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Topic: Limit superior and limit inferior

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	Limit superior and limit inferior
		In mathematics, the limit inferior and limit superior of a sequence can be thought of as limiting bounds on the sequence.
		The value of this limit inferior is conjectured to be 2 - this is the Twin Prime Conjecture - but as yet has not even been proved finite.
		The power set P(X) of a set X is a complete lattice, and it is sometimes useful to consider limits superior and inferior of sequences in P(X), that is, sequences of subsets of X.
	www.ebroadcast.com.au /lookup/encyclopedia/li/Lim_sup.html (340 words)

	Limit superior and limit inferior - Wikipedia, the free encyclopedia
		In mathematics, the limit inferior and limit superior (also called infimum limit and supremum limit, or liminf and limsup) of a sequence can be thought of as limiting bounds on the sequence.
		Whenever the ordinary limit exists, the limit inferior and limit superior are both equal to it; therefore, each can be considered a generalization of the ordinary limit which is primarily interesting in cases where the limit does not exist.
		Limits inferior/superior are related to big-O notation in that they bound a sequence only "in the limit"; the sequence may exceed the bound.
	en.wikipedia.org /wiki/Limit_superior_and_limit_inferior (1006 words)

	Gray, Henry. 1918. Anatomy of the Human Body. Page 824
		The superior temporal gyrus lies between the posterior ramus of the lateral fissure and the superior temporal sulcus, and is continuous behind with the supramarginal and angular gyri.
		The inferior temporal gyrus is placed below the middle temporal sulcus, and is connected behind with the inferior occipital gyrus; it also extends around the infero-lateral border on to the inferior surface of the temporal lobe, where it is limited by the inferior sulcus.
		Lateral to this fissure is the narrow tentorial part of the inferior temporal gyrus, and medial to it the fusiform gyrus, which extends from the occipital to the temporal pole; this gyrus is limited medially by the collateral fissure, which separates it from the lingual gyrus behind and from the hippocampal gyrus in front.
	www.bartleby.com /107/pages/page824.html (446 words)

	PlanetMath: limit of sequence of sets
		denote the limit superior and the limit inferior of
		Having shown both the existence and equality of the limit superior and limit inferior of the
		This is version 5 of limit of sequence of sets, born on 2005-02-06, modified 2006-01-12.
	planetmath.org /encyclopedia/LimitOfSequenceOfSets.html (300 words)

	PlanetMath: Banach limit
		Like the limit superior and limit inferior, the Banach limit can be applied for situations where one wants to algebraically manipulate limit equations or inequalities, even when it is not assured beforehand that the limits in question exist (in the classical sense).
		-- the Banach limit of a constant sequence is that constant.
		This is version 4 of Banach limit, born on 2005-07-08, modified 2005-07-09.
	planetmath.org /encyclopedia/BanachLimit.html (440 words)

	Gray, Henry. 1918. Anatomy of the Human Body. Page 1201
		the groove between the duodenum and the right lateral and lower borders in front are the anastomosing superior and inferior pancreaticoduodenal arteries; the common bile duct descends behind, close to the right border, to its termination in the descending part of the duodenum.
		The superior mesenteric artery passes down in front of the left half across the uncinate process; the superior mesenteric vein runs upward on the right side of the artery and, behind the neck, joins with the lienal vein to form the portal vein.
		The inferior surface (facies inferior) is narrow on the right but broader on the left, and is covered by peritoneum; it lies upon the duodenojejunal flexure and on some coils of the jejunum; its left extremity rests on the left colic flexure.
	www.bartleby.com /107/pages/page1201.html (716 words)

	Special Study: Display of Customer Limit Orders
		Because of the importance of limit order display to our markets, and indications that many limit orders are not being handled appropriately, the examination staff will focus efforts on ensuring that specialists and OTC market makers comply with limit order display obligations, and when appropriate, will refer serious violations to the Division of Enforcement.
		Limit orders compete for trades because limit orders that are displayed have a greater chance of attracting other orders in the market.
		The exchange represented that it reviewed limit order display compliance as part of each of the 322 investigations and found no instances in which the order(s) were not displayed in accordance with the exchange's rules and, therefore did not discipline any dealers for failing to display the best available customer limit orders.
	www.sec.gov /news/studies/limitorder.htm (10546 words)

	eMedicine - Brown Syndrome : Article by Kenneth Wright, MD
		Inferior orbital fibrous adhesions to the posterior globe are caused by the following: orbital floor fracture and fat adherence syndrome associated with inferior orbital trauma.
		A significant limitation of elevation in abduction is present in 70% of patients, but it is the difference between elevation in adduction versus elevation in abduction that differentiates Brown syndrome from such disorders as double elevator palsy (where elevation is equal to or worse in abduction).
		Superior oblique and trochlear luxation consists of removing the tendon from the trochlea by luxating the trochlea.
	www.emedicine.com /oph/topic552.htm (3271 words)

	Limitations of Nanoweapons
		These limits mean that countermeasures based on pre-nano technologies are often effective at slowing the advance of nanoweapons and sometimes capable of stopping nanotechnology altogether.
		Nanotech devices are limited to using ultraviolet light or visible light in the blue to violet range as a medium of sensing or as a photovoltaic power source.
		This well-known limitation means that purely military installations that require protection from nanoweapons are often built in places that are poor in those frequencies of light.
	www.orionsarm.com /tech/Limitations_of_Nanoweapons.html (2787 words)

	Springer Online Reference Works (Site not responding. Last check: 2007-11-03)
		The upper (lower) limit of a sequence is the largest (respectively, smallest) limit among all partial (finite and infinite) limits of a given sequence of real numbers.
		The upper limit is also called the limes superior or limit superior, and the lower limit the limes inferior or limit inferior.
		The limit superior and limit inferior of a sequence of subsets
	eom.springer.de /U/u095830.htm (453 words)

	Approaching Web services transactions (Site not responding. Last check: 2007-11-03)
		Inferior is not bound to initiate a cancellation action on the expiry of timeout; it takes a cancellation decision at its own discretion, which could even be before the expiry of timeout.
		This time limit allows a Superior to tell Inferiors that they should be prepared to hold on to their promises after a prepared message is sent for a minimum period of time.
		This indicates to the Inferior that the Superior is aware of the contradictory decision taken by it.
	www-128.ibm.com /developerworks/webservices/library/ws-tranart (7436 words)

	limit
		If the system cannot compute a limit, but can assert that the function f is bounded when x approaches x0, then a bounding interval, of type Dom::Interval, for f(x) in a sufficiently small neighborhood of x0 is returned if the option Intervalsis selected.
		limit works on a symbolic level and should not be called with arguments containing floating point arguments.
		For cases where a limit cannot be computed, you can make limit issue a warning with a possible reason, as shown in examples 5.
	www.sciface.com /support/doc/40/en/stdlib/limit.html (688 words)

	Neuro Lab 1
		Of the three peduncles (superior, middle and inferior) which attach it to the brainstem, the middle is the largest.
		Next, identify superior to the lateral cerebral fissure: the central sulcus (fissure of Rolando), the precentral sulcus and the postcentral sulcus (Fig.
		The inferior aspect of the temporal lobe is bounded medially by a broad cortical strip, the (para)hippocampal gyrus (Fig.
	web.indstate.edu /thcme/duong/Neuroscience/Schedule/NeuroLab1.html (2320 words)

	Developing Intelligence: Multiple Capacity Limitations for Visual Working Memory
		A fundamental debate concerns whether memory capacity limitations may be due to some central bottleneck, or whether there is an array of lower-level limitations that give rise to the simple "span" measures, or to the magic number "seven plus or minus two," frequently observed in behavioral experiments.
		In the March issue of Nature, Xu & Chun describe their work to dissociate the contributions of inferior and superior intraparietal sulcus to visual short term memory, based on a visual short-term memory task in which both set size and object complexity was manipulated.
		To further investigate whether VSTM capacity limits are due to item complexity, number of items, or both, Xu and Chun had subjects attempt to detect a change in the shape of 1 item from a display of 1, 2, 3, 4, or 6 "simple" or "complex" objects, while inside an fMRI magnet.
	develintel.blogspot.com /2006/07/multiple-capacity-limitations-for.html (733 words)

	[No title] (Site not responding. Last check: 2007-11-03)
		For the superior and inferior recti, turning the eye outward (abduction) by approximately 25 degrees places the superior rectus in position to raise the eye and the inferior rectus to lower the eye.
		The inferior division of the oculomotor nerve innervates inferior rectus, inferior oblique, and medial rectus.
		The correct answer is: Superior fornix of the conjunctiva Lacrimal fluid is produced by the lacrimal gland, which lies in a fossa in the superolateral part of each orbit.
	www-personal.umich.edu /~benwei/cgi-data/shared/linked/Eye(PQ).doc (2811 words)

	eMedicine - Brown Syndrome : Article Excerpt by: Kenneth Wright, MD (Site not responding. Last check: 2007-11-03)
		Brown attributed the limited elevation to a short or tight anterior superior oblique tendon sheath.
		Subsequent studies confirmed the cause of the syndrome to be a tight or inelastic superior oblique tendon.
		In constant or intermittent acquired Brown syndrome, reduced telescoping elongation of the superior oblique tendon would be due to one of the following: vascular dilatation of the tendon sheath vessels and local edema occurring within the confined area of the trochlea.
	www.emedicine.com /oph/byname/brown-syndrome.htm (445 words)

	John Locke's Limited State
		He explains that legislative power is superior to executive power and that the power of the government must be limited by law.
		Limited rule is justified under a government that gains its authority from the people and holds its power in trust for their benefit.
		The natural fact of spoilage drastically limits property in the state of nature and acts as a type of rule to maintain a fair distribution of goods in the state of nature.
	rebirthofreason.com /Articles/Younkins/John_Lockes_Limited_State.shtml (5818 words)

	Technology Liquidmetal Technologies
		The superior properties of Liquidmetal alloys are made possible by revolutionary scientific and technological innovations.
		This is in distinct contrast to conventional metals where the as-cast forms have inferior mechanical properties compared to their wrought and forged forms, which limits the fabrication of intricate and sophisticated designs.
		This very unique combination of superior properties in the domain of high-strength metals and the fabrication characteristics of plastics positions the family of Liquidmetal alloys as the new paradigm in materials science.
	www.liquidmetal.com /technology/default.asp (624 words)

	Limit of a function - Wikipedia, the free encyclopedia
		In mathematics, the limit of a function is a fundamental concept in mathematical analysis.
		The limit of a function f(x) as x approaches c is a number L with the following property: given any target neighborhood of L, there is a neighborhood of c over which the values of f(x) remain within the target neighborhood.
		This explicit statement is quite close to the formal definition of the limit of a function with values in a Hausdorff topological space.
	en.wikipedia.org /wiki/Limit_of_a_function (1610 words)

	Beating the 50 lines per mm Resolution Limit (Site not responding. Last check: 2007-11-03)
		See film resolution limits table for a listing of common films and their resolution limits with real-world average contrast scenes (1:1.6).
		Autofocus cameras are inherently limited to around 50-60 lpmm, based on the discrete nature of their sensors and other technical issues.
		It may be a film limitation, since the Summicron 90, at least, is supposed to be able to do far better than this (around 100 lp/mm, even out at the edges of the field, and even wide open).
	medfmt.8k.com /mf/limits.html (9903 words)

	Lim sup and Lim inf
		That is the purpose of the concept of "limit superior" (or "upper limit") and "limit inferior" (or "lower limit").
		Notice that it is implicit in the definition that every real sequence has a limit supremum and a limit infimum.
		As we predicted in the remark, the lim inf is the least subsequential limit, and the lim sup is the greatest subsequential limit.
	www.utdallas.edu /~mackey/webproject.htm (493 words)

	Darse's No-Limit Hold'em Tournament Primer
		The difference with having early callers already in the pot is that they are more likely to call a raise, so your chance of winning the pot uncontested is greatly reduced compared to being the first one in.
		If you have AA, KK, or QQ, or some other hand you believe to be superior to the raiser's, then re-raise the size of the pot or move all-in with your whole stack.
		In limit Hold'em, these hands can be quite powerful because the small bet sizes ensure that it will almost always be correct to call on the turn as well.
	www.cs.ualberta.ca /~darse/Papers/no-limit-tnmt-primer.html (4501 words)

	Math Forum - Ask Dr. Math Archives: College Analysis
		I assumed from the graph that the function had a limit at x=0 of 0, but since it involves sin(1/0) I can not prove this using the basic trigonometric limits (sin x/x and (1-cos x)/x), L'Hopital's rule, or by rearranging the equation.
		We are required to find a limit (informally), then prove that our answer is correct by using the formal definition of limits.
		Epsilon-delta definitions of the limit of a function and the limit of a sequence.
	mathforum.org /library/drmath/sets/college_analysis.html?s_keyid=12471862&f_keyid=12471863&start_at=41&num_to_see=40 (1002 words)

	Pelvis and Perineum Objectives
		The superficial pouch is between the inferior fascia of the UG diaphragm and Colles’ fascia.
		The deep pouch is between the superior and inferior fascia of the UG diaphragm.
		Inferior rectal nerves (branches of Pudendal N.)// sensitive to pain, touch, and temperature.
	www.meddean.luc.edu /depts/camplife/studorgs/2002/docs/pelvis-per.html (1411 words)

	DoctorYourself.com - Supplement Dose Limits
		The validity of an "upper limits" standard may later be called into question should the public not have a voice in their formation.
		There is concern that the establishment of "tolerable upper limits" would cause some consumers to needlessly seek the counsel of a physician or other health professional when high-dose vitamin usage is in question.
		Specifically, if an upper limit of consumption is established for magnesium, and excessive dosage may produce known symptoms of "loose stool," then this fact should be provided to consumers with the notation that the remedy is to reduce the dosage and that this symptom is completely reversible.
	www.doctoryourself.com /supplement_limit.html (4309 words)

	MUG: Limit Superior & Limit Inferior (9.11.02) (Site not responding. Last check: 2007-11-03)
		I would like to know, if there is a Maple command for building the Limit Superior or Limit Inferior respectivly.
		But it will not be very powerful, because in many cases limit just returns undefined even though there may be a lim sup.
		Maple's ordinary limit command sometimes returns results as a range.
	www.math.rwth-aachen.de /mapleAnswers/html/1627.html (215 words)

	Superior Culture Policy (Site not responding. Last check: 2007-11-03)
		The new policy, conceived as a response to the state's multicultural education policy, is the handiwork of the board's chairman, Pat Hart, who describes herself as a patriot, a Christian and a Republican.
		In 1992 she was joined by two other religious conservatives who, like her, espouse the views of the Christian Coalition, a group founded by Pat Robertson, and with their support, she became board chairman.
		Hart or her allies have also sought to limit sex education, to mandate creationism in the science curriculum and to limit some reading material in schools, primarily children's books by Shel Silverstein.
	www.cofc.edu /hettinger/Intro_to_Philosophy_Sp_05/Superior_Culture_Policy.htm (932 words)

	Liquidmetal Technologies News and PR
		Another unique characteristic of Liquidmetal alloys is the availability of its superior mechanical properties in as-cast form.
		The solidification of Liqudmetal alloys shows fundamentally distinct characteristics compared to the solidification of ordinary metals due to the lack of phase transformation from the molten metal state during solidification.
		Liquidmetal alloys also have a superior elastic limit, that is the ability to retain its original shape (memory) after undergoing very high loads and stress.
	www.liquidmetal.com /news/dsp.news.11x104.asp (1104 words)

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