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Topic: Induction

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	PlanetMath: induction
		Induction is the name given to a certain kind of proof, and also to a (related) way of defining a function.
		Proof by induction is a variety of proof by contradiction, relying, in the elementary cases, on the fact that every non-empty set of natural numbers has a least element.
		This is version 11 of induction, born on 2002-02-19, modified 2005-02-28.
	planetmath.org /encyclopedia/Induction.html (861 words)

	Giving birth: Is induction for convenience safe?
		Induction of labor, by whatever means, holds fundamental risks to mother and child and comes at a higher economic cost as well.
		Invalid reasons for induction include: discomfort in the last few days of pregnancy, a normal pregnancy that goes beyond the due date, a doctor who is going out of town, a planned visit by a family member, new jobs, trips and tax relief.
		Although the literature is divided on whether or not induction of labor leads to a higher incidence of cesarean birth, it is an intervention which tends to medicalize the birth process and takes control away from the mother and father.
	parenting.ivillage.com /pregnancy/plabor/0,,45s3,00.html (1000 words)

	Induction (philosophy) - Wikipedia, the free encyclopedia
		Induction or inductive reasoning, sometimes called inductive logic, is the process of reasoning in which the premises of an argument support the conclusion, but do not ensure it.
		The classic philosophical treatment of the problem of induction, meaning the search for a justification for inductive reasoning, was by the Scotsman David Hume.
		Induction is sometimes framed as reasoning about the future from the past, but in its broadest sense it involves reaching conclusions about unobserved things on the basis of what is observed.
	en.wikipedia.org /wiki/Induction_(philosophy) (1148 words)

	CATHOLIC ENCYCLOPEDIA: Induction
		Induction is the conscious mental process by which we pass from the perception of particular phenomena (things and events) to the knowledge of general truths.
		Although induction is equally applicable in all departments of generalization from experience, in the historical and anthropological no less than in the physical sciences, still it is in its application to the discovery of the causes and laws of physical phenomena, animate and inanimate, that it lends itself most readily to logical analysis.
		Induction is really a logical method involving many stages and processes besides the central step of generalization itself; and it is opposed to deduction only in the sense that it approaches reality from the side of the concrete and individual, while deduction does so from that of the abstract and universal.
	www.newadvent.org /cathen/07779a.htm (2653 words)

	The Problem of Induction, by Sir Karl Popper
		In other words, the logical problem of induction arises from (1) Hume's discovery (so well expressed by Born) that it is impossible to justify a law by observation or experiment, since it 'transcends experience'; (2) the fact that science proposes and uses laws 'everywhere and all the time'.
		The place of the problem of induction is usurped by the problem of the comparative goodness or badness of the rival conjectures or theories that have been proposed.
		Induction is logically invalid; but refutation or falsification is a logically valid way of arguing from a single counterinstance to - or, rather, against - the corresponding law.
	www.dieoff.org /page126.htm (13219 words)

	The Induction Cooktop (Site not responding. Last check: 2007-10-22)
		The induction cooktop, while not yet a part of most households, is becoming increasingly accepted as a useful, energy efficient method of preparing food.
		Induction cooktops can be used with any type of food, and will cook as throughly and evenly as any electric or gas range.
		Although induction ranges are currently more expensive than their electric or gas counterparts, when all of these advantages are taken into account, the induction cooktop will definitely pay for itself.
	stuweb.ee.mtu.edu /~mtromble/induction/cooktops.html (801 words)

	Induction coils (Site not responding. Last check: 2007-10-22)
		Page's induction coil employed a primary coil of some turns of heavy copper around a bundle of soft iron rods and a secondary coil of many turns of fine wire wrapped on the outside of this primary coil.
		Ruhmkorff, from Hannover, around the middle of the nineteenth century was able to improve Callan's two-winding induction spark-coils, on the basis of the research conducted in Paris by Masson and Breguet in 1842, in such a way that since then these devices bear his name.
		Induction coils were rated according to the length of their sparks, and many a laboratory prided itself on the length of the spark their induction coil could jump.
	chem.ch.huji.ac.il /~eugeniik/instruments/archaic/induction_coils.htm (751 words)

	CS312 Induction Examples (Site not responding. Last check: 2007-10-22)
		While it discusses briefly how induction works, you are encouraged to read the Induction Handout for a more thorough discussion of induction.
		Induction is really important, so the best thing to understand induction is to do it yourself.
		Induction is a powerful method of proof, but in the wrong hands it can be dangerous.
	www.cs.cornell.edu /courses/cs312/2001sp/handouts/induct-examples.html (1416 words)

	USS Clueless - Inductive logic
		Induction can operate at many levels of sophistication, and it can be implemented at a level of practical usefulness with far less compute power than exists in the human brain.
		Induction increases in reliability as a function of how much data and experience and computational power are applied to it, but induction is never certain.
		Induction can never prove anything; all it can do is to assign an extremely high conviction level to it.
	denbeste.nu /cd_log_entries/2003/05/Inductivelogic.shtml (5479 words)

	Peter Suber, "Mathematical Induction"
		Prove that the property of complying with the theorem is "hereditary" and extends to all the successors of the minimal case.
		The induction step is the proof of a conditional statement, namely, "if the theorem is true of the ancestor case, then it is true of the descendant cases." The if-clause of this conditional statement, asserting that the theorem is true of the ancestor case, is called the induction hypothesis.
		Notice that the induction step is to prove a conditional statement, of which the induction hypothesis is the antecedent.
	www.earlham.edu /~peters/courses/logsys/math-ind.htm (1191 words)

	Induction (Site not responding. Last check: 2007-10-22)
		Induction means that your labor will start artificially and before your body initiates it on its own.
		Patient convenience inductions are on the rise as the induction conditioning has infiltrated our American society over the last couple of decades.
		If induction becomes necessary make sure you are informed of the benefits as well as the risks to yourself as well as the baby.
	www.icgold.net /mother/induction.html (736 words)

	Principle of Mathematical Induction
		Similarly the principle of mathematical induction is the means by which we have often proved (as opposed to defining) properties about numbers, or statements involving the natural numbers.
		The underlined portion, called the Induction hypothesis, is an assumption that is necessary for the conclusion to be proved.
		The proof of the induction step essentially tells us that the reasoning involved in proving the statement involving the other natural numbers is the same once the basis has been proved.
	www.cse.iitd.ernet.in /~suban/CSL102/lecture/node7.html (512 words)

	Educator Induction Programs (Site not responding. Last check: 2007-10-22)
		The intent of a teacher induction program is to provide a systematic structure of support for beginning teachers.
		Induction programs also have the potential of elevating the teaching profession and fostering a collaborative learning community for all educators.
		While the regulations took effect on October 1, 2001, it is the Department's expectation that districts are developing their programs and that most induction programs will be implemented with the start of the 2002-2003 school year.
	www.doe.mass.edu /eq/mentor/teachers.html (760 words)

	INDUCTION
		Induction of labour (the process where hormones cause contractions of the uterus (labour pains) to open the cervix is a fairly common and minor procedure that is currently done in about one in five pregnancies.
		When the cervix remains closed or unripe, it may be difficult to achieve adequate progress in labour and there is always a chance that the induction of labour may fail to have adequate contractions and progressive dilatation of the cervix.
		Induction of labour, when appropriate, is an intervention that should help you and your baby.
	www.wcox.com.au /inductio2.htm (1098 words)

	The Physics Classroom
		In the induction process, a charged object is brought near but not touched to a neutral conducting object.
		When an object is charged by induction, the charge received by the object is opposite the charge of the object which was used to charge it.
		During the induction process, there is never any movement of electrons from the charged object to the sphere.
	www.physicsclassroom.com /mmedia/estatics/isop.html (534 words)

	Mathematical Induction
		I found that what I wrote about geometric series provides a natural lead-in to mathematical induction, since all the proofs presented, other than the standard one, use mathematical induction, with the formula for each value of n depending on the formula for the previous value of n.
		It is a little like explaining why a row of dominoes will fall down after pushing the first one by showing that the fall of each domino causes the fall of the next one.
		To appreciate the power of mathematical induction, we will see in the next section how to create a proof for the geometric series formula in a somewhat mechanical manner.
	www.geocities.com /Athens/Delphi/5136/Induction.html (1109 words)

	Mechanism of adipose tissue iNOS induction in endotoxemia -- Kapur et al. 276 (4): 635 -- AJP - Endocrinology and ...
		Induction of diaphragmatic nitric oxide synthase after endotoxin administration in rats: role on diaphragmatic contractile dysfunction.
		In vivo and in vitro evidence for the involvement of tumor necrosis factor-alpha in the induction of leptin by lipopolysaccharide.
		Induction of L-arginine transport and nitric oxide synthase in vascular smooth muscle cells: synergistic actions of pro-inflammatory cytokines and bacterial lipopolysaccharide.
	ajpendo.physiology.org /cgi/content/full/276/4/E635 (4378 words)

	Welcome to Induction Dynamics
		Induction Dynamics is an official distributor of high performance brake systems from Baer Racing Inc. Baer produces upgrades for many car and truck applications.
		Induction Dynamics is an official distributor of high performance and racing fuel injector systems from RC Engineering.
		Induction Dynamics is an official distributor of Electromotive Inc.
	www.induction-dynamics.com /products.html (328 words)

	Mathematical Induction
		Mathematical Induction is way of formalizing this kind of proof so that you don't have to say "and so on" or "we keep on going this way" or some such statement.
		The idea is to show that the result is true for n=1 and then show how once you've shown it to be true for some integer, you can see that it must be true for the next one as well.
		Prove by induction that the sum 1 + 3 + 5 + 7 +...
	www.math.sc.edu /~sumner/numbertheory/induction/Induction.html (1878 words)

	Atkins Induction - Atkins Diet Induction Phase
		Purpose of Atkins induction phase is to start a change in our body metabolism, from burning fat rather than the carbohydrates.
		Depending on how much weight you need to lose, the induction phase lasts for a minimum of two weeks and a maximum of one year.
		Atkins enthusiasts recommend that you follow Induction until you have lost half of the weight you need to lose, and then go on to complete the Ongoing Weight Loss portion of the diet.
	www.the-atkins-diet.info /atkins-induction-phase.htm (709 words)

	Mathematical induction
		The hypothesis of Step 1) -- "The statement is true for n = k" -- is called the induction assumption, or the induction hypothesis.
		We have now fulfilled both conditions of the principle of mathematical induction.
		According to the principle of mathematical induction, to prove a statement that is asserted about every natural number n, there are two things to prove.
	www.themathpage.com /aPreCalc/mathematical-induction.htm (1019 words)

	Nebulised salbutamol administered during sputum induction improves bronchoprotection in patients with asthma -- Delvaux ...
		Figure 1 Time course of bronchoconstriction during sputum induction by inhalation of hypertonic or isotonic saline in 20 patients with moderate to severe asthma.
		Safety and reproducibility of sputum induction in asthmatic subjects in a multicenter study.
		Sputum induction in severe asthma by a standardized protocol: predictors of excessive bronchoconstriction.
	www.thoraxjnl.com /cgi/content/full/59/2/111 (2471 words)

	Induction (Site not responding. Last check: 2007-10-22)
		Induction indicates facts about the world beyond what we actually observe; but this also makes induction open to the possibility of error.
		Given the truth of the premisses, the conclusion is probably true, but even true premisses cannot guarantee a true conclusion.
		In induction the minor premiss is a CASE, as it is in deduction - a class subsumed under a rule that we propose to test.
	www.cuyamaca.net /bruce.thompson/Fallacies/induction.asp (284 words)

	Induction Proofs Lesson - I
		If you're reading this module, then you've probably just covered induction in your algebra class, and you're feeling somewhat uneasy about the whole thing.
		Induction makes perfect sense to him, and he honestly thinks he's explained it clearly.
		You have been working with some numbers, and have noticed something that seems to be a pattern.
	www.purplemath.com /modules/inductn.htm (592 words)

	Atkins Diet Induction Menu
		Spacing meals throughout the day atkins diet induction menu instead of eating heavy meals once or twice a day can help a person avoid extremely high or low blood glucose levels.
		Since the amount of protein needed depends on the amount of lean body mass and not fat ideal weight is atkins diet induction menu used instead of actual weight.
		Most people are unaware of the amount of protein and fat that is contained in the atkins diet induction menu foods they eat.
	www.b2-diet.com /vegetarian-diet-food/atkins-diet-induction-menu.htm (234 words)

	Atkins Diet Induction
		Atkins diet induction phase is crucial as it helps the atkins dieters jump-start their atkins diet weight loss program by severely limiting the total carbohydrate intake to 20 grams of net carbs daily.
		This is commonly referred to as "induction flu".
		Atkins induction phase meal plan requires the Atkins dieter to eat three regular-size meals a day, or four or five smaller meals.
	www.aboutatkinsdiet.com /atkins_diet_induction_phase.htm (777 words)

	About Induction Heating
		Although the basic principles of induction are well known, modern advances in solid state technology have made induction heating a remarkably simple, cost-effective heating method for applications which involve joining, treating, heating and materials testing.
		The basic components of an induction heating system are an AC power supply, induction coil, and workpiece (material to be heated or treated).
		The induction coil, typically made from copper tubing with a 1/8" to 3/16" diameter, is normally cooled with water.
	www.ameritherm.com /aboutinduction.html (981 words)

	Mathematical Induction
		Some of the statements of theorems which can be proved using mathematical induction involve an integer variable.
		This principle of strong mathematical induction is used for example to prove the result that every positive integer is a prime number, a power of a prime or a product of primes.
		As with the principle of mathematical induction, there is a variation on this to cover those statements that are true for all integers beyond a certain value
	www.math.csusb.edu /notes/proofs/pfnot/node10.html (291 words)

	Inducing labor (Site not responding. Last check: 2007-10-22)
		Castor oil is a strong laxative and stimulating your bowels may cause some contractions, but no good studies have proven it to be consistently effective, and you're likely to find the effect on your gut to be very unpleasant.
		There are a variety of herbs touted to be useful for labor induction, but their safety and effectiveness remains unproven.
		What's more, having a c-section after a failed induction is associated with higher rates of complications, especially infection, and longer hospital stays.
	www.babycenter.com /refcap/pregnancy/childbirth/173.html (1857 words)

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