Introduction
While perusing certain articles on the news-aggregator app Flipboard, I came across a blog post from the Huffington Post entitled ‘The Infinity Inside.’ The compelling title gave way to an even more intriguing body, which referred to infinity not in mathematical terms but as an abstract principle that governs the universe. This encounter instigated a profound curiosity in me, spurring me to investigate the concept of infinity further; after searching “how large is infinity” on the Internet, I discovered a TedEd video exploring the central question ‘How Big is Infinity?’ This video introduced me to the idea that there exist multiple forms of infinity, many of which are actually larger than each other. This prompted
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To define infinity, I will first explain the underlying logical framework of Cantor’s Infinite Set Theory. To prove the existence of multiple, larger infinities, I will work through Cantor’s Theorem of power sets. Through listing, I will also explore the different types of possible infinities and test whether or not it is true that all mathematical objects can be arranged in sets.
Basic Concepts of Set Theory
Set theory is considered a fundamental basis of modern mathematics whose notions can be built upon to form more complex areas of study. A set is simply a collection of objects . These objects are called members or elements of the set and are governed by well-defined membership criteria. In order to know whether or not an object belongs or does not belong to a set, there must be clear rules that delineate which objects are acceptable for inclusion. For example, if we had a set of all prime numbers, the number 4 could not belong to the set as it has more positive divisors than just 1 and itself -- it violates the specific criteria for membership in the set.
There are two types of sets as defined by Georg Cantor: finite and infinite. A finite set is simply one whose size, or cardinality, can be defined by a natural number. Cardinality describes the number of elements contained in a set. The members of any set (finite or infinite) can be placed in a
The book, I chose for my Book Talk #4 is The Infinite Sea by Rick Yancey. It is the second book of the trilogy of the 5th Wave Book series. This book has a Lexile level of HL640L, the grade interest is ninth to twelfth, and the age range extends from 14 to 18 years.The Infinite Sea is a Science Fiction book, but it has hints of horror in the trope of the story.
Imagine the number eight. People would probably think that it’s just eight and nothing but eight. Now imagine the number eight tilted 90° to the left. People now see the infinity symbol. Now, people would probably think of it as an expanding number that never ends.
Religious spaces, characterized by Thomas Tweed, are “differentiated,” “interrelated,” and “kinetic.” As a sacred city with spiritual significance in three major religions, Jerusalem is depicted thoroughly in the Hebrew Bible and illustrated as one of the spaces Tweed defines. The Bible emphasizes that Jerusalem was chosen by God and honored by Israelites, which differentiates it as a special, singular space; the description of Solomon’s Temple shows that the Holy City was interrelated to economic power and involved in the judgment of civil cases. Moreover, the conquest, development and destruction of Jerusalem illustrate the city as a kinetic space, reflecting the unsettled history of the Iron Age. These characteristics all make Jerusalem a religious and political center from the ancient Near East time to present day, guiding the footsteps of believers around the world.
12. Briefly define the following: Matter is anything that takes up space. Element is any substance that can’t be broken down into substances with different properties. Atom is the smallest part of an element that displays the properties of the element.
The human mind seems incapable of comprehending the idea of infinity, yet we accept the idea of an immortal being. A
objects (e.g. a chair), definitions may vary, however they are all based on the existence of
In Wendell Berry’s chapter, The Body and the Earth, he discusses the connection between all earthly inhabitants, and its descent into misguided chaos by impact of time, evolution, and industry. He uses evidence from historical literature, religious mindset, the development of gender roles and consumerism of the 1950s, and how one defines love, marriage, and interconnectedness between what Berry calls “members of Creation.” His opinions of sexual monogamy and the importance of self-discovery via entrance into the “wilderness” are expressed clearly, but as the essay moves through each sub-chapter, his explanations become scattered and difficult to follow. For example, Berry’s ideas on religion and the relationship between body and soul as
is basically a definition that can be broken down by the word itself. Essentially, a
"Man comes closer to God through the questions he asks Him, he liked to say" (Wiesel 23). Questions were very common during the Holocaust (Shoah). They expressed the frustration the Jews had towards God. The same frustration Elie Wiesel had in the book The Night Trilogy. The author uses the exposition of these questions, (i.e. Where is God? How can he abandon us?), to show the large impact the Holocaust had on Jewish faith and to make the reader dwell deeper on God's purpose in his/her life the same way Elie Wiesel did.
Harold Crick in Stranger Than Fiction is a man who starts and ends every day the same way for twelve years. He starts off each day by brushing his teeth seventy-six times. He leaves for the bus at the same time each day calculating his steps. However, Harold was brushing his teeth on an average Wednesday and he heard a voice. He did not know where the voice was coming from; eventually, he concluded the voice was a narrator in his head. The voice in Harold’s head changed his life forever.
Always preach in such a way that if the people listening do not come to hate their sin, they will instead hate you – Martin Luther. When I first read this quote, a thought of me in high school came to my mind. When I was in high school my catholic religion teacher use to constantly give me detentions because I didn’t want to take flowers to a Virgin Mary statue. I use to end up getting in an argument and actually telling her that one of the commandments say do not worship any idols, and she will fight back saying it is part of the gospel. But did she really know what the gospel was?
By God I understand a being absolutely infinite, i.e., a substance consisting of an infinity of attributes, of which one expresses an eternal and infinite essence (1def6)
The implications of infinity (co) are actualiy not that old. The Greeks were some of the first mathematicians recorded to have imagined the concept of infinity. However, they did not actuaily delve into the entirety of this number. The Greeks used the term “potentially infinite," for the concept of an actual limitless value was beyond their comprehension. The actual term “infinity” was defined by Georg Cantor, a renowned German mathematician, in the late nineteenth century. It was originally used in his Set Theory, which is a very important theory to the mathematical world. The value of infinity can get a bit confusing, as there are different types of infinity. Many claim that infinity is not a number. This is true, but it does have a value. So, infinity may be used in mathematical equations as the greatest possible value. i The value of infinity Infinity (00) is the greatest possibleivalue that can exist. However, there are different infinities that, by logic, are greater than other forms of itself. Here is one example: to the set of ait Naturai numbers Z43, 2, 3, 4,...}, there are an infinite amount of members. This is usualiy noted by Ko, which is the cardinality of the set of alt natural numbers,
Eliade, in his book “The Sacred and Profane,” poses an interesting conjecture that all people are inherently religious. What one does and the decision they make in their lives are all reflections on what they find sacred. Sacred in this context is an extension of one’s belief held up in high esteem to the point where what is deemed sacred is god like. Religion is the frame that interprets what is sacred and gives it a name and a face. Christians, for example, view Christmas as a sacred time as it is the season of the birth of their savior; Jews view the Passover as sacred as it represents a time in their religious history where God passed over the Jews while sending a message to their enemies. What is sacred can manifest itself in any shape, form, or time; truly entering the fourth dimension of space. If something sacred is god like, what is sacred to those who do not have a God? How can something be sacred if there is not a frame of reference for the thing to be sacred? How can every decision a person makes be reflect what they find sacred, if they do not have a religious language to reflect this phenomena?
The idea of omnipotence has been a tricky concept for philosophers for many years. Many philosophers have tried to define it without success. In this essay, I intend to look at, as the question poses, whether ‘A being is omnipotent if it has every power which it is logically possible to possess’ is an adequate definition of omnipotent and then move on to look at some other ways of defining omnipotence to see if they do any better.