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Reverted 1 edit by 213.181.229.101 identified as test/vandalism using STiki

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	~~{{See also\|Forcing (set theory)#The countable chain condition}}~~		<br><br>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>Here is more information on [http://www.youtube.com/watch?v=90z1mmiwNS8 Dentists in DC] have a look at the web page.
	~~In [[order theory]], a [[partially ordered set]] ''X''~~ is ~~said~~ to ~~satisfy the '''countable chain condition'''~~, or ~~to be '''ccc''', if every [[strong antichain]] in ''X''~~ is ~~[[countable]]~~. ~~There are really two conditions:~~ the ~~''upwards''~~ and ~~''downwards'' countable chain conditions~~. ~~These~~ are ~~not equivalent~~. ~~We adopt~~ the ~~convention~~ the ~~countable chain condition means the downwards countable chain condition~~, in ~~other words no two elements have~~ a ~~common lower bound~~.

	This ~~is called the "countable chain condition" rather than~~ the more ~~logical term "countable antichain condition" for historical reasons related~~ to ~~complete Boolean algebras~~. (~~If κ is~~ a ~~cardinal, then~~ in a ~~complete Boolean algebra every antichain has size less than κ if and only if there is no descending κ-sequence~~ of ~~elements, so chain~~ conditions ~~are equivalent~~ to ~~antichain conditions~~.)

	~~Partial orders and spaces satisfying~~ the ~~ccc are used in~~ the ~~statement~~ of ~~[[Martin's axiom]]~~.

	In the ~~theory of [[forcing (set theory)\|forcing]]~~, ~~ccc partial orders are used because forcing with any generic set over such~~ an ~~order preserves cardinals and cofinalities~~.

	~~More generally~~, if ~~κ is~~ a ~~cardinal then~~ a ~~poset~~ is ~~said~~ to ~~satisfy~~ the ~~'''κ-chain condition''' if every antichain has size less than κ~~. ~~The countable chain condition is~~ the ~~&alefsym;~~<~~sub~~>1<~~/sub~~>~~-chain condition~~.

	~~==Examples~~ and ~~properties in topology==~~
	~~A [[topological space]] is said to satisfy~~ the ~~countable chain condition~~, or ~~'''Suslin's Condition''', if~~ the ~~partially ordered set of non-empty [[open subset]]s~~ of ~~''X'' satisfies~~ the ~~countable chain condition, i~~.~~e. every [[pairwise disjoint]] collection of non-empty open subsets of ''X'' is countable. The name originates from [[Suslin~~'s ~~problem\|Suslin's Problem]].~~

	* Every [[separable topological space]] is ~~ccc~~. ~~Furthermore~~, the ~~[[Product topology\|product space]]~~ of ~~at most [[Cardinality of the continuum\|c]] separable spaces is~~ a ~~separable space and, thus, ccc~~.

	* Every [[metric space]] is ccc if and ~~only if~~ it~~'s separable, but~~ in ~~general~~ a ~~ccc topological space need not be separable~~.

	~~For example~~,

	:<~~math~~>~~\{ 0, 1 \}^{ 2^{ 2^{ \aleph_0 }\ } }~~<~~/math~~>
	~~with~~ the ~~[[product topology]] is ccc but not separable~~.

	~~==References==~~
	*{{Citation \| last1=Jech \| first1=Thomas \| author1-link=Thomas Jech \| title=Set Theory: Millennium Edition \| publisher=[[Springer-Verlag]] \| location=Berlin, New York \| series=Springer Monographs in ~~Mathematics \| isbn=978-3-540-44085-7 \| year=2003}}~~
	*Products of ~~Separable Spaces, K~~. A. ~~Ross,~~ and A. H. ~~Stone~~. ~~The American Mathematical Monthly 71(4):pp~~. ~~398-403 (1964)~~

	~~[[Category:Order theory]]~~
	~~[[Category:Forcing (mathematics)]]~~

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2014-01-06T09:12:28Z

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216.99.65.83: /* Direct Measurement of API gravity (Hydrometer method) */

2012-08-08T17:53:43Z

Direct Measurement of API gravity (Hydrometer method)

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en>Strike Eagle: Reverted 1 edit by 213.181.229.101 identified as test/vandalism using STiki

en>CyberXRef: fixed link rot

216.99.65.83: /* Direct Measurement of API gravity (Hydrometer method) */