Kőnig's theorem (set theory) and Chupacabra: Difference between pages

Revision as of 04:32, 4 April 2005

Revision as of 15:49, 12 July 2007

Line 1:

{{otheruses}}

''There is also a proposition in [[graph theory]] called [[König's lemma]].''

{{Infobox Paranormalcreatures

|Creature_Name = Chupacabra

|Image_Name = Chupacabras.JPG

|Image_Caption = Artist's depiction of a chupacabra

|Grouping = [[Cryptid]]<br>[[extraterrestrial life|Extraterrestrial]]

|Sub_Grouping =

|Spanish Translation = Goat Sucker

|Country = [[Puerto Rico]],<br>[[Mexico]],<br>[[United States]], [[Chile]],<br>[[Russia]]

|Region = Unknown

|First_Reported = Early [[1990s]]

|Last_Sighted = Present Day

|Status = [[Legendary creature]]}}

'''Chupacabra''' (also '''chupacabras''' /tʃupa'kabɾas/, from Spanish '''''chupar: to suck''''', '''''cabra: goat; goats sucker''''') is a [[cryptid]] said to inhabit parts of both of the [[Americas]]. It is associated particularly with [[Puerto Rico]] (where it was first reported), [[Mexico]], and the [[United States]], especially in the latter's [[Latin American]] communities. The name translates literally from the [[Spanish language|Spanish]] as "goat sucker." It comes from the creature's reported habit of attacking and drinking the blood of livestock, especially [[goat]]s. Physical descriptions of the creature vary. Eyewitness sightings have been claimed as early as 1990 in Puerto Rico, and have since been reported as far north as [[Maine]], and as far south as Chile. Though some argue that the chupacabras may be real creatures, mainstream scientists and experts generally contend that the chupacabra is a [[legendary creature]], or a type of [[urban legend]].

----

It is supposedly a heavy creature, the size of a small bear, with a row of spines reaching from the neck to the base of the tail.

[[Category:Set theory]]

==History==

In [[set theory]], '''K&ouml;nig's theorem''' states that if ''I'' is a [[set]] and ''m_i'' and ''n_i'' are [[cardinal number]]s for every ''i'' in ''I'', and

The legend of ''cipi chupacabra'' began approximately in [[1987]], when Puerto Rican newspapers ''[[El Vocero]]'' and ''[[El Nuevo Dia]]'' began reporting the killings of many different types of animals, such as birds, horses, and, as its name implies, goats. It is predated by ''El Vampiro de Moca'' (The Vampire of Moca), a creature blamed for similar killings that occurred in the small town of [[Moca, Puerto Rico|Moca]] in the 1970s. While at first it was suspected that the killings were done randomly by some members of a [[Satanic]] [[cult]], eventually these killings spread around the island, and many farms reported loss of animal life. The killings had one pattern in common: each of the animals had their bodies bled dry through a series of small circular incisions.

:<math>\forall i\in I\quad m_i<n_i,</math>

Puerto Rican comedian and entrepreneur [[Silverio Pérez]] is credited with coining the term "chupacabras" soon after the first incidents were reported in the press.<ref>{{cite web| url=http://www.crystalinks.com/chupacabras.html|title= Chupacabras Bio| accessdate=2007-05-10}}</ref> Soon after the animal deaths in Puerto Rico, other animal deaths were reported in other countries, such as the [[Dominican Republic]], [[Argentina]], [[Bolivia]], [[Chile]], [[Colombia]], [[Honduras]], [[El Salvador]], [[Panama]], [[Peru]], [[Brazil]], the United States and Mexico.

then

:<math>\sum_{i\in I}m_i<\prod_{i\in I}n_i.</math>

The ''sum'' here is the cardinality of the [[disjoint union]] of the sets ''n_i''; and the product is the cardinality of the [[cartesian product]]; we can similarly state it for arbitrary sets (not necessarily cardinal numbers) by replacing < by ''strictly less than in [[cardinality]],'' i.e. there is an [[injective]] [[function (mathematics)|function]] from ''m_i'' to ''n_i,'' but not one going the other way. The union involved need not be disjoint (a non-disjoint union can't be any bigger than the disjoint version, anyway).

==Alleged sightings==

(Of course this is trivial if the cardinal numbers ''m_i'' and ''n_i'' are [[finite]] and the index set ''I'' is finite. If ''I'' is [[empty set|empty]], then the left sum is the empty sum and therefore 0, while the right hand product is the [[empty product]] and therefore 1).

In July 2004, a rancher near [[San Antonio]], killed a hairless dog-like creature, which was attacking his livestock. This creature is now known as the [[Elmendorf Creature]]. It was later determined to be a [[coyote]] with demodectic or sarcoptic [[mange]]. In October 2004, two animals said to resemble the Elmendorf Creature were supposedly observed in the same area. The first was dead, and a local zoologist who was called to identify the animal noticed the second while she was traveling to the ___location where the first was found. Specimens of the dead animals were studied by biologists in Texas, who found that the creatures were coyotes suffering from very severe cases of mange.<ref>{{cite web| url=http://www.banderasnews.com/0603/art-chupacabra.htm| title=Texas' Blood-Sucking Monster| accessdate=2007-06-12}}</ref>

K&ouml;nig's theorem is remarkable because of the strict inequality in the conclusion. There are many easy rules for the arithmetic of infinite sums and products of cardinals in which one can only conclude a weak inequality &#8804;, for example: IF ''m_i < n_i'' for all ''i'' in ''I'', THEN we can only conclude <math>\sum_{i\in I} m_i \le \sum_{i\in I} n_i </math>.

In [[Coleman, Texas]], a farmer named Reggie Lagow caught an animal in a trap he set up after the deaths of a number of his chickens and turkeys. The supposed animal was described as a mix between a hairless dog, a rat and a kangaroo. The animal was provided to Texas Parks and Wildlife in order to determine what species it belonged to, but Lagow reported in a September 17th, 2006, phone interview with John Adolfi, founder of the Lost World Museum, that the "critter was caught on a Tuesday and thrown out in Thursday's trash."<ref>{{cite news|url=http://www.nbc4.tv/news/4895053/detail.html|title=Texas Farmer Claims He Caught Legendary 'Chupacabra'|publisher=KNBC Los Angeles|date=[[2005-08-25]]}}</ref>

==Corollary of König's theorem==

In April of 2006, ''MosNews'' reported that the chupacabra was spotted in Russia for the first time. Reports from Central Russia beginning in March 2005 tell of a beast that kills animals and sucks out their blood. Thirty-two turkeys were killed and drained overnight. Reports later came from neighboring villages when 30 sheep were killed and had their blood drained. Finally eyewitnesses were able to describe the chupacabra. In May of 2006, experts were determined to track the animal down.<ref>{{cite news|url=http://www.mosnews.com/news/2006/04/27/chupacabra.shtml|title=Chupacabra the Goatsucker Vampire Sightings Reported in Central Russia|publisher=MosNews|date=[[2006-04-17]]}}</ref>

If we take ''m_i'' = 1, and ''n_i'' = 2 for all ''i'', then the left hand side of the above inequality is just |''I''|, the cardinality of the index set ''I'', while the right hand side is 2^|''I''|, or the cardinality of the power set of ''I''.

In mid-August 2006 Michelle O'Donnell of [[Turner, Maine]], described an "evil looking" rodent-like creature with fangs that had been found dead alongside a road. The mystery beast was apparently struck by a car, and was otherwise unidentifiable. Photographs were taken and witness reports seem to be in relative agreement that the creature was canine in appearance, but unlike any dog or wolf in the area. The carcass was picked clean by vultures before experts could examine it. For years, residents of Maine have reported a mysterious creature and a string of dog maulings.<ref>{{cite news|url=http://hosted.ap.org/dynamic/stories/M/MYSTERY_BEAST?SITE=WWL&TEMPLATE=STRANGEHEADS.html&SECTION=HOME| title='Hybrid Mutant' Found Dead in Maine|publisher=Associated Press|date=[[2006-08-16]]}}</ref>

In December 2006, a local farmer in Peru claimed to have seen a creature resembling a Chupacabra attacking a wild boar on his farm. The man, who referred to the creature as "Zahir," later told the authorities that he feared for his life when he saw the creature devour the boar within minutes. The creature then ran faster than any animal the farmer had ever seen. Shocked at the sight of the creature, the farmer stated that he is haunted by the evil in the Zahir's eyes.

Thus, one can conclude [[Cantor's theorem]] from König's theorem. (Historically of course Cantor's theorem was proved much earlier.)

In May 2007, a series of reports on national Colombia news reported more than 300 dead sheep in the region of [[Boyaca]], and the capture of a possible specimen to be analysed by zoologists at [[Universidad Nacional]] of Colombia.<ref>{{cite news|url=http://www.eltiempo.com/nacion/boyaca/2007-05-02/ARTICULO-WEB-NOTA_INTERIOR-3539469.html| title=''Bestia' chupasangre asusta a los campesinos de Chiscas: ha matado 310 animales'|publisher=El Tiempo|date=[[2007-05-02]]}}</ref>

==Appearance==

The most common description of Chupacabra is a [[lizard]]-like being, appearing to have leathery or scaly greenish-gray skin and sharp spines or quills running down its back.<ref>{{cite web|url=http://skepdic.com/chupa.html|title=Chupacabras Biography|accessdate=2007-05-10}}</ref> This form stands approximately 3 to 4 feet (1 to 1.2 m) high, and stands and hops in a similar fashion to a [[kangaroo]]. In at least one sighting, the creature hopped 20 feet (6 m). This variety is said to have a dog or panther-like nose and face, a [[forked tongue]] protruding from it, large fangs, and to hiss and screech when alarmed, as well as leave a sulfuric stench behind. When it screeches, some reports note that the chupacabra's eyes glow an unusual red, then give the witnesses nausea. For some witnesses, it was seen with bat-like wings.<ref>{{cite web|title=Chupacabras=Giant Bat?|url=http://www.cryptomundo.com/bigfoot-report/chupa-giant-bat/| accessdate=2007-05-10}}</ref>

Another description of Chupacabra, although not as common, is described as a strange breed of wild dog. This form is mostly hairless, has a pronounced spinal ridge, unusually pronounced eye sockets, fangs, and claws. It is claimed that this breed might be an example of a dog-like reptile. The account during the year 2001 in [[Nicaragua]] of a chupacabra's corpse being found supports this conclusion. The corpse of the animal was found in [[Leon, Nicaragua]], and forensically analyzed at UNAN-Leon. Pathologists at the University found that it was an unusual-looking dog-like creature of unknown species.<ref>{{cite web| url=http://www.uforc.com/chupas/journal2-UFORCE_page21.html| title=Chupacabras Remains Found| accessdate=2007-06-20}}</ref> Unlike conventional predators, the chupacabra is said to drain all of the animal's blood (and sometimes organs) through a single hole or two holes.

==See also==

*[[Cryptozoology]]

*[[Fauna of Puerto Rico]]

Similar creatures include:

*[[Banshee]]

*[[Demon]]

*[[Greys]]

*[[Jersey Devil]]

*[[Loveland Lizard]]

*[[Mothman]]

*[[Monkey-man of New Delhi]]

*[[Peuchen]]

*[[Skunk Ape]]

==References==

<references/>

==External links==

*[http://alienvideo.net/video-chupacabra.php Alleged video footage of a Chupacabra]

*[http://www.skepticworld.com/cryptozoology/chupacabra.asp Cryptozoology] - Skeptic World

*[http://www.lostworldmuseum.com Alleged photographic evidence of a Chupacabra]

[[Category:Set theoryCryptids]]

[[Category:Hominid cryptids]]

[[Category:UFO-related entities]]

[[de:Chupacabras]]

[[et:Chupacabra]]

[[es:Chupacabras]]

[[eo:Chupacabras]]

[[fr:Chupacabra]]

[[hr:Chupacabra]]

[[it:Chupacabra]]

[[he:צ'ופקברה]]

[[lt:Čiupakabra]]

[[hu:Chupacabra]]

[[nl:Chupacabra]]

[[ja:チュパカブラ]]

[[pl:Chupacabra]]

[[pt:Chupa-cabra]]

[[ru:Чупакабра]]

[[simple:Chupacabra]]

[[sr:Чупакабра]]

[[fi:Chupacabra]]

[[sv:Chupacabra]]

[[zh:卓柏卡布拉]]