infinity - 1 Infinity: Are We There Yet? Jason Harrington...

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Infinity: Are We There Yet? Jason Harrington Infinity: when most people hear this word, they think of something large or something vast. Some people think of space or time, while others think of life after death. Mathematicians are faced with this concept almost everyday. Yet, what does it really mean? Is it practical to even think about infinity? What did the early civilizations think about infinity? How has our thinking of infinity changed overtime? To start off, a mental experiment needs to be done to see how complex infinity can be. Let’s say there are two bags that hold numbers. In both bags, we place the first 10 numbers starting from 1 to 10. In the first bag, we remove the smallest number, 1. In the second bag, we remove the largest number, 10. Then we put in the next 10 numbers in both bags from 10 to 20. Again, in the first bag, we remove the smallest number, in this case, 2. In the second bag, we remove the largest number, which is the number 20. Now we repeat again. Both bags have the same number of items in them along each step, since we always put in 10 items and remove one. However, in the first bag, every number will eventually be removed since the smallest is removed each time, while in the second bag there are infinitely many numbers that will never be removed, such as 2. So even though both bags have the same number of items along each step, the way we remove an item affects what happens as we do this process an infinite number of times. The first bag will be empty after we do this process an infinite number of times, while the second bag will become infinitely large. So infinity cannot be thought of simply as a large number as most people tend to think. So there must be something else to infinity, something that 1
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philosophers, mathematicians, astronomers, and others have tried to wrap their minds around throughout time. Since the very dawn of civilization, people have looked toward the skies and wondered what lies beyond. Philosophers still debate whether there is more to life than what we perceive and what it means in terms of the vast universe. The early religions and mythologies tell us much about whether people believed that there was an after life, about places where people go forever after passing, or whether life is finite and ends at death. Nearly all believed in infinity of the spirit, although ultimate destination of the spirit remained unique to the religion and the culture. The Egyptians, for example, did believe in an after life. Once a person died, their spirit would go to Horus, the god of all good deeds. Then Osiris would weigh their heart against a feather, to determine whether they will vanish to nothing, or live in the Kingdom of Osiris. The Egyptians were mainly concerned with arithmetic math, so we know very little on whether they even thought about the complexity of infinity other than in death. The Egyptians saw the world as being very cyclic, since they lived near the Nile River that would flood and recede in a predictable fashion. Most scholars tend to think
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This note was uploaded on 07/22/2011 for the course MGF 1107 taught by Professor Staff during the Spring '08 term at University of Florida.

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infinity - 1 Infinity: Are We There Yet? Jason Harrington...

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