~of <math>X^\omega</math> is of~~ the ~~form <math>[T]</math>~~ for ~~some pruned tree <math>T</math> (namely, <math>T:= \{ \vec x\|n: n \~~in ~~\omega~~, ~~x\in C\}</math>)~~. ~~Conversely, every set~~ <~~math~~>~~[T]~~<~~/math~~> is ~~closed~~.

	~~Frequently trees on [[cartesian product]]s <math>X\times Y</math> are considered. In this case~~, ~~by convention~~, the ~~set <math>(X\times Y)^{\omega}</math> is identified in~~ the ~~natural way with~~ a ~~subset~~ of <~~math~~>~~X^{\omega}\times Y^{\omega}~~<~~/math~~>, and ~~<math>[T]</math> is considered as~~ a ~~subset~~ of ~~<math>X^{\omega}\times Y^{\omega}</math>~~. ~~We may then form~~ the ~~'''projection'''~~ of <~~math~~>~~[T]~~<~~/math~~>,
	~~: <math>p[T]=\{\vec x\in X^{\omega} \|~~ (~~\exists \vec y\in Y^{\omega}~~)~~\langle \vec x~~,~~\vec y\rangle \in [T]\}</math>~~

	~~Every tree in the sense described here~~ is ~~also a [[tree (set theory)\|tree in~~ the ~~wider sense]], i~~.e.~~, the pair (''T'', <), where < is defined~~ by
	~~:''x''<''y'' ⇔ ''x'' is~~ a ~~proper initial segment~~ of ~~''y'',~~
	~~is a partial order~~ in ~~which each initial segment is well-ordered~~. The ~~height~~ of ~~each sequence ''x'' is then its length,~~ and ~~hence finite~~.

	~~Conversely, every partial order (''T'', <) where each initial segment { ''y'': ''y'' < ''x''~~<~~sub~~>0<~~/sub~~> ~~} is well-ordered is isomorphic~~ to ~~a tree described here, assuming that all elements have finite height~~.

	~~==See also~~==
	*[[Laver tree]]
	* [[Tree (set theory)]]
	* [[König'~~s lemma]]~~

	~~==References==~~
	* {{Cite book\| last = Kechris \| first = Alexander S. \| authorlink = Alexander S. ~~Kechris \| title = Classical Descriptive Set Theory \| others = [[Graduate Texts in Mathematics]] 156 \| publisher = Springer \| year = 1995 \| id = ISBN 0-387-94374-9 ISBN 3-540-94374-9}}~~

	~~{{DEFAULTSORT:Tree (Descriptive Set Theory)}}~~
	~~[[Category:Descriptive set theory]]~~
	~~[[Category:Trees (set theory)]]~~
	~~[[Category:Determinacy]]~~

en>Bender235: citation cleanup

2013-12-16T17:57:36Z

citation cleanup

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68.175.6.10: /* Example */

2011-06-20T03:45:41Z

Example

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Leontief production function - Revision history

en>Woohookitty: Disambiguate Limiting case to Limiting case (mathematics) using popups

en>Bender235: citation cleanup

68.175.6.10: /* Example */