boundaries. Intuitively, we feel that where there is a separation, a border, a threshold – there is bound to be at least one thing finite out of a minimum of two. This, of course, is not true. Two infinite things can share a boundary. Infinity does not imply symmetry, let alone isotropy. An entity can be infinite to its “left” – and bounded on its right. Moreover, finiteness can exist where no boundaries can. Take a sphere: it is finite, yet we can continue to draw a line on its surface infinitely. The
Fractals and the Cantor Set Fractals are remarkable designs noted for their infinite self-similarity. This means that small parts of the fractal contain all of the information of the entire fractal, no matter how small the viewing window on the fractal is. This contrasts for example, with most functions, which tend to look like straight lines when examined closely. The Cantor Set is an intriguing example of a fractal. The Cantor set is formed by removing the middle third of a line
infinities whose values are greater than other infinities. He also proved there are an infinite number of infinities. While all these ideas take a while to explain, I will go over how Cantor proved that the infinity for real numbers is greater than the infinity for natural numbers. The first important concept to learn, however, is one-to-one correspondence. Since it is impossible to count all the values in an infinite set, Cantor matched numbers in one set to a value in another set. The one set with
this proves that the cardinality of both is the same being o. This correspondence leads to the conclusion that o+1=o. When we add two infinite sets together, we also get the sum of infinity; o+o=o. This being said we can try to find larger sets of infinity. Cantor was able to show that some infinite sets do have cardinality greater than o, given 1. We must compare the irrational numbers to the real numbers to achieve this result. 1 0
Georg Cantor I. Georg Cantor Georg Cantor founded set theory and introduced the concept of infinite numbers with his discovery of cardinal numbers. He also advanced the study of trigonometric series and was the first to prove the nondenumerability of the real numbers. Georg Ferdinand Ludwig Philipp Cantor was born in St. Petersburg, Russia, on March 3, 1845. His family stayed in Russia for eleven years until the father's sickly health forced them to move to the more acceptable environment of Frankfurt
criteria are the entity must have the capacity for speech and act from knowledge. His justifications that machines do not meet these two criteria are sound; however, he fails to verify that animals do the same. Descartes’ argument that humans have an infinite capacity to make appropriate responses is true as well as his implication that this capacity is non-material. Descartes’ first argument is only humans have the capacity for speech. In the opening of Discourse on Method Descartes remarks that machines
limited to the perception of only certain things. Whereas our will, ability to choose is not limited; it is has an infinite capacity. Therefore we sometimes attempt to will things which we do not have a complete understanding of. Descartes’ argument, as I will briefly describe, is quite sound, if you agree to all his conditions (being that the intellect is limited and the will infinite). I am not, as of yet, sure if I necessarily agree to the later of his two conditions. I will strive to evaluate different
self-contained little world. The question many have pondered is whether or not there is intelligent life beyond earth. In the words of Metrodorus, a Greek philosopher of the fourth century, "To consider the Earth as the only populated world in infinite space is as absurd as to assert that in an entire field of millet, only one grain will grow." I believe that intelligent extraterrestrial life does exist. Critics of the theory of intelligent life beyond earth will argue that there is
of God? Descartes' attempts to stay deductive when attempting to prove the existence of God are indeed laudable, but some of his arguments are lacking. In proving the existence of God, his two main arguments are as follows: the idea of a perfect, infinite being in his own head could only have been created by God Himself, and God's existence cannot be separated from His essence . Descartes must first prove that he exists. He writes, ?For example, during these few days I was examining whether anything
Although the desire may seem impossible, it becomes possible when expressed spiritually. Kierkegaard calls the second movement the "infinite resignation": this involves the person acknowledging the impossibility of her/his wish. By resigning the finite desire, says Kierkegaard, the wish is bent inward. With this, the wish becomes religious, and thus not finite, but infinite. The third step involves...
found to be inconsistent with Classical mechanics. The data showed that as the wavelength of the incoming radiation approaches zero, the amount of energy being radiated also approaches zero, whereas Classical mechanics says the emitted energy is infinite. The second difficulty with the theory was its inability to correctly describe the photoelectric effect. The photoelectric effect says that photons from a surface are released when light hits it. Classical mechanics says that electrons will be emitted
regress cannot, nevertheless, be infinite; we must in the end reach a first idea, the cause of which is, as it were, the archetype in which all the reality that is found objectively in these ideas is contained formally.'; The only problem with Descartes’ argument is when the existence of God arises as a notion, for there is no sustenance or idea for the notion of God to originate from. Is it possible, then, to create the idea of a finite being from an infinite existence, outside of the physical
and his infinite store of knowledge allow him to capture and draw the reader into the realm of the terrestrial hell. In Canto 6, the Gluttons; Canto 13, the Violent Against Themselves; and Canto 23, the Hypocrites; Dante excels in his detailed portrayal of the supernatural world of hell. In each canto, Dante combines his mastery of language with his sensitivity to the sights and sounds of nature to set the stage. He then reinforces the image with examples that call upon his infinite store of
combing of attributes that would seem impossible in one person. He is unique, one of a kind. There is no one and nothing we could compare Him to. He is “Incomparable because in Him meet infinite glory and lowest humility, infinite majesty and transcendent meekness, deepest reverence toward God and equality with God, infinite worthiness of good and greatest patience to suffer evil, supreme dominion and exceeding obedience, divine self-sufficiency and childlike trust.” The Beauty and Excellency of Jesus
is precisely through thinking the contraction of [the modern] essence [of consciousness] that Levinas thinks otherwise than being, beyond essence, thinks "a thought profounder and 'older' than the cogito." Humanity signifies a "new image" of the Infinite in the preoriginary freedom by which the Self shows the Other mercy. The curve on the hither side of consciousness is 'a concave without a convex': the cuspidal infinity of interiority turned absolutely inside outside the other within: an interiority
itself as revolutionary by expanding the style matrix, and as clever, by belonging to the once-problematic category of artwork called ‘indiscernibles.’ However, it can be shown that “Missing Van Gogh’s” lack of spatial and temporal boundaries adds infinite predicates to the style matrix and thus reveals a flaw in Danto’s theory. Danto’s theory of artistic identification requires only that the sentence “x is P,” where x is a given work and P a predicate functioning as an interpretation of that work
our Minds Italicized-as 'twere. As We went out and in Between Her final Room And Rooms where Those to be alive Tomorrow were, a Blame That Others could exist While She must finish quite A Jealousy for Her arose So nearly infinite-- (P-1100) It is presumed that Dickinson wrote this piece of verse in circa 1886. In May of that year, Laura Dickey, the wife of Frank W. of Michigan, ... ... middle of paper ... ...Dickinson. 2 vols. 1974. Cambridge: Harvard UP, 1994
Eighteen, I have decided, is an interesting age to be. For the first time in my life, the things I want to learn outnumber the number of hours in the day to learn them. The effect, somewhat to my surprise, is a kind of buoyancy. Transcendence is too fancy a word for this change. And yet it does feel sometimes as if I have lifted up off the surface of things like a balloon straining at its tether. In junior-high school I caught my first real glimpse of "the big picture." That is, I began to
must try to abandon this pre-conception. Aristotle argued that the universe is spherical and finite. Spherical, because that is the most perfect shape; finite, because it has a center, viz. the center of the earth, and a body with a center cannot be infinite. He believed that the earth, too, is a sphere. It is relatively small compared to the stars, and in contrast to the celestial bodies, always at rest. For one of his proofs of this latter point, he referred to an empirically testable fact: if the
of itself. From this conclusion of God as an infinite being, Aquinas moves to the third question, concerning the simplicity of God. In article four of question three, Aquinas determines that God is ultimately simple in that his essence does not differ from his being. He writes, "Therefore, since in God there is no potentiality, it follows that in Him essence does not differ from being. Therefore, His essence is His being." God is an unchanging, infinite being. There is no conceivable way in which