User talk:Fjid NOTfjild

Welcome!

Hello, Fjid NOTfjild, and welcome to Wikipedia! I hope you like the place and decide to stay. Unfortunately, one or more of the pages you created, such as Axis of Irish evil, may not conform to some of Wikipedia's guidelines, and may soon be deleted.

There's a page about creating articles you may want to read called Your first article. If you are stuck, and looking for help, please come to the New contributors' help page, where experienced Wikipedians can answer any queries you have! Or, you can just type helpme on this page, and someone will show up shortly to answer your questions. Here are a few other good links for newcomers: I hope you enjoy editing here and being a Wikipedian! Please sign your name on talk pages using four tildes ( ~ ); this will automatically produce your name and the date. If you have any questions, check out Questions or ask me on my talk page. Again, welcome! ... disco spinster   talk  15:29, 7 July 2011 (UTC)
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Speedy deletion nomination of Axis of Irish evil


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If you think that this notice was placed here in error, contest the deletion by clicking on the button labelled "Click here to contest this speedy deletion," which appears inside of the speedy deletion tag (if no such tag exists, the page is no longer a speedy delete candidate). Doing so will take you to the talk page where you will find a pre-formatted place for you to explain why you believe the page should not be deleted. You can also visit the the page's talk page directly to give your reasons, but be aware that once tagged for speedy deletion, if the page meets the criterion, it may be deleted without delay. Please do not remove the speedy deletion tag yourself, but don't hesitate to add information to the page that would render it more in conformance with Wikipedia's policies and guidelines. ... disco spinster   talk  15:29, 7 July 2011 (UTC)

Speedy deletion nomination of Irish evil and rude


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If you think that this notice was placed here in error, contest the deletion by clicking on the button labelled "Click here to contest this speedy deletion," which appears inside of the speedy deletion tag (if no such tag exists, the page is no longer a speedy delete candidate). Doing so will take you to the talk page where you will find a pre-formatted place for you to explain why you believe the page should not be deleted. You can also visit the the page's talk page directly to give your reasons, but be aware that once tagged for speedy deletion, if the page meets the criterion, it may be deleted without delay. Please do not remove the speedy deletion tag yourself, but don't hesitate to add information to the page that would render it more in conformance with Wikipedia's policies and guidelines. ... disco spinster   talk  15:29, 7 July 2011 (UTC)

Speedy deletion nomination of Problem of Irish evil


Please refrain from introducing inappropriate pages, such as Problem of Irish evil, to Wikipedia. Doing so is not in accordance with our policies. If you would like to experiment, please use the sandbox.

If you think that this notice was placed here in error, contest the deletion by clicking on the button labelled "Click here to contest this speedy deletion," which appears inside of the speedy deletion tag (if no such tag exists, the page is no longer a speedy delete candidate). Doing so will take you to the talk page where you will find a pre-formatted place for you to explain why you believe the page should not be deleted. You can also visit the the page's talk page directly to give your reasons, but be aware that once tagged for speedy deletion, if the page meets the criterion, it may be deleted without delay. Please do not remove the speedy deletion tag yourself, but don't hesitate to add information to the page that would render it more in conformance with Wikipedia's policies and guidelines. ... disco spinster   talk  15:29, 7 July 2011 (UTC)

July 2011
This is your last warning; the next time you create an inappropriate page, you may be blocked from editing without further notice. Gurt Posh (talk) 15:31, 7 July 2011 (UTC)

You have been blocked indefinitely from editing for creating nonsense pages. If you would like to be unblocked, you may appeal this block by adding the text, but you should read the guide to appealing blocks first. Favonian (talk) 15:45, 7 July 2011 (UTC)

{ {unblock|1=I didn't realise these things weren't part of Wikipedia - I'd seen other humorous articles that had been listed for deletion and thought that if something was clearly not serious, and not damaging any other article, it was allowed. I didn't check the user page properly until after I'd created all of the pages. I apologise and won't create nonsense articles again.}} Since so far your only use of Wikipedia has been vandalism, you had better indicate what constructive editing you plan to do from now on, if you wish to be unblocked. JamesBWatson (talk) 16:33, 7 July 2011 (UTC)

My "Edit" tab is gone because I am blocked. How do I get the source?
 * You click on the "view source" tab that has appearede in its place. Reaper Eternal (talk) 18:10, 7 July 2011 (UTC)

DRAFT
Actual infinity is the idea that numbers, or some other type of mathematical object, can form an actual, completed totality; namely, a set. Hence, in the philosophy of mathematics, the abstraction of actual infinity involves the acceptance of infinite entities, such as the set of all natural numbers or an infinite sequence of rational numbers, as given objects.

Aristotle's potential–actual distinction
Aristotle handled the topic of infinity in Physics and in Metaphysics. Aristotle distinguished between infinity in respect to addition and in respect to division.

"But Plato has two infinities, the Great and the Small."

- Physics, book 3, chapter 4.

Aristotle also distinguished between actual and potential infinities. An actual infinity is something which is completed and definite and consists of infinitely many elements, and according to Aristotle, a paradoxical idea, both in theory and in nature. In respect to addition, a potentially infinite sequence or a series is potentially endless; being a potentially endless series means that one element can always be added to the series after another, and this process of adding elements is never exhausted.

"For generally the infinite has this mode of existence: one thing is always being taken after another, and each thing that is taken is always finite, but always different."

- Aristotle, Physics, book 3, chapter 6.

As an example of a potentially infinite series in respect to increase, one number can always be added after another in the series that starts 1,2,3,... but the process of adding more and more numbers cannot be exhausted or completed, because there is no end to the process.

In respect to division, a potentially infinite series of divisions is e.g. the one that starts as 1, 0.5, 0.25, 0.125, 0.0625. According to Aristotle, the process of division never comes to an end, and the limit value 0 is never reached, although the division can be continued as long as one wants. This is a crucial difference to the transfinitists, who start with the very notion that the limit value exists and is reached (this is not to say that 0 would not exist; zero is at our disposal).

"For the fact that the process of dividing never comes to an end ensures that this activity exists potentially, but not that the infinite exists separately."

- Metaphysics, book 9, chapter 6.

In contrast to the potential infinity, all the elements of an actually infinite (= transfinite) set are assumed to exist together simultaneously as a completed totality. The term 'transfinite' ought to be used instead of 'actually infinite' to denote the transfinite sets, because the set-theoretical notion of actual infinity has nothing to do with actualization in nature.

The Urantia Book Definition
In the Urantia Book both Absoluta and Absolutum are discussed in detail and is connected with divine values. According to the glossary painstakingly compiled by Dr. Sadler, Absoluta is described with space potency as being solely a prereality. It is the domain of the Unqualified Absolute and is responsive only to the personal grasp and understanding of the Universal Father, notwithstanding that it is seemingly modifiable by the presence of the Primary Master Force Organizers. On Uversa, space potency is spoken of as ABSOLUTA. (469.5) 42:2.5 Also see (126.1) 11:8.5)

The absolute level is beginningless, endless, timeless, and spaceless. For example: On Paradise, time and space are nonexistent; the time-space status of Paradise is absolute. This level Is Trinity attained, existentially, by the Paradise Deities, but this third level of unifying Deity expression is not fully unified experientially. Whenever, wherever, and however the absolute level of Deity functions, Paradise-absolute values and meanings are manifest. (2.13) 0:1.13

On absolutum, the eternal Isle is composed of a single form of materialization—stationary systems of reality. This literal substance of Paradise is a homogeneous organization of space potency not to be found elsewhere in all the wide universe of universes. It has received many names in different universes, and the Melchizedek sons of Nebadon (the Latin name of our local universe) have long since named it absolutum. This Paradise source material is neither dead nor alive: it is the original nonspiritual expression of the First Source and Center; it is Paradise, and Paradise is without duplicate. (120.1) 11:2.9

Opposition from the Intuitionist school
The mathematical meaning of the term "actual" in actual infinity is synonymous with definite, completed, extended or existential, but not to be mistaken for physically existing. The question of whether natural or real numbers form definite sets is therefore independent of the question of whether infinite things exist physically in nature.

Proponents of intuitionism, from Kronecker onwards, reject the claim that there are actually infinite mathematical objects or sets. (Also, according to Aristotle, a completed infinity cannot exist even as an idea in the mind of a human.) Consequently, they reconstruct the foundations of mathematics in a way that does not assume the existence of actual infinities. On the other hand, constructive analysis does accept the existence of the completed infinity of the integers.

For intuitionists, infinity is described as potential; terms synonymous with this notion are becoming or constructive. For example, Stephen Kleene describes the notion of a Turing machine tape as "a linear tape, (potentially) infinite in both directions." To access memory on the tape, a Turing machine moves a read head along it in finitely many steps: the tape is therefore only "potentially" infinite, since while there is always the ability to take another step, infinity itself is never actually reached.

Classical mathematicians generally accept actual infinities. Georg Cantor is the most significant mathematician who defended actual infinities, equating the Absolute Infinite with God. He decided that it is possible for natural and real numbers to be definite sets, and that if one rejects the axiom of Euclidean finiteness (that states that actualities, singly and in aggregates, are necessarily finite), then one is not involved in any contradiction.

The philosophical problem of actual infinity concerns whether the notion is coherent and epistemically sound.

History
The ancient Greek term for the potential or improper infinite was apeiron (unlimited or indefinite), in contrast to the actual or proper infinite aphorismenon. Apeiron stands opposed to that which has a peras (limit). These notions are today denoted by potentially infinite and actually infinite, respectively.

"Anaximander (610-546 BC) held that the apeiron was the principle or main element composing all things. Clearly, the 'apeiron' was some sort of basic substance. Plato's notion of the apeiron is more abstract, having to do with indefinite variability. The main dialogues where Plato discusses the 'apeiron' are the late dialogues Parmenides  and the Philebus."

Aristotle sums up the views of his predecessors on infinity thus: "Only the Pythagoreans place the infinite among the objects of sense (they do not regard number as separable from these), and assert that what is outside the heaven is infinite. Plato, on the other hand, holds that there is no body outside (the Forms are not outside because they are nowhere), yet that the infinite is present not only in the objects of sense but in the Forms also. (Aristotle)"

The theme was brought forward by Aristotle's consideration of the apeiron in the context of mathematics and physics (the study of nature).

"Infinity turns out to be the opposite of what people say it is. It is not 'that which has nothing beyond itself' that is infinite, but 'that which always has something beyond itself'. (Aristotle [1])"

Belief in the existence of the infinite comes mainly from five considerations:
 * 1) From the nature of time - for it is infinite.
 * 2) From the division of magnitudes - for the mathematicians also use the notion of the infinite.
 * 3) If coming to be and passing away do not give out, it is only because that from which things come to be is infinite.
 * 4) Because the limited always finds its limit in something, so that there must be no limit, if everything is always limited by something different from itself.
 * 5) Most of all, a reason which is peculiarly appropriate and presents the difficulty that is felt by everybody - not only number but also mathematical magnitudes and what is outside the heaven are supposed to be infinite because they never give out in our thought. (Aristotle [1])

"With magnitudes the contrary holds. What is continuous is divided ad infinitum, but there is no infinite in the direction of increase. For the size which it can potentially be, it can also actually be. Hence since no sensible magnitude is infinite, it is impossible to exceed every assigned magnitude; for if it were possible there would be something bigger than the heavens. (Aristotle [1])"

"Our account does not rob the mathematicians of their science, by disproving the actual existence of the infinite in the direction of increase, in the sense of the untraversable. In point of fact they do not need the infinite and do not use it. They postulate only that the finite straight line may be produced as far as they wish. (Aristotle [1])"

Scholastic philosophers
The overwhelming majority of scholastic philosophers adhered to the motto Infinitum actu non datur. This means there is only a (developing, improper, "syncategorematic") potential infinity but not a (fixed, proper, "categorematic") actual infinity. There were exceptions, however, for example in England.

"It is well known that in the Middle Ages all scholastic philosophers advocate Aristotle's 'infinitum actu non datur' as an irrefutable principle. (G. Cantor [3, p. 174])"

"The number of points in a segment one ell long is its true measure. (R. Grosseteste [9, p. 96])"

"Actual infinity exists in number, time and quantity. (J. Baconthorpe [9, p. 96])"

During the Renaissance and by early modern times the voices in favor of actual infinity were rather rare.

"The continuum actually consists of infinitely many indivisibles (G. Galilei [9, p. 97])"

"I am so in favour of actual infinity. (G.W. Leibniz [9, p. 97])"

The majority agreed with the well-known quote of Gauss:

"I protest against the use of infinite magnitude as something completed, which is never permissible in mathematics. 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. (C.F. Gauss [in a letter to Schumacher, 12 July 1831])"

The drastic change was initialized by Bolzano and Cantor in the 19th century.

Bernard Bolzano who introduced the notion of set (in German: Menge) and Georg Cantor who introduced set theory opposed the general attitude. Cantor distinguished three realms of infinity: (1) the infinity of God (which he called the "absolutum"), (2) the infinity of reality (which he called "nature") and (3) the transfinite numbers and sets of mathematics.

"A multitude which is larger than any finite multitude, i.e., a multitude with the property that every finite set [of members of the kind in question] is only a part of it, I will call an infinite multitude. (B. Bolzano [2, p. 6])"

"There are twice as many focuses as centres of ellipses. (B. Bolzano [2a, § 93])"

"Accordingly I distinguish an eternal uncreated infinity or absolutum which is due to God and his attributes, and a created infinity or transfinitum, which has to be used wherever in the created nature an actual infinity has to be noticed, for example, with respect to, according to my firm conviction, the actually infinite number of created individuals, in the universe as well as on our earth and, most probably, even in every arbitrarily small extended piece of space. (G. Cantor [3, p. 399; 8, p. 252])"

"One proof is based on the notion of God. First, from the highest perfection of God, we infer the possibility of the creation of the transfinite, then, from his all-grace and splendor, we infer the necessity that the creation of the transfinite in fact has happened. (G. Cantor [3, p. 400])"

"The numbers are a free creation of human mind. (R. Dedekind [3a, p. III])"

Classical set theory
Classical set theory accepts the notion of actual, completed infinities. However, some finitist philosophers of mathematics and constructivists object to the notion.

"If the positive number n becomes infinitely great, the expression 1/n goes to naught (or gets infinitely small). In this sense one speaks of the improper or potential infinite. In sharp and clear contrast the set just considered is a readily finished, locked infinite set, fixed in itself, containing infinitely many exactly defined elements (the natural numbers) none more and none less. (A. Fraenkel [4, p. 6])"

"Thus the conquest of actual infinity may be considered an expansion of our scientific horizon no less revolutionary than the Copernican system or than the theory of relativity, or even of quantum and nuclear physics. (A. Fraenkel [4, p. 245])"

"To look at the universe of all sets not as a fixed entity but as an entity capable of 'growing', i.e., we are able to 'produce' bigger and bigger sets. (A. Fraenkel et al. [5, p. 118])"

"(Brouwer) maintains that a veritable continuum which is not denumerable can be obtained as a medium of free development; that is to say, besides the points which exist (are ready) on account of their definition by laws, such as e, pi, etc. other points of the continuum are not ready but develop as so-called choice sequences. (A. Fraenkel et al. [5, p. 255])"

"Intuitionists reject the very notion of an arbitrary sequence of integers, as denoting something finished and definite as illegitimate. Such a sequence is considered to be a growing object only and not a finished one. (A. Fraenkel et al. [5, p. 236])"

"Until then, no one envisioned the possibility that infinities come in different sizes, and moreover, mathematicians had no use for “actual infinity.” The arguments using infinity, including the Differential Calculus of Newton and Leibniz, do not require the use of infinite sets. (T. Jech )"

"Owing to the gigantic simultaneous efforts of Frege, Dedekind and Cantor, the infinite was set on a throne and revelled in its total triumph. In its daring flight the infinite reached dizzying heights of success. (D. Hilbert [6, p. 169])"

"One of the most vigorous and fruitful branches of mathematics [...] a paradise created by Cantor from which nobody shall ever expel us [...] the most admirable blossom of the mathematical mind and altogether one of the outstanding achievements of man's purely intellectual activity. (D. Hilbert on set theory [6])"

"Finally, let us return to our original topic, and let us draw the conclusion from all our reflections on the infinite. The overall result is then: The infinite is nowhere realized. Neither is it present in nature nor is it admissible as a foundation of our rational thinking - a remarkable harmony between being and thinking. (D. Hilbert [6, 190])"

"Infinite totalities do not exist in any sense of the word (i.e., either really or ideally). More precisely, any mention, or purported mention, of infinite totalities is, literally, meaningless. (A. Robinson [10, p. 507])"

"Indeed, I think that there is a real need, in formalism and elsewhere, to link our understanding of mathematics with our understanding of the physical world. (A. Robinson)"

"Georg Cantor's grand meta-narrative, Set Theory, created by him almost singlehandedly in the span of about fifteen years, resembles a piece of high art more than a scientific theory. (Y. Manin )"

"Thus, exquisite minimalism of expressive means is used by Cantor to achieve a sublime goal: understanding infinity, or rather infinity of infinities. (Y. Manin )"

"There is no actual infinity, that the Cantorians have forgotten and have been trapped by contradictions. (H. Poincaré [Les mathématiques et la logique III, Rev. métaphys. morale 14 (1906) p. 316])"

"When the objects of discussion are linguistic entities [...] then that collection of entities may vary as a result of discussion about them. A consequence of this is that the 'natural numbers' of today are not the same as the 'natural numbers' of yesterday. (D. Isles )"

"There are at least two different ways of looking at the numbers: as a completed infinity and as an incomplete infinity. (E. Nelson )"

"A viable and interesting alternative to regarding the numbers as a completed infinity, one that leads to great simplifications in some areas of mathematics and that has strong connections with problems of computational complexity. (E. Nelson )"

"During the renaissance, particularly with Bruno, actual infinity transfers from God to the world. The finite world models of contemporary science clearly show how this power of the idea of actual infinity has ceased with classical (modern) physics. Under this aspect, the inclusion of actual infinity into mathematics, which explicitly started with G. Cantor only towards the end of the last century, seems displeasing. Within the intellectual overall picture of our century ... actual infinity brings about an impression of anachronism. (P. Lorenzen)"