Copper-copper(II) sulfate electrode: Difference between revisions

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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 liked this write-up and you would such as to get additional facts concerning [http://www.youtube.com/watch?v=90z1mmiwNS8 Washington DC Dentist] kindly browse through our own site.
In [[probability theory]] and [[logic]] a set of events is '''jointly''' or '''collectively exhaustive''' if at least one of the events must occur.  For example, when rolling a [[dice|six-sided die]], the outcomes 1, 2, 3, 4, 5, and 6 are collectively exhaustive, because they encompass the entire range of possible outcomes.
 
Another way to describe collectively exhaustive events, is that their union must cover all the events within the entire sample space. For example, events A and B are said to be collectively exhaustive if
:<math>A  \cup B = S</math>
 
where S is the [[sample space]].
 
Compare this to the concept of a set of [[mutually exclusive]] events. In such a set no more than one event can occur at a given time. (In some forms of mutual exclusion only one event can ever occur.) The set of all possible die rolls is both collectively exhaustive and mutually exclusive. The outcomes 1 and 6 are mutually exclusive but not collectively exhaustive. The outcomes "even" (2,4 or 6) and "not-6" (1,2,3,4, or 5) are collectively exhaustive but not mutually exclusive. In some forms of mutual exclusion only one event can ever occur, whether collectively exhaustive or not. For example, tossing a particular biscuit for a group of several dogs cannot be repeated, no matter which dog snaps it up.
 
One example of an event that is both collectively exhaustive and mutually exclusive is tossing a coin. The outcome must be either heads or tails, or p(heads or tails) = 1, so the outcomes are collectively exhaustive. When heads occurs, tails can't occur, or p(heads and tails) = 0, so the outcomes are also mutually exclusive.
 
== History ==
The usage of the term "exhaustive" has existed in the literature since at least 1914. Here are a few examples:
 
The following appears as a footnote on page 23 of Couturat 1914:
:"As Mrs. LADD·FRANKLlN has truly remarked (BALDWIN, Dictionary of Philosophy and Psychology, article "Laws of Thought"), the principle of contradiction is not sufficient to define contradictories; the principle of excluded middle must be added which equally deserves the name of principle of contradiction. This is why Mrs. LADD-FRANKLIN proposes to call them respectively the principle of exclusion and the ''principle of exhaustion'', inasmuch as, according to the first, two contradictory terms are exclusive (the one of the other); and, according to the second, they are ''exhaustive (of the universe of discourse)''." (italics added for emphasis)
 
In [[Stephen Kleene]]'s discussion of cardinal numbers in Kleene 1952, he uses "mutually exclusive" together with "exhaustive":
 
:"Hence, for any two cardinals M and N, the three relationships M < N, M = N and M > N are 'mutually exclusive', i.e. not more than one of them can hold. ¶ It does not appear till an advanced stage of the theory . . . whether they are '' 'exhaustive' '', i.e. whether at least one of the three must hold". (italics added for emphasis, Kleene 1952:11; original has double bars over the symbols M and N).
 
== References ==
* Louis Couturat, translated by Lydia Gillingham Robinson, 1914, The Algebra of Logic, The Open Court Publishing Company, Chicago and London.
* John G. Kemeney et. al. 1958/9, ''Finite Mathematical Structures'', ''Prentice-Hall, Inc. Englewood Cliffs, N.J. LCCCN: 59-12841.
* Stephen C. Kleene 1952, 6th edition 1971, ''Introduction to Medtamathematics'', North-Holland Publishing Company, Amsterdam NY, ISBN 0 7204 2103 9.
* Alfred Tarski 1941, reprint of 1946 2nd edition, ''Introduction to Logic and to the Methodology of Deductive Sciences'', Dover Publicationbs, Inc, NY, ISBN 0-486-28462-X (pbk.)
 
[[Category:Probability theory]]
[[Category:Statistical terminology]]

Latest revision as of 02:47, 4 January 2014

In probability theory and logic a set of events is jointly or collectively exhaustive if at least one of the events must occur. For example, when rolling a six-sided die, the outcomes 1, 2, 3, 4, 5, and 6 are collectively exhaustive, because they encompass the entire range of possible outcomes.

Another way to describe collectively exhaustive events, is that their union must cover all the events within the entire sample space. For example, events A and B are said to be collectively exhaustive if

where S is the sample space.

Compare this to the concept of a set of mutually exclusive events. In such a set no more than one event can occur at a given time. (In some forms of mutual exclusion only one event can ever occur.) The set of all possible die rolls is both collectively exhaustive and mutually exclusive. The outcomes 1 and 6 are mutually exclusive but not collectively exhaustive. The outcomes "even" (2,4 or 6) and "not-6" (1,2,3,4, or 5) are collectively exhaustive but not mutually exclusive. In some forms of mutual exclusion only one event can ever occur, whether collectively exhaustive or not. For example, tossing a particular biscuit for a group of several dogs cannot be repeated, no matter which dog snaps it up.

One example of an event that is both collectively exhaustive and mutually exclusive is tossing a coin. The outcome must be either heads or tails, or p(heads or tails) = 1, so the outcomes are collectively exhaustive. When heads occurs, tails can't occur, or p(heads and tails) = 0, so the outcomes are also mutually exclusive.

History

The usage of the term "exhaustive" has existed in the literature since at least 1914. Here are a few examples:

The following appears as a footnote on page 23 of Couturat 1914:

"As Mrs. LADD·FRANKLlN has truly remarked (BALDWIN, Dictionary of Philosophy and Psychology, article "Laws of Thought"), the principle of contradiction is not sufficient to define contradictories; the principle of excluded middle must be added which equally deserves the name of principle of contradiction. This is why Mrs. LADD-FRANKLIN proposes to call them respectively the principle of exclusion and the principle of exhaustion, inasmuch as, according to the first, two contradictory terms are exclusive (the one of the other); and, according to the second, they are exhaustive (of the universe of discourse)." (italics added for emphasis)

In Stephen Kleene's discussion of cardinal numbers in Kleene 1952, he uses "mutually exclusive" together with "exhaustive":

"Hence, for any two cardinals M and N, the three relationships M < N, M = N and M > N are 'mutually exclusive', i.e. not more than one of them can hold. ¶ It does not appear till an advanced stage of the theory . . . whether they are 'exhaustive' , i.e. whether at least one of the three must hold". (italics added for emphasis, Kleene 1952:11; original has double bars over the symbols M and N).

References

  • Louis Couturat, translated by Lydia Gillingham Robinson, 1914, The Algebra of Logic, The Open Court Publishing Company, Chicago and London.
  • John G. Kemeney et. al. 1958/9, Finite Mathematical Structures, Prentice-Hall, Inc. Englewood Cliffs, N.J. LCCCN: 59-12841.
  • Stephen C. Kleene 1952, 6th edition 1971, Introduction to Medtamathematics, North-Holland Publishing Company, Amsterdam NY, ISBN 0 7204 2103 9.
  • Alfred Tarski 1941, reprint of 1946 2nd edition, Introduction to Logic and to the Methodology of Deductive Sciences, Dover Publicationbs, Inc, NY, ISBN 0-486-28462-X (pbk.)
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