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Topic: Completed infinity

Related Topics

Ultraintuitionism

Absolute Infinite

Mathematical intuitionism

Intuitionistic logic

Heyting algebra

Stephen Kleene

Luitzen Egbertus Jan Brouwer

Bantu

Constantinople

	infinity
		Infinity is merely a way of speaking, the true meaning being a limit which certain ratios approach indefinitely close, while others are permitted to increase without restriction.
		By confining their attention to potential infinity, mathematicians were able to address and develop crucial concepts such as those of infinite series, limit, and infinitesimals, and so arrive at the calculus, without having to grant that infinity itself was a mathematical object.
		This infinity of spatial points, known as the power of the continuum, c, is the set of all real numbers (all rational numbers plus all irrational numbers).
	www.daviddarling.info /encyclopedia/I/infinity.html (1638 words)

	Potential vs. Completed Infinity
		Completed infinity, or actual infinity, is an infinity that one actually reaches; the process is already done.
		Infinity cannot be found in the physical universe.
		But more complicated notions such as infinity, less grounded in physical reality, are harder to explain; it is harder to be sure that we are successfully conveying a concept from the inside of one head to the inside of another.
	www.math.vanderbilt.edu /~schectex/courses/thereals/potential.html (1976 words)

	RedOrbit - Science - Infinity Reports Strong Operational Results and Continued Progress in the Fort Worth Basin
		Infinity Oil and Gas of Texas, Inc. ("Infinity-Texas") announced that a previously-announced 3-D seismic survey in Erath County, which was sponsored by another operator and which generally overlies Infinity-Texas' current and near-term operations, has been completed.
		Infinity continues to expect the execution of the development and production contract with the government of Nicaragua during the third quarter and will commence a technical evaluation process thereafter to assess the prospect and potentially market the prospect to a larger industry partner or partners.
		Infinity, Inc., through its wholly-owned subsidiaries Infinity Oil and Gas of Texas, Inc. and Infinity Oil & Gas of Wyoming, Inc., is an independent energy company engaged in the exploration, development and production of natural gas and oil and the operation and acquisition of natural gas and oil properties.
	www.redorbit.com /news/display?id=205249&source=r_science (1907 words)

	petroleumworld
		In May 2003, Infinity was awarded 24 blocks of acreage, consisting of approximately 1.4 million acres, and entered into the negotiation process with the Instituto Nicaraguense de Energia ("INE") to finalize the initial exploration and production contracts for the two underlying prospects (Tyra and Perlas).
		Infinity's management and consultants believe that: (i) numerous analogies can be made between the Infinity concession blocks and production from fractured Cretaceous carbonates in Mexico, Venezuela and Guatemala and (ii) the presence of Cretaceous source rocks onshore Honduras and Nicaragua can be projected into the offshore Caribbean Shelf.
		Infinity's management and consultants believe that there are five distinct, large structures which underlie its acreage, each of which could potentially hold substantial oil and gas reservoirs.
	www.petroleumworld.com /story06051612.htm (908 words)

	Nirvikalpa
		Infinity is the state of becoming and can never have an end for it is never completed.
		Infinity has to do with value fulfillment, and the unfoldings of ever new possibilities, the exploration of moment points, the traveling through dimensions that ever creates the illusion of time.
		Infinity contains all that will ever be known, and, of course, all that will ever be known is known within the spacious present.
	nirvikalpa.com /exercise.php4?row=76&book=TheEarlySessions,Book7 (740 words)

	The New Yorker: The Critics: Books (Site not responding. Last check: 2007-11-01)
		It arose amid ancient paradoxes, proceeded to baffle philosophers for a couple of millennia, and then, by a daring feat of intellect, was finally made to yield its secrets in the late nineteenth century—though not without leaving a new batch of paradoxes.
		Others, however, dismissed Cantor’s infinity of infinities as a “fog on a fog” and “mathematical insanity.” Cantor felt persecuted by these critics, which worsened his nervous condition (he seems to have suffered from a bipolar disorder).
		Still, Wallace’s enthusiasm for the theory of infinity is evident on every page (not least in his conviction that Cantor is “the most important mathematician of the nineteenth century,” a view that few mathematicians or intellectual historians would agree with).
	www.newyorker.com /critics/books/?031103crbo_books (2375 words)

	Cantor's Concept of Infinity:
		Cantor introduced into mathematics the notion of a completed set, so that the integers, for example, could be considered together as a set in themselves, and so as a completed infinite magnitude.
		Gutberlet was concerned to show that actual, completed, mathematical infinity did not challenge the unique, absolute infinity of God's existence.
		That the transfinites cannot be completely understood out of themselves is a specific example illustrating that the universe cannot be understood out of itself.
	www.asa3.org /ASA/PSCF/1993/PSCF3-93Hedman.html (5863 words)

	Hector Parr's Essays: Infinity
		This paper asks why so few philosophers and scientists have turned their attention to the idea of infinity, and it expresses surprise at the readiness with which infinity has been accepted as a meaningful concept even in fields where it causes serious logical difficulties.
		The idea of infinity has been used increasingly over the centuries by mathematicians, and in general they have been more circumspect than have astronomers in their use of the word.
		Cantor and others were not able to treat in a similar fashion their discussion of the equality or inequality of the different infinities they had discovered, but it must be conceded that their arguments had no relevence in the real world of material particles and real magnitudes.
	www.c-parr.freeserve.co.uk /hcp/infinity.htm (4801 words)

	Peter Suber, "Infinite Reflections"
		They constitute a completed or actual infinity when they are all bundled together and said to form a set of some definite cardinality.
		Cantor not only flew in the face of the traditional objection to completed infinities, he used completed infinities in the form of infinite sets as an intrinsic part of his solution to the classical paradoxes of the infinite.
		Those who argued that completed infinities are self-contradictory appeal to the apparent contradictions contained in the classical paradoxes like Galileo's.
	www.earlham.edu /~peters/writing/infinity.htm (11084 words)

	Mathematics: Reality And Infinity - Objectivism Online Forum
		Ayn Rand and Leonard Peikoff both made reference to mathematical concepts such as infinity for specific purposes in their writing, but Objectivism, as general philosophy, does not depend on technical concepts of advanced sciences such as mathematics or physics, and in particular does not depend on technical concepts of infinity in advanced mathematics.
		Cantor, who was a mystic, of course thought that he had demonstrated a whole world of actual infinities in a regular "order" extending all the way to the infinity of all infinities at the end, which was supposed to be God.
		All of these mathematical concepts show how to properly conceptualize infinite processes in strictly finite terms and without invoking any notion of a "completed infinity" for either the processes or the collection of numbers to which they apply (although it is often not presented that way when dealing with infinite sets).
	forum.objectivismonline.net /index.php?showtopic=2064 (5265 words)

	INFINITY AND THE PAST
		This argument is based on a fallacy of equivocation with respect to the phrases “actual infinity” and “potential infinity.” Whitrow’s proof that the past if infinite is “actually infinite” is based on a different sense of “actually infinite” than that belonging to his proof that an “actually infinite past” is impossible.
		For if the past is an “actual infinity” in the sense of being an infinity of events that have really occurred, it does not follow that it is also an “actual infinity” in the sense that some past events are separated from the present event by an infinite number of intermediate events.
		Another thesis common to several of the contemporary “anti-infinitists” is the belief that an actual or completed infinity cannot be instantiated in the past since the set of past events is never completed but is always being added to.
	www.qsmithwmu.com /infinity_and_the_past.htm (5159 words)

	PRESS RELEASE Medico Labs Going Public via Satellite Organizing Solutions; Infinity Capital Group to Invest in Medico (Site not responding. Last check: 2007-11-01)
		Infinity has agreed to use its best efforts to make a $1,000,000 minimum investment in Medico in the form of a two-year convertible note by April 30, 2005, and to provide Medico with bridge financing of $250,000 on the date that the merger is completed.
		Infinity Capital Group, Inc. (http://www.infinitybdc.com) is a private investment firm that intends to be regulated as a Business Development Corporation under the Investment Company Act of 1940, as amended.
		Infinity is an active investor in the Companies to which it provides its services and focuses on companies that are seeking to become publicly traded through a reverse merger.
	www.marketwire.com /mw/release_html_b1?release_id=80133 (738 words)

	Infinity, St. Thomas Villa (Site not responding. Last check: 2007-11-01)
		An electronic gate gives privileged access to Infinity's lushly landscaped grounds; the moment you enter, you'll be enchanted with the beautifully-designed floorplan and its inviting interiors, elegant and superbly equipped but ultimately comfortable and relaxing.
		Thomas beckons - it has an infinity edge and artistically tiled with mosaic tile in many shades of blue, dotted with palm trees, and bordered by a hot tub on one end and a romantic gazebo on the other.
		Infinity is truly in a realm of its own, beautifully designed and executed with a refined touch, and offers many delightful and luxurious details.
	www.islandhideaways.com /villa.php?villa_id=10217 (564 words)

	Company History - Infinity Construction Company, Inc
		INFINITY Construction Co., Inc. was incorporated in Ohio on November 20, 1996 and began its business operations on January 1, 1997.
		Infinity continues to build on its reputation for on time and on budget project performance coupled with superior quality and client satisfaction.
		Infinity provides an array of construction services to meet the specific project requirements of each project.
	www.infinityconstruction.com /history.html (176 words)

	PRESS RELEASE Infinity Mining's Audit Is Completed (Site not responding. Last check: 2007-11-01)
		Infinity Mining Corp.'s second goal is completion of all filings required for Bulletin Board recognition.
		There are several commercially successful methods for recovering metals, but Infinity Mining Corp. (Canada) has developed a patent pending extraction method that recovers substantially more precious metal from the ore than any extraction methods currently in use.
		Infinity Mining Corp. (Canada) assumes no obligation to update these forward-looking statements, and does not intend to do so.
	www.marketwire.com /mw/release_html_b1?release_id=113037 (375 words)

	Paradoxes Resolved, Origins Illuminated - Hilberts hotel
		Cantor's diagonal proof of different cardinalities of infinities and his one to one correspondence discriminating between countable and uncountable infinities is pretty controversial actually.
		(assumes an infinite list is completed) which then led to a circular argument (since he assumes, instead of having proven, that he has generated a new number using his diagonal method to prove that the number is not in the original list).
		An infinite set is complete when it is defined even if its members are defined by the infinite iterations of some function.
	www.metaresearch.org /msgboard/topic.asp?TOPIC_ID=483&whichpage=2 (2473 words)

	Time, Successive Addition, and Kalam Cosmological Arguments
		According to one of these sub-arguments, it is impossible for there to be completed infinities: since the past would be a completed infinity if it were infinite, it follows that the past must be finite.
		According to the other of these sub-arguments, it is impossible for there to be completed infinities formed by successive addition: since the past would be a completed infinity formed by successive addition if it were infinite, it follows that the past must be finite.
		Where there is genuine continuity, there is--in at least one good sense--completed infinity; but the familiar puzzle cases pose no kind of challenge to this kind of completed infinity.
	www.infidels.org /library/modern/graham_oppy/gifford.html (3941 words)

	RIGZONE - Infinity Reports Progress in Texas and Nicaragua
		Infinity's management believes the first new well had a lower-than-average peak daily production rate, partially as a result of the use of variable completion rates and volumes in connection with micro-seismic conducted on this well.
		In addition, Infinity is using a second drilling rig to drill a vertical well in Comanche County, Texas, targeting both the Barnett Shale and the Lower Marble Falls formations.
		Infinity's previous 2006 drilling guidance of 18 to 20 horizontal wells in Erath County via use of a drilling rig under long-term contract and a limited number of wells in Comanche and Erath counties with a second drilling rig remains unchanged.
	www.rigzone.com /news/article.asp?a_id=31142&rss=true (530 words)

	RIGZONE - Infinity Wins 24 Blocks Offshore Nicaragua
		Infinity, Inc. has been awarded 24 blocks totaling approximately two million acres in the first international Nicaraguan oil and gas offshore tender.
		"The award gives Infinity two contracts in an area that has previously been proven to contain hydrocarbons and is west of the territory claimed by Colombia and south of the territory claimed by Honduras.
		Hydrocarbons were detected in 10 of the wells; in three of these, oil flowed to the surface from the shallow Eocene formation, including a well drilled by Shell in the late 1960s.
	www.rigzone.com /news/article.asp?a_id=6680 (470 words)

	A Tale of Two Paradoxes
		David Foster Wallace refers to the "infinity" of transfinite theory as a "hyper-abstraction." This description encapsulates the goal of the transfinite theorists.
		One of the strangest things about infinity is that there is no way to express a completed infinity with a finite number of characters from a finite alphabet.
		The new view of infinity as some sort of hyper-abstraction that forms the foundation of universe filled with Platonic forms is a step backward.
	descmath.com /diag/tale.html (9210 words)

	MIND Exchange
		Infinity is really one of the simplest concepts to grasp, once you stop trying to fit it into your finite imagination.
		Infinity, in my opinion, is just a tool we use to try and understand the universe as we perceive it.
		The trouble with trying to conceive of infinity, then, is to try to think of it as a static state, when possibly it is better thought of as an active twoness.
	www.kurzweilai.net /mindx/show_thread.php?rootID=45570&o=date (608 words)

	Infinity Pharmaceuticals Merger Provides Public Solution :: Bio-IT World
		Infinity Pharmaceuticals, a pioneer in the field of chemical genomics small molecule drug discovery for cancer, is to merge with publicly traded Discovery Partners International (DPI), based in San Diego.
		This merger is a creative and cost-efficient means by which Infinity gains access to public markets and the necessary capital to pursue development of important new medicine.” Holtzman says Infinity aims to have at least one new drug enter clinical trials each year over the next several years.
		Infinity employs about 100 staff, or as Holtzman calls them, “citizen owners.” Together with president and CSO Julian Adams and chief business officer Adelene Perkins, Holtzman will assume management of the newly company.
	www.bio-itworld.com /newsitems/2006/april/04-12-06-news-infinity (1178 words)

	[No title]
		If it be insisted that the infinite reward is actual a double infinity of an eternity of infinite happiness, this could be handled in a similar fashion by taking also the limit of a boundless H as it approaches infinity.
		One might object that the infinity thus approached is only a potential infinity, not an actual completed infinity.
		To this we respond that, first of all, it is not clear that Pascal's Wager requires an actual, completed infinity.
	www.csc.twu.ca /byl/wager.fin.doc (1909 words)

	President's Message - Infinity Construction Company, Inc
		At Infinity, we are well aware that our success in recent years and the growth that we have enjoyed must be credited to both our clients and our subcontractors.
		It is because of your efforts and our partnerships with all of you that Infinity has not only stayed the course in the recent difficult years in our industry, but has in fact grown while others simply tried to survive.
		In February Infinity completed the interior renovation and construction of the 90,000 s.f.
	www.infinityconstruction.com /pres-message.html (410 words)

	The Kalam Cosmological Argument Yet Again: The Question of the Metaphysical Possibility of an Infinite Temporal Series
		But this response is clearly inadequate, for the years of an infinite past could be enumerated by the negative numbers, in which case a completed infinity of years would, indeed, entail a countdown from infinity [i.e., countdown through an infinity].
		For (1) then he would have completed an actual infinite by successive addition, which is impossible because you can always add one more, and (2) as we saw with Tristam Shandy, the man's task would have always been done, and hence never been done, which is contrary to our seeing him doing it now.
		An infinite temporal series, just as any other real infinite, is never completed but always complete, in the sense that it does not involve a necessarily-always-finite set which never can be completed so as to be an infinite set by the addition of members.
	www.infidels.org /library/modern/arnold_guminski/kalam2.shtml (8642 words)

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