Trevor Gillhouse
Math 108
2/16/17
Enrichment Paper #1
My favorite quote of all time in the Toy Story series, is something that Buzz Lightyear said- “To infinity and beyond!” For this paper, I decided to read a chapter in a book named To Infinity and Beyond by Dr. Kent A. Bessey. In this book, he explains about how the number infinity can be comprehended and can be counted. He explained this through something called cardinality, through the Counting Theory, and through different dimensions.
Dr. Bessey went on and on about this law called Cardinality and how is refers to the number of elements in a set. “Through pairing, we can determine whether the cardinality of a set is less than, more than, or the same as the cardinality of another set
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without knowing the number of objects in either set.” What this means is that we can essential pair numbers together which can then explain infinity without even knowing the number of objects in a set. For example, 1 will pair with 2, 2 will pair with 4, 3 will pair with 6, and so on. We can pair numbers together which will then lead to an infinity. This law leads to finding infinity with finite numbers. My first semester of college I took a Math 111 class, and at the end we learned about this infinity theory.
My professor told us that we can comprehend God through finite numbers even though he is infinite. I have always wondered how. After reading more of this book I figured out how. Some infinite sets are tremendously larger than others and how Dr. Bessey explains it, he says, “We have already shown that the power set of {1, 2, 3} contains 23 or 8 subsets. Using the general formula, we conclude that the power set of {1, 2, 3, 4} contains 24 or 16 subsets; the power set of {1, 2, 3, 4, 5, 6, 7, 8, 9, 10} contains 210 or 1,024 subsets; and the power set of {1, 2, 3, 4, . . . , 100} contains 2100 or 1,267,650,600,228,229,401,496,703,205,376 subsets, which is more than one million trillion trillion. Exploring further, we discover that the power set of {1, 2, 3, 4, . . . , 1000} contains 21000 subsets, where 21000 equals a number that has 302 digits! Thus, by means of the power set, any finite set can be used as a stepping-stone to build another, much larger, finite set.” It is so crazy to me to think that we can understand infinity and even eternity by using finite numbers. Not only that but we can understand the eternities by understanding dimensions as
well. Dr. Bessey goes on to talk about dimensions and how each dimension has the same number of points. Therefore, we can now understand how God conducted miracles like feeding thousands with just a little bit of bread. He then goes on and talks about how we can move in each dimension. Essentially that is an uncountable dimension space and we can move freely in it. Therefore, we can now imagine how the eternities is going to be. Infinity is something so reachable now after I read this book. It makes me think how the eternities will be. Dr. Bessey is a smart man, who was able to be inspired by God to explain infinity in such a finite way. View as PageDownloadToggle Fullscreen
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