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Topic: Trichotomy

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Axiom of choice

Cardinal number

Hausdorff dimension

Topological space

Dichotomy

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	Trichotomy - Wikipedia, the free encyclopedia
		If applied to cardinal numbers, the law of trichotomy is equivalent to the axiom of choice.
		In taxonomy a trichotomy is speciation of three groups from a common ancestor, where it is unclear or unknown in what chronological order the three groups split.
		In the anthropologic field of theology, and in philosophy, trichotomy is the belief that man consists of three parts; a body, soul, and spirit.
	en.wikipedia.org /wiki/Trichotomy (188 words)

	PlanetMath: law of trichotomy
		Note that trichotomous binary relations are equivalent to tournaments (although the study of tournaments is usually restricted to the finite case).
		The law of trichotomy for cardinal numbers is equivalent (in ZF) to the axiom of choice.
		This is version 5 of law of trichotomy, born on 2004-03-06, modified 2005-06-25.
	planetmath.org /encyclopedia/LawOfTrichotomy.html (128 words)

	Nelson v. Freeland, 349 NC 615 (216A98) 12/31/1998
		Lastly, opponents of abolishing the trichotomy argue that retention of the scheme is necessary to ensure predictability in the law.
		First, these jurisdictions note that the trichotomy was created during feudal times when land formed the principal basis of wealth and when it was desirable to provide a landowner free reign to use and exploit his land, without need for vigilant protection of those who entered his property.
		Lastly, the trichotomy is unjust and unfair because it usurps the jury's function either by allowing the judge to dismiss or decide the case or by forcing the jury to apply mechanical rules instead of focusing upon the pertinent issue of whether the landowner acted reasonably under the circumstances.
	www.aoc.state.nc.us /www/public/sc/opinions/1998/216-98-1.htm (6719 words)

	Trichotomy: Facts and details from Encyclopedia Topic (Site not responding. Last check: 2007-11-06)
		(a trichotomy is a splitting into three disjoint parts.
		In mathematics, the concept of binary relation is exemplified by such ideas as "is greater than" and "is equal to" in arithmetic, or "is congruent to" in geometry,...
		(trichotomy is equivalent to the axiom of choice axiom of choice quick summary:
	www.absoluteastronomy.com /encyclopedia/t/tr/trichotomy.htm (755 words)

	Spirit, Soul, and Body: Chapter 5
		Platonic trichotomy is further removed from a biblical one due to Plato's view of the three parts of soul.
		A factor that hindered the church's acceptance of trichotomy was its reaction to dualism.
		The theological vindication of trichotomy in the nineteenth century gave fertile soil to a variety of teachers and ministries that have been teaching from this perspective in the twentieth century.
	www.gracenotebook.com /trichotomy_ch_5.htm (2306 words)

	Pilgrims Between Two Ages > Articles & Sermons
		trichotomy is very likely the reigning notion of human nature in American Evangelical circles today.With few exceptions, the Christian church has affirmed, with one voice, that human nature is two-fold.
		In this case, trichotomy allows Pentecostals to argue that because the spirit is the higher element of human nature, "speaking in tongues" is the divinely appointed means of bypassing the lower elements of human nature, such as the rationality of mind and soul.
		When one considers, however, several of the notes advocating trichotomy contained in the Scofield Reference Bible, the reader is immediately intrigued, for example, by the affinities between the notes on 1 Corinthians 2:14, and the mystical and speculative philosophy of Plotinus.
	www.twoagespilgrims.com /files/show_article.php?id=146 (3428 words)

	"Trichotomists, Charismatics, and 1 Corinthians 14" by David Brown
		Based on a trichotomy or tri-partite view of man, he claims that his spirit speaks a heavenly language that bypasses the mental understanding of his soul.
		Trichotomy also has a strong effect in evangelical denominations who would not normally call themselves Charismatic, particularly the more liberal denominations who have little to no emphasis on the historic creeds and confessions.
		Trichotomy breeds a hyper-independence and individualistic mindset that is blind to the covenantal and corporate aspects of the Holy Spirit.
	www.the-highway.com /tricho-charis_Brown.html (2920 words)

	AS/SA No 10, Article 2 : Thorkild THELEFFSEN, "The Epistemology of Peirce's Sign Trichotomies"
		The first division of the three trichotomies is identical with Firstness and the representamen, and it consists of Qualisign, Sinsign and Legisign.
		It is important to notice that this trichotomy describes the dyadic relation between representamen and object.
		This trichotomy is the least used, I find that this is an misunderstanding as in fact it is the third trichotomy which makes it possible for us to understand the relation between Firstness and Secondness.
	www.chass.utoronto.ca /french/as-sa/ASSA-No10/No10-A2.html (4094 words)

	DNA hybridization bibliography
		The authors acknowledge the previously undisclosed data alterations and admit that the resolution of the trichotomy was predicated upon them.
		In the best case, the research would be characterized methodological poverty; the omission of the vital information would be coincidental; and the refusal of the authors to allow others to see their data would also be coincidental.
		Ruvolo does not provide any evidence to support her contention that the length "correction" was not responsible for generating the results, but rather she cites only unpublished "work in preparation".
	personal.uncc.edu /jmarks/dnahyb/Biblio.html (4481 words)

	Soul, Spirit & Knowing God - Part Two
		In this form of trichotomy the anti-intellectualism of Nee and other trichotomists is avoided.
		Moses declares in Deut 6:5, "You shall love the LORD your God with all your heart, with all your soul, and with all your strength." It appears Moses is also teaching a trichotomy of sorts.
		Though some find here support for the view that a human being is basically a trichotomy consisting of body, soul, and spirit, the context is against it.
	www.dtl.org /dtl/treatise/soul-spirit-2.htm (2900 words)

	Euclid's Elements, Book V, Definition 7
		These are various transitivities and the law of trichotomy, some of the same properities of greater and lesser that magnitudes have.
		The other side of the law of trichotomy, the one that says at least one of the three cases holds, is a bit harder to prove, and it depends on treating V.Def.4 as an axiom of comparability.
		In summary, since we have a proof of trichotomy that uses V.Def.4 as an axiom of comparability, and a counterexample of trichotomy that violates the axiom of comparability, we can conclude that any proof trichotomy requires the axiom of comparability.
	aleph0.clarku.edu /~djoyce/java/elements/bookV/defV7.html (700 words)

	CAEE > People > Environmental Impacts > Deforestation : Perceptions
		Each of these rules can generate information either in trichotomy or dichotomy form depending on how strict our requirements are.
		The average rule procedure used to rank local and non-local perceptions in trichotomy form has two main steps: a) the determination of the average perception score(AV) for each row in the perception tables; and b) the classification of the score found as being either Not Important(NI) or Important(I) or Very Important(VI).
		This means that the average trichotomy perception for this characteristic is Very Important.
	www.garrobo.org /eng/people/impacts/deforest/dfper.htm (2068 words)

	Sharper Iron Forums - Trichotomy or Dichotomy?
		I personally believe that we are a trichotomy (as you probably could tell).
		I also believe that being created in His image lends to the idea of trichotomy based upon the truth of the Trinity.
		My unlearned reaction to your descriptions of "dichotomy" or "trichotomy" is that they sound suspiciously like Manichaeism or gnosticism, cults that denigrated the body.
	www.sharperiron.org /showthread.php?t=479 (1554 words)

	The Trichotomy Theorem Does Not Hold For Short Sequences (ResearchIndex) (Site not responding. Last check: 2007-11-06)
		Abstract: The Trichotomy Theorem deals with sequences of ordinal functions on an infinite modulo some ideal I.
		I - increasing sequence of ordinal functions has regular length which is larger than +, then by the Trichotomy Theorem the sequence satisfies one of three structural conditions.
		It was of some interest to find out if the Trichotomy Theorem could hold also for sequences of length +.
	citeseer.ist.psu.edu /465273.html (281 words)

	A Limit Set Trichotomy for Order-Preserving Random Systems - Arnold, Chueshov (ResearchIndex) (Site not responding. Last check: 2007-11-06)
		Sublinear random systems are contractive with respect to the part metric, hence random equilibria are unique and asymptotically stable in each part of the cone.
		Our main result is a random limit set trichotomy, stating that in a given part either (i) all orbits are unbounded, or (ii) all...
		with the investigation of sublinear random systems whose asymptotic behavior is described by a limit set trichotomy.
	citeseer.ist.psu.edu /36327.html (514 words)

	Among any two integers or real numbers one is larger, another smaller. But you can't compare two complex numbers.
		Trichotomy holds for the usual order of real numbers.
		But, as we just saw, the order between complex numbers for which (1) holds, could not satisfy the law of trichotomy and vice versa.
		satisfies the Trichotomy law) then (1) could not possibly hold.
	www.cut-the-knot.org /do_you_know/complex_compare.shtml (322 words)

	Discovering Your Identity (Understanding the trichotomy of man)
		Note: This is not meant to be a real deep comprehensive study, but a basic outline for further study.
		We can also see man as being a trichotomy in the nature of Jesus being both man and God.
		Finally, it should also guard us from judging others by looking at their soul from the outside while God looks on the inside at man's spirit.
	www.wholeperson-counseling.org /id/trichotomy.html (4347 words)

	Witchcraft - Wikipedia, the free encyclopedia
		Many similar models exist in the fields of psychology and magic, such as the ego, id and superego of Freud, or the Qabalistic concept of three parts of the self, being the Ruach (intellect and ego), the Nephesch (body, lower instinct and subconscious) and the Neschamah (the highest divine self).
		This is also similar to the Eastern Christian trichotomy of the Greek words σώμα (soma), ψυχή (psyche), and νους (nous), wherein the soma is the living body, psyche is the "mind" as we normally use the term, and nous is the faculty capable of apprehending the Divine.
		It differs from Starhawk's model in that it assigns a place for the physical body in and of itself as part of a "whole" human being's spiritual existence.
	en.wikipedia.org /wiki/Witchcraft (3905 words)

	Emotion
		In view of the acknowledged complexity of emotional functions, it seems wise to rephrase the question not in terms of ontology, but in terms of levels of explanation.
		The second designates the actual neuro-physiological processes whereby, in animals built on a specific plan such as mammals or humans such as we, these sub-functions are normally carried out.
		It is generally agreed that the simpler emotions, those whose expression and recognition Ekman (1972, 1989) has shown to be universal, are driven by the basic needs of organisms such as mating, defense or avoidance of predators, and social affiliation.
	plato.stanford.edu /entries/emotion (12581 words)

	Citebase - The condition in the Trichotomy Theorem is optimal
		Citebase - The condition in the Trichotomy Theorem is optimal
		The condition in the Trichotomy Theorem is optimal
		in the Trichotomy Theorem cannot be relaxed to lambda > kappa.
	citebase.eprints.org /cgi-bin/citations?id=oai:arXiv.org:math/9712289 (463 words)

	internet culture
		The notion of profundity in this trichotomy acknowledges the influence of Martin Heidegger on the philosophy of technology, especially his The Question Concerning Technology.
		The stage is set for a critical illustration of balance utopianism, in the next section; then inherence dystopian; and then inherence instrumentalism; and finally some concluding remarks, including some caveats and qualifications about the framework just bruited.
		Reflecting on her experience and the experience of others with the new Apple and IBM PC computers, She conceived of the relationship of a person to her computer as one-on-one, a person alone with a machine.
	www.brandeis.edu /pubs/jove/HTML/V6/iculture.html (8643 words)

	Vladimir Solovyov [Internet Encyclopedia of Philosophy]
		Solovyov concludes, again as he always does, with a triadic distinction between the empirical subject, the logical subject and the philosophical subject.
		And although he labels the first the "soul," the second the "mind" and the third the "spirit," the trichotomy is contrived and the labeling, at best, imaginative with no foundation other than in Solovyov's a priori architectonic.
		Solovyov's relatively early death, brought on to some degree by his erratic life-style, precluded the completion of his last philosophical work.
	www.iep.utm.edu /s/solovyov.htm (6701 words)

	CATHOLIC ENCYCLOPEDIA: Fathers of the Church
		The Old Testament was to him full of errors, lies, and blasphemies, so far as the letter was concerned, and his defence of it against the pagans, the Gnostics, and especially the Marcionites, was to point only to the spiritual meaning.
		Theoretically he distinguished a triple sense, the somatic, the psychic, and the pneumatic, following St. Paul's trichotomy; but in practice he mainly gives the spiritual, as opposed to the corporal or literal.
		St. Augustine sometimes defends the Old Testament against the Manichaeans in the same style, and occasionally in a most unconvincing manner, but with great moderation and restraint.
	www.newadvent.org /cathen/06001a.htm (17381 words)

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