"To infinity and beyond!" the famous quote by Buzz Lightyear. But there may be a problem with this famous saying. Is there really anything beyond infinity? Is it even possible? What about when you were a little kid and you fought with one of your friends, "I have infinity points!" "Well, I have infinity plus one points!" "I have infinity times two points!" But are these possible? What is infinity plus one? Or infinity times two? These questions are hard to contemplate but the definition of infinity
Zeno’s Paradox and its Contributions to The Notion of Infinity Name: Dejvi Dashi School: King’s-Edgehill School IB nr: 000147-0006 Mathematics Exploration May 2014 Date: March 31st, 2014 Word Count: 2681 Achilles and the Tortoise is one of the many mathematical and philosophical paradoxes that were expressed by Zeno of Elea. His purpose was to present the idea that motion is nothing but an illusion. Many solutions have been offered as an explanation to these paradoxes for many years
In The Metaphysics, Aristotle states, “All men by nature desire to know.” Although, this is a generalization, of this insightful statement about the nature of humans and human understanding this statement truly captures what Aristotle was trying to figure out about humans and their thinking. Everyone has a desire to know or to understand. As rational beings we tend to contemplate very simple ideas to the most complicated, like our existence, or parts of the universe, or the universe as a whole.
Early elements of the Cosmological Argument were developed by the world renowned philosophers Plato and Aristotle between the years 400 and 200 BC (Boeree). Medieval philosopher Saint Thomas Aquinas expanded upon their ideas in the late 13th Century when he wrote, “The Five Ways.” Since then the Cosmological Argument has become one of the most widely accepted and criticized arguments for the existence of God. My objective in this paper is to explain why the Cosmological Argument is a reasonable
that the number of transcendental numbers, values such as pi(3.14159) and e(2.71828) that can never be the solution to any algebraic equation, were much larger than the number of integers. Before in mathematics, infinity had been a sacred subject. Previously, Gauss had stated that infinity should only be used as a way of speaking and not as a mathematical
Aristotle is arguably the most important Philosopher who ever lived. He is known as the father of philosophy. The questions he had back then are still some of the questions that philosophers of today’s world are trying to answer. He focused in on some topics that we still abide by today. Many of his ideas were later proven wrong, but he was the first to say anything about the topics. If he were alive today he would most likely be disappointed that it took so long for anyone to raise questions about
Nietzsche uses symbolism to further advance and lay out his image of society’s portrayal of the world. This idea of the land being burned is not meant literally, but metaphorically speaking with the thought in mind that people are moving forward without actual thought that they are leaving things behind. It seems as if people go through life without truly being conscious, almost as if going through the motion and not really realizing where they are in the world. Nietzsche further states that“[the ocean]
On considering the comparison of cardinalities of the set of natural numbers and real numbers, we turn to Cantor’s Diagonal Argument and Cantor’s supposed proof that there exist more real numbers than natural numbers. In this essay I will firstly outline this argument and continue by setting out some of its implications. I next consider Wittgenstein and his remarks on Cantor’s argument, namely the abstract nature of transfinite numbers, the use of the term infinite and the assumption that all sets
The window was cold to the touch. The glass shimmered as the specks of sunlight danced, and Blake stood, peering out. As God put his head to the window, at once, he felt light shining through his soul. Six years old. Age ceased to define him and time ceased to exist. Silence seeped into every crevice of the room, and slowly, as the awe of the vision engulfed him, he felt the gates slowly open. His thoughts grew fluid, unrestrained, and almost chaotic. An untouched imagination had been liberated,
The mathematical notion of infinity can be conceptualized in many different ways. First, as counting by hundreds for the rest of our lives, an endless quantity. It can also be thought of as digging a whole in hell for eternity, negative infinity. The concept I will explore, however, is infinitely smaller quantities, through radioactive decay Infinity is by definition an indefinitely large quantity. It is hard to grasp the magnitude of such an idea. When we examine infinity further by setting up one-to-one
The ‘Motorcycle Diaries’ transforms the concept of discovery through Che’s indefatigable nature, thus leading to a new profound dimension of discovery, that was once left hidden; revealing both threatening and polarizing ideas, leading to a provocative change of thought about our society. Che has revealed these new dimensions of discovery within the text’s vignettes. Che has revealed that the Ocean has a metaphorical connotation for infinite discoveries, enveloping Alberto and himself, leading to
Absence and Loss in Emily Dickinson’s Poem 67, Poem 1036, and Poem 870 Emily Dickinson often refers to loss and absence in her poetry. It is not often seen as strictly negative though. It is, however, seen as inevitable. It is not always inevitable in the negative sense though. It is sometimes seen as necessary in order to understand life. There seems to be an overall theme of loss being a part of life. This theme can be seen upon examining poems 67, 1036, and 870. Poem 67 is a good
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
Fun is something every human being has experienced one before in their life. Some may have more fun than others, but it's all something we can relate to. What we can't agree on is what fun is defined as. Everyone has and feels fun in a different way. If you asked two people to define fun you would get two different answers. People don't just feel fun differently they also have fun doing different things as well. Fun is a word that can be used very loosely. For intense one person can have skydiving
For the purposes of this debate, I take the sign of a poor argument to be that the negation of the premises are more plausible than their affirmations. With that in mind, kohai must demonstrate that the following premises are probably false: KCA 1. Whatever begins to exist has a cause. 2. The universe began to exist. 3. Therefore, the universe has a cause. We come first to premise (1), which is confirmed in virtually ever area of our sense experience. Even quantum fluctuations, which many
The Beginnings of Greek Philosophy The Milesians and Heraclitus Long before the time of Thales, a citizen of Miletus, in the district of Ionia on the west coast of Asia Minor, Chaldaen astrologers had listed data on the position of the stars and planets. As Thales studied these tables he thought he discerned a pattern or regularity in the occurrence of eclipses, and he ventured to predict a solar eclipse that occurred on May 28th 585BC. Some scholars think that this was just a lucky empirical
Set Theory in the Flesh The idea of infinity has been around for thousands of years. It it impossible to even conceive of this number or anything that pertains to the infinite. There is always one more. A billion is a fairly large number, 1 with 9 zeros after it. If one counted by seconds without breaks, it would take over 32 years to reach it. A Google, is a number written as 1 with one hundred zeros after it. One couldn't even count the number of lifetimes it would take to count to this number
and the aesthetic. Higher immediacy or religious faith is the most important achievement made by a person because only faith offers an individual to have a chance to become a "true self". Self is what is done throughout life which God judges for infinity. Consequently, humans have a huge responsibility because those decided choices in life constitute the eternal salvation or damnation. With the religious faith, the ethical and aesthetic are needed to form it, that is why they can not be the same
existence of 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
When referring to labyrinths, Kolter states that there are usually three types that are widely considered: The unicursal maze, the multicursal or mannerist maze, and the rhizome or network maze. The first type poses no challenge to the individual traversing its pathways because it consists of a single pathway that leads to a centre and then further on to an exit. The second type creates more of a challenge as it is made up of numerous pathways, many of which lead to dead ends, but there is only one