61. Class Highlights Ball worksheet, cantor's Diagonal Argument reading part 1 cantor's Diagonal Argument Eureka!'about Ivars Peterson's MatheTrek Ancient infinities and Scholars http://www.cs.appstate.edu/~sjg/class/3010/highlights.html

Class Highlights Tues Mar 18 Discussion based on questions about The Proof video. Review history of algebraic geometry. Algebraic geometry worksheet. Spring Break Tues Feb 25 WebCT test 3. Check WebCT mail to see whether your attachment came through. If not, resend this ASAP. Read ONLY up to the Fields section of Galois Theory Read Progression of Solutions of Polynomials by Radicals to the beginning of Modern Algebra Dr. Sarah's Maple Quintic Demo Dihedral group as the symmetries of a square worksheet . Worksheet on Galois and the pentagon. Thur Feb 27 Grad students only day: Algebraic structures continued. An overview of groups, rings and fields. An intro to Galois Theory. Algebra versus Modern Algebra/ Abstract Algebra. History of Modern Algebra. Applications. Tues Feb 18 Web searching . Worksheets on Diophantus, False Position (Egyptian), Three Linear Equations (Chinese), Quadratic Formula, Recorde, Rhind Papyrus. Thur Feb 20 Grad students only day: History of Matrices and Determinants A Brief History of Linear Algebra and Matrix Theory Introduction to Olga Taussky Todd and the Gerschgorin Circle Theorem Tues Feb 11 Collect remaining worksheets. Go over the

62. What's A Number? set of real numbers. One of the many cantor's contributions was toestablish various kinds of infinities. While it is true that http://www.cut-the-knot.com/do_you_know/numbers.shtml

CTK Exchange Front Page Movie shortcuts Personal info ... Recommend this site What is a number? When I considered what people generally want in calculating, I found that it always is a number. Mohammed ben Musa al-Khowarizmi. From The Treasury of Mathematics , p. 420 H. O. Midonick Philosophical Library, 1965 Indeed there are many different kinds of numbers. rational and irrational real and complex imaginary algebraic and transcendental ... square and triangular numbers Let's talk a little about each of these in turn. Rational and Irrational numbers A number r is rational if it can be written as a fraction r = p/q where both p and q are integers. In reality every number can be written in many different ways. To be rational a number ought to have at least one fractional representation. For example, the number may not at first look rational but it simplifies to 3 which is 3 = 3/1 a rational fraction. On the other hand, the number 5 by itself is not rational and is called irrational. This is by no means a definition of irrational numbers. In Mathematics, it's not quite true that what is not rational is irrational. Irrationality is a term reserved for a very special kind of numbers. However, there are numbers which are neither rational or irrational (for example, infinitesimal numbers are neither rational nor irrational). Much of the scope of the theory of rational numbers is covered by Arithmetic. A major part belongs to Algebra. The theory of irrational numbers belongs to Calculus. Using only arithmetic methods it's easy to prove that the number

63. Plato And Cantor Vs. Wittgenstein And Brouwer notion of infinite totalities, at least implicitly. Without infinitetotalities, or actual infinities, cantor's paradise would fall. http://www.angelfire.com/az3/nfold/plato.html

Plato and Cantor vs. Wittgenstein and Brouwer Axiomatic thought realms and the foundations of mathematics N-fold: Quirky thoughts on math and science Notes to myself that you can read If you spot an error, please email me Pertinent N-fold pages When truth is vacuous; is infinity a bunch of nothing? What is an algorithm? A geometric note on Russell's paradox When axioms collide ... Thoughts on diagonal reals Prove all things. Hold fast to that which is good. I Thes 5:21 [This page was begun in January 2002; as of Aug. 1, 2002, it remains a work in progress.] Integers and intuition Without going into an extensive examination of phenomenology and the psychology of learning, perception and cognition, let us consider the mind of a child. Think of Mommy controlling a pile of lollipops and crayons, some of which are red. In this game, the child is encouraged to pick out the red objects and transfer them to 'his' pile. The child employs a mental act of separation (some might call this 'intuition') to select out an item, in this case by direct awareness of the properties of redness and of ease of holding with his hands. This primal separation ability is necessary for the intuition of replication. Crayon and lollipop are 'the same' by virtue of redness. In turn, this intuition of replication, or iteration, requires a time sense, whereby if the child hears 'more' he associates the word with an expectation of a craving being satisfied ('more milk'). The child becomes able to associate name-numbers with iteration, such that 'one thing more for me' becomes 'one thing,' which in time is abstracted to 'one.' A sequence of pulses is not truly iterative, because there is no procedure for enumeration. The enumeration procedure is essentially a successor function, with names (integers) associated with each act of selection by replication intuition. Likewise, we must have amorphous 'piles' before we can have sets. As adults we know that the 'mine' pile and the 'Mommy' pile have specific, finite numbers of elements. But we cannot discern the logico-mathematical objects of set and element without first having a concept of counting.

64. Sammelpunkt.philo.at8080/archive/00000438/01/11-2-94.TXT So there is no proof, because in general 2 to the nth power is greater than n, thatthere are infinities of different sizes. Indeed 'cantor's Paradise' proves http://sammelpunkt.philo.at:8080/archive/00000438/01/11-2-94.TXT

65. CommonSense the politics of mathematics around the work of Georg Cantor on infinities, a very Wefind that before and after cantor's work, infinity was a truly troubling http://www.cs-journal.org/lll1/lll1science1.html

Home News Subscribe Advertisers ... Format Article to Print or Save To Infinity and Beyond by Georg Essl Nigel Spencer challenges us by raising the question "Do Lines Exist?" in his recent article.1 I was very thrilled to read the title of this article, because this question has come up for me, though as it turns out in a different context. The question as it has been studied in the mentioned article refers to something I would call a "mathematical line", whereas I have been occupied with a different "beast" that I'd like to call the "physical line" for contrast. I will get to this beast later. First, I will deal with the "mathematical line" with which Spencer grappled in his article. Nigel Spencer presents to us a number of mathematical statements, which address the following questions: What is the "size" of a mathematical point? What is the "length" of a mathematical line? How does the "size" of a mathematical point make up a mathematical line? Zeros and infinities are lurking behind many of the statements he makes. In fact the first infinity that remains unmentioned is an interesting one, which Spencer hasn't worked out clearly but is in fact answered in Eischen and Lipshitz's earlier article. The answer involves the consideration of a second question: what is a transcendental number? The answer to that question which, I think, best captures the essence of the problem is: A transcendental number is a number that requires uncountably ("infinitely") many steps to construct. While Kronecker may have answered the question "Does infinity exist?" with a no, for whatever reason, Cantor answers this question with a yes. The way he does that involves construction by rules that exist by definition. So, in fact, transcendental numbers are numbers that - in a strict sense - can never be completely written down. The reason why this is not a completely useless concept is that from those rules, all sorts of useful things can be derived, and the machinery that these things entail is powerful.

66. Meru Foundation E-TORUS(tm) Newsletter Vol.1 No. 11 was the first modern explorer in the mathematical realm of multiple infinities. whereTruth, while a hotly contested goal (enmities in cantor's academia were http://www.meru.org/Newsletter/number11.html

Meru Foundation eTORUS(tm) Newsletter Number 11 – 16 November 2001 Written by Cynthia Tenen NEWS First, I want to thank those who emailed their comments on eTORUS(tm) #10 . We appreciate your kind words. Each person has their own unique response to the Meru material from simple curiosity to profound, life-changing interest. It is an honor and a privilege for the Meru team to be doing this work, and your letters remind us of this by sharing how these ideas affect your lives. Thank you for your thoughtfulness in writing to us. FEATURES As promised in our previous newsletter, this issue includes two features which we didn't have room for in eTORUS(tm) #10 . First, there is a poem by Stan Tenen, based on the "Model of Continuous Creation" (see link below). Thank you again for your interest in Meru Foundation's work. ESSAY by STAN TENEN: THE POETRY OF CONTINUOUS CREATION (c)2001 Stan Tenen As will be immediately obvious, I'm not a poet. Nevertheless, I thought it might be worthwhile to try to describe the "Continuous Creation" model, and the meditative process that leads to Pardes (Paradise) and the Garden of Eden, poetically. My purpose is to demonstrate that it's not difficult to find literary and poetic metaphors and allegories for the life-dynamics that the Meru thesis suggests was described more precisely in geometric metaphor at the deepest level of the Hebrew text of Genesis, and the other writings of the Western traditions. This exercise is not a substitute for the search for the explicit geometric metaphor(s) that may have been the basis for the actual writings that have come down to us from the ancient sages. But I hope it gives a sense of the feasibility and plausibility of the Meru thesis that there is a precise geometric metaphor serving a true science of consciousness that predated and inspired the "poetry" of the traditional record.

67. Infinity 23 cantor's New Look at the Infinite In actuality (no pun intended), thedistinction between potential and actual infinities is meaningless. http://www.trottermath.com/infinity.html

Cantor's Quest to Understand the Infinite by Dina Gohar The biography of Georg Cantor can be found by clicking HERE Introduction The infinite! No other question has ever moved so profoundly the spirit of man; no other idea has so fruitfully stimulated his intellect; yet no other concept stands in greater need of clarification than that of the infinite. Infinity has many faces but however we look at the infinite, we are ultimately led back to mathematics, for it is here that the concept has its deepest roots. It is in mathematics that the concept of infinity has been developed and reshaped innumerable times, and where it finally celebrated its greatest triumph. Throughout the history of mathematics, the concept of infinity was regarded with a suspicious eye, as a concept better left alone, for infinity may seem like a concept that is impossible to bring within the confines of human understanding. Despite harsh criticism, the nineteenth century mathematician Georg Cantor accomplished this feat, however, and his mathematics makes infinity clear and consistent without diminishing its astounding grandeur. Cantor's work with infinity essentially originated from his deceptively innocent observation that we need not be able to count objects in sets (finite or infinite) in order to determine whether or not the sets are equinumerous. Cantor used his notion of one-to-one correspondence to examine various infinite sets and found that there are actually different "sizes" of infinity: the set of rational numbers and many subsets of the natural numbers are countably infinite, while the larger set of real numbers is uncountably infinite.

68. Number As Archetype any infinities that lie between the infinity of the integers and the infinity ofthe geometric continuum? CANTOR’S CONTINUUM HYPOTHESIS. cantor's continuum http://www.goertzel.org/dynapsyc/1996/num.html

DynaPsych Table of Contents NUMBER AS ARCHETYPE Robin Robertson This paper has been adapted from the final chapter of Jungian Archetypes: Jung, Godel and the History of Archetypes The sequence of natural numbers turns out to be unexpectedly more than a mere stringing together of identical units: it contains the whole of mathematics and everything yet to be discovered in this field. Carl Jung It has turned out that (under the assumption that modern mathematics is consistent) the solution of certain arithmetical problems requires the use of assumptions essentially transcending arithmetic; i.e., the domain of the kind of elementary indisputable evidence that may be most fittingly compared with sense perception. Kurt Godel Mathematics followed a similar path. When it came out of its slumber early in the 17th century, the first product was analytic geometry, which demonstrated the equivalence of geometry and arithmetic. And with no clearly defined problem, there was no mathematical Kant to resolve the problem. Instead Euler was the chief representative of the era, and Euler was more concerned with building a great edifice based on mathematics, than with examining its foundations. Though still consciously unresolved, the issue continued to evolve in the unconscious. By the 2nd half of the 19th century, psychology finally emerged from the unconscious, wearing the twin faces of experimental and clinical psychology. It took someone like Freud, who bridged both camps, to discover the unconscious. It took someone like C. G.

69. Page3 - Philosophy - Http://maxpages.com/cantoriswrong/page3 cantor's DT shows you how some people think i insist that a grave misunderstandingof the nature of infinity leads to this acceptance of infinities http://www.maxpages.com/cantoriswrong/page3

Refer This Site To A Friend Home var AdLoaded = false; var bsid = '11616'; var bsloc = ''; var bswx = 468; var bshx = 60; var bsw = '_blank'; var bsb = 'FFFFFF'; var bsf = '0000FF'; var bsalt = 'off'; var defaultImage = 'http://maxpages.com/maxad2.gif'; var defClick = 'http://maxpages.com'; var defNoRich = 1; var bsads = '6'; Calling All Girls! Free Cartoon Dolls! E-Commerce $49.99/year! Click Here for Details Graphics Gallery! Graphics Gallery and Search Animated GIFs Photos Icons Clip Art (last updated 8/4/01...by Cobb Stregagobo) (19)...here's the upshot of the WHICH ONES?/HOW MANY? dichotomy...apply it to Cantor's DT and watch the whole thing fall apart...and it's the crux of the matter, so important that i'm gonna be annoying and put it all in capitals: IF THE NUMBER OF INTEGERS YOU NEED IS N*, THEN YOU DON'T NEED THEN ALL!... (20)...i am astonished to discover that there are professional mathematicians, called constructivists, who don't believe in a hierarchy of infinities...good for them...to construct the infinite, we can only use finite components after all...(a quick search of the net reveals "constructivist" also refers to a wacko new way to non-teach kids arithmetic...so maybe we need a new word...constructist?...constructionist?...i could even live with kroneckerists or kroneckerians...) (21)...what starts out as a joke may be found, on reflection, to have a serious and important point behind it...likewise, what starts out as seemingly serious may prove to be merely a joke, which, of course, everyone will be too embarressed to acknowledge...

70. Page2 - Philosophy - Http://maxpages.com/cantoriswrong/page2 ALL infinities ARE EQUAL (ie THERE IS ONLY ONE INFINITY) bogus, existing neitherin the real world nor even in principle cantor's Diagonal Theorem (DT http://www.maxpages.com/cantoriswrong/page2

Refer This Site To A Friend Home var AdLoaded = false; var bsid = '11616'; var bsloc = ''; var bswx = 468; var bshx = 60; var bsw = '_blank'; var bsb = 'FFFFFF'; var bsf = '0000FF'; var bsalt = 'off'; var defaultImage = 'http://maxpages.com/maxad2.gif'; var defClick = 'http://maxpages.com'; var defNoRich = 1; var bsads = '6'; Calling All Girls! Free Cartoon Dolls! E-Commerce $49.99/year! Click Here for Details Graphics Gallery! Graphics Gallery and Search Animated GIFs Photos Icons Clip Art (last updated 8/4/01...by Cobb Stregagobo...) ALL INFINITE SETS HAVE THE SAME NUMBER OF MEMBERS... ALL "INFINITIES" ARE EQUAL...(i.e. THERE IS ONLY ONE INFINITY)... THE SO-CALLED TRANSFINITES?...aleph-NOT!... note: i use N to represent the set of integers, and N* to indicate how many of them there are...N* should be taken to be the traditional ("naive" if you will) infinity, usually denoted by an "8" lying on its side...also, when i say "integers", i am refering to the positive integers, a.k.a. the natural or counting numbers...and a special thanx for the link at http://www.crank.net/maths.html~

71. Re: Tegmark's TOE & Cantor's Absolute Infinity From Tim May; Subject Re Tegmark's TOE cantor's Absolute Infinity; Date t necessarilyalways believe that in any existential sense there are infinities. http://www.mail-archive.com/everything-list@eskimo.com/msg03996.html

everything-list Chronological Find Thread From: Tim May Date: Mon, 23 Sep 2002 12:31:36 -0700 http://www.hep.upenn.edu/~max/toe.html http://arXiv.org/abs/gr-qc/9704009 (continued) Wei Dai Bruno Marchal Wei Dai Bruno Marchal Bruno Marchal Osher Doctorow Russell Standish Hal Finney Russell Standish Hal Finney Tim May Bruno Marchal Russell Standish Chronological Thread Reply via email to

72. Bret Willet's Paper On Infinity cantor's set theory incorporated infinity in the form of infinite cardinal numbers Cantorwent on to prove that there is a hierarchy of infinities; there are an http://www.facstaff.bucknell.edu/udaepp/090/w3/bretw.htm

Ghosts in a Surreal Land by Kenneth Bret Willet "To infinity and beyond!" These were the inspired words of Buzz Lightyear in the Disney movie Toy Story. Granted, one would not expect to find much mathematical content in an animated film directed toward children, but these words raise an interesting issue that mathematicians and the general public struggled with for many years. Can one go beyond infinity? How can such a concept be possible or even imaginable? These questions led to the development of many new theories and even a new system of numbers. Disney's Buzz Lightyear A study of infinity must begin with an introduction to set theory. A set is merely a collection of objects. Georg Cantor was the sole creator of set theory; he published an article in 1874 that marks the beginning of set theory and has come to change the course of mathematics. Cantor's theory was met with a great deal of opposition due to its assertion of infinite numbers. The famous mathematician Leopold Kronecker was especially opposed to Cantor's revolutionary new way of looking at numbers. Kronecker believed only in constructive mathematics, those objects that can be constructed from a finite set of natural numbers. Despite this opposition from influential thinkers, set theory laid the foundation for twentieth century mathematics. Although there were some flaws in Cantor's theory, sets became an essential part of new mathematics and therefore set theory was adapted to eliminate its original paradoxes [2].

73. Untitled cantor's aleph notation provides an important refinement $\aleph_0$ denotes countableinfinity, while other infinities are denoted $\aleph_\alpha$ where http://www.math.psu.edu/katok_s/paper.tex.html

74. Set Theory Survey from the Stanford Encyclopedia of Philosophy by Thomas Jech.Category Science Math Logic and Foundations Set Theory...... 7, 1873, the date of cantor's letter to Dedekind informing him of his discovery.)Until then, no one envisioned the possibility that infinities come in http://plato.stanford.edu/entries/set-theory/

version history HOW TO CITE THIS ENTRY Stanford Encyclopedia of Philosophy A B C D ... Z content revised JUL Set Theory 1. The Essence of Set Theory 2. Origins of Set Theory 3. The Continuum Hypothesis 4. Axiomatic Set Theory ... Related Entries 1. The Essence of Set Theory The objects of study of Set Theory are sets . As sets are fundamental objects that can be used to define all other concepts in mathematics, they are not defined in terms of more fundamental concepts. Rather, sets are introduced either informally, and are understood as something self-evident, or, as is now standard in modern mathematics, axiomatically, and their properties are postulated by the appropriate formal axioms. The language of set theory is based on a single fundamental relation, called membership . We say that A is a member of B (in symbols A B ), or that the set B contains A as its element. The understanding is that a set is determined by its elements; in other words, two sets are deemed equal if they have exactly the same elements. In practice, one considers sets of numbers, sets of points, sets of functions, sets of some other sets and so on. In theory, it is not necessary to distinguish between objects that are members and objects that contain members the only objects one needs for the theory are sets. See the supplement Basic Set Theory for further discussion.

75. Untitled consider many dimensions. What about cantor's grading of infinities?That's well beyond experience, surely? True. But Cantor only http://www.maths.unsw.edu.au/~jim/interview.html

An Interview With James Franklin Philosopher 1 (2) (Winter, 1995), 31-38) James Franklin is a senior lecturer in Mathematics at the University of New South Wales. He holds a PhD in algebra from Warwick University, and has written on the history of ideas and on neural nets as well as on the philosophy of mathematics. He is co-author of the textbook Introduction to Proofs in Mathematics and the history The Science of Conjecture and is completing a book on recent Australian philosophy. Here he talks to David Shteinman about his views on a new direction for the philosophy of mathematics, based on what mathematics actually tells us about the world. Jim, as a philosopher and a mathematician, how do you see relations between these two disciplines? Philosophy and mathematics are the two great armchair disciplines, and it is time there was a rapprochement between the two. Unfortunately, at the moment cold war conditions apply. Philosophers often want to 'use' mathematics somehow, but forget that if you want to pontificate about x, you need to know something about x. On the other side, mathematicians typically talk garbage when they're asked philosophical questions. The New Zealand philosopher, Alan Musgrave, said in this connection, "fish are good at swimming, but poor at hydrodynamics", and that exactly describes mathematicians who dabble a bit in philosophy in their spare time. So, in a nutshell, what is your position? What is mathematics about?

76. SET THEORY And ASSEMBLAGES Certainly cantor's array of different infinities were impossible underthis way of thinking. Cantor however continued with his work. http://www.kyproducts.com/q/coprobe3.htm

The beginnings of set theory The history of set theory is rather different from the history of most other areas of mathematics. For most areas a long process can usually be traced in which ideas evolve until an ultimate flash of inspiration, often by a number of mathematicians almost simultaneously, produces a discovery of major importance. Set theory however is rather different. It is the creation of one person, Georg Cantor. Before we take up the main story of Cantor's development of the theory, we first examine some early contributions. The idea of infinity had been the subject of deep thought from the time of the Greeks. Zeno of Elea, in around 450 BC, with his problems on the infinite, made an early major contribution. By the Middle Ages discussion of the infinite had led to comparison of infinite sets. For example Albert of Saxony, in Questiones subtilissime in libros de celo et mundi, proves that a beam of infinite length has the same volume as 3-space. He proves this by sawing the beam into imaginary pieces which he then assembles into successive concentric shells which fill space. Bolzano was a philosopher and mathematician of great depth of thought. In 1847 he considered sets with the following definition ;

77. 3. XX Century Paradoxes. role is played by the new 'infinite' ideas connected with cantor's theory. The ''diagonalmethod'' allows us to face different infinities, starting from the http://www.dm.uniba.it/~psiche/bas3/node4.html

Next: 4. Logic and Up: BEING AND SIGN Previous: 2. Wittgenstein and 3. XX century paradoxes. The same procedure allows Cantor to prove that, for any set S, its cardinality is strictly less than the cardinality of its power set P(S). If now we apply this result to the ''set of all sets'', we have the ''Cantor paradox''. In fact the power set of the ''set of all sets'' is a set of sets and then a subset of ''the set of all sets'', and hence this power-set must have a lesser or equal cardinality than the set, in spite of the above theorem. Maybe the most important modern paradox was the Russell paradox, discovered at the beginning of our century and fatal for the Fregean logic foundation of arithmetic. In such theory it was possible to define S, the ''set of all sets which are not members of themselves''. The problem is: S belonging to S ? If the answer is yes, from the definition of S, it follows that S is not member of itself, and then S does not belong to S. If the answer is not, for the same reason, we have that S belongs to S. The argument can be set in the form of the ''diagonal'' argument, putting member(T,T') = 1 iff T belongs to T', otherwise. Then we define S as build by the sets T such that member(T,T) = 0. It is evident that member(S,S) = == member(S,S) =1, and vice versa member(S,S) = 1 ==

78. Infinity--Cardinality Can R really be bigger, if they're both infinite? Are there differenttypes of infinities? Georg alphabet). cantor's theorem states w c. http://www.math.lsa.umich.edu/mmss/courses/infinity/Cardinality/Lesson3.shtml

So are All infinities the same infinity? Do all infinite sets have the same cardinality? In other words, is it possible to construct a one-to-one correspondence between any two infinite sets? At first blush, it seems that the answer should be "yes," because if we start matching them up, then we'll never run out of either set, so we'll keep going forever, and then we'll have our matching. This reasoning isn't quite right, though, because who's to say after that "forever" process, that we've actually used up all the elements of both sets? A good example might be to take one to be the set N of all positive integers, and to take the other to be the set R of all real numbers. We could try to match them up in a one-to-one correspondence: 1 (in N) matches with 1 (in R) 2 (in N) matches with 2 (in R) 3 (in N) matches with 3 (in R) 4 (in N) matches with 4 (in R) etc. Certainly we never run out of elements from either set, but when we're done, we don't have anything close to a one-to-one correspondence, because of all the real numbers which have been left out of the game. 3.5, for example, never gets mentioned. Pi, e, 23/19, and lots of other numbers have been completely forgotten, so this is not a matching. no one-to-one correspondence. In other words, we have to demonstrate that no scheme for matching the integers in N to the real numbers in R can possibly work. These seems a daunting task, because it's hard to account for the arbitrary ingenuity of other mathematicians trying to match up N with R, but in fact it is possible.

79. Crank Dot Net | Cantor Was Wrong All 'infinities' are equal (ie, there is only one infinity cantor's Diagonal Theorem,which supposedly demonstrates there are more reals (R) than integers, is http://www.crank.net/cantor.html

Dilworth v. Dudley 2001 Oct 09 Cantor was wrong legal "The decision handed down by Judge Posner in the lawsuit brought by William Dilworth against Underwood Dudley, author of Mathematical cranks . The plaintiff was upset about being referenced in Dudley's book regarding his (cranky) refutation of Cantor's diagonal construction, and sued for defamation. The suit was dismissed 'for failure to state a claim.'" Fatal Mistake of Georg Cantor 2001 Oct 05 Cantor was wrong "Thus, Cantor's diagonal method proved to be applicable, without any changes , to both infinite and finite enumerations. Consequently, that method does not distinguish and does not take into account quantitative characteristics (properties) of those sets and enumerations which it is applied to. We come to the following, very significant for the mathematics philosophy conclusion: The only method, which hitherto allowed meta-mathematicians to differentiate sets according to the number of their elements, i.e. by their 'power-cardinality', does not differentiate (distinguish) finite sets from infinite sets just by their power!"

80. Infinity And Jesus' Humanity cantor's transfinite number sets are only mental constructs and are not actuallyfound within the space The infinite attributes of God are absolute infinities. http://muhammadanism.org/Jesus/JesusInfinite.htm

Jesus "In these last days has spoken to us in Son, whom He appointed heir of all things, through whom also He made the world. And He is the radiance of His glory and the exact representation of His nature, and upholds all things by the word of His power. When He had made purification of sins, He sat down at the right hand of the Majesty on high; Hebrews 1:2-3 Home Revelation Muhammad Islam ... Search Jesus Christ Did Jesus say I am God? Jesus in the Qur'an Jesus' Uniqueness in the Qur'an Jesus makes clay birds Infinity and Jesus' Humanity Infinity and Jesus' Humanity Summary: Is the concept of an infinite God compatible with the finiteness of Jesus Christ's body? It seems to be contradictory, because infinite means by definition to be not finite. A contradiction would follow if infinite and finite were used in the same sense. However, there is not a real contradiction, because infinite and finite are used in different senses. The finiteness of Jesus' body refers to its spatial dimensions. Since God is not a material object, His divine infinitude could not refer to spatial dimensions. Thus, the finiteness of Jesus' body is not used in the same sense as the infinitude of Deity. To resolve this question, the different types of infinities are discussed: potential infinity

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