infiniti - 1 of 5 C.J. Gorrell Math 274 The History of...

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1 of 5 C.J. Gorrell Math 274 The History of Infiniti Before entering any in depth view of the history of math, it is important to note that there were two paths I could have taken in formulating this work. The first method would be to take advantage of the infinite monkey theorem. This theorem states that if a monkey were to randomly hit keys on a typewriter for a very long time (for an infinite period of time), then he would most likely have typed a replica of any work such as a Shakespearian play. Therefore by this method, I would just have to randomly type for a very long time, and this essay would have been eventually produced any way. The other method would be to do the research, and write the essay straight out. I chose the later. Infinity is an extremely vast subject, whose progression still continues today. The classical ideas of infinity, started with Aristotle, and continued up until the era of Cantor and Weierstrass. While infinity was a subject across many subjects other than mathematics, it was such a powerful tool in the development of mathematics that it is worth only considering the mathematical importance in the sum of this analysis. The start of the study of infinity started in the 4 th century BC, with ancient India and ancient Greece. The Grecians however, made the most significant progress on the subject at this time. Starting with Zeno an early contributor to Infinity, and perhaps the first to introduce a paradox in the analysis of infinity. Zeno observed that in an analysis of movement, that for a man to span a distance, he must first span half the distance, and then half the remaining distance. By repeating this procedure, Zeno observed that by his analysis it would become impossible for anyone to span and finite distance. 1 This became Zeno’s most famous paradox, however he had numerous others. The paradoxes of Zeno became a popular subject in the arguments between Aristotle and Plato. Plato first introduced the idea of infinity through the subject of religion. He defined infinity through the comparison of God to man. Plato’s student, Aristotle, takes on the subject of his teacher, and defines to separate identities to infinity. These are potential infinity and actual infinity. 2 Actual infinity or Aperion as Aristotle labels it, is divine, and in a sense beyond the comprehension of man. He therefore states that actual infinity cannot exist. Instead Aristotle says that man only deals with potential infinities. Aristotle uses potential infinity to define the use of infinity in the mathematics of his time. For example, the method of exhaustion as used by Archimedes was considered 1 Victor J. Katz, A History of Mathematics , 3 rd Ed. (Boston: Pearson, 2009), 45-47 2 Paolo Zellini, A brief History of Infinity , 3 rd ed. (London, Penguin, 2005) Pg. 31
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2 of 5 C.J. Gorrell Math 274 The History of Infiniti potential infinity because the method of exhaustion was not considered to have any reference to actual existence. 3
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infiniti - 1 of 5 C.J. Gorrell Math 274 The History of...

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