I chose to read chapter 3 on the Pigeonhole concept in Kent Bessey’s book, To Infinity and Beyond. The Pigeonhole principle is a really simple concept, discovered all the way back in the 1800s, by a man named Peter Gustav Lejeune Dirichlet. It is one of the most straightforward but useful ideas in mathematics. It has been used to explain everything from the amount of hair on people’s heads to quantum mechanics. A basic version of Pigeonhole is, if (N+1) pigeons occupy N holes, then some hole must have at least 2 pigeons. This principle can be a powerful way to look at different mathematical problems, it’s process can be very useful when trying to gather and analyze numerical data.
In Kent Bessey’s book, I found that by using this principle, amazing conclusions can be drawn that would be impossible, or difficult but, on the other hand turn out to be true. I wasn’t sure why this type of information was
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It makes sense now and that I have learned a little bit more about the use of pigeonhole in mathematics. Now I understand that there is a way to make a conclusion that contains “at least” in it with absolute certainty. The pigeonhole principle shocked me and I found it interesting that such declarations can be made and such conclusions drawn and they be accurate. As I read the first principle, it seemed to me like chance, that two people in the same city would be eating breakfast at the same time, but I learned that instead of chance, it is certainty. This fascinating principle of being able to absolutely imagine that there is a possibility for an event to happen based solely on mathematic raw data is indeed intriguing. I loved the ending to this chapter, Bessey said, “We are not only certain there is a solution, but also confident that once a solution is found we can end our search—for there are no others.” I realized after reading this chapter, that there is always a solution for every
The two pieces of art that I have chosen to compare reside in Toronto’s ‘Art Gallery of Ontario’. While the two pieces are very different in terms of artistic medium and period, the painting, “The Academy”, by Kent Monkman, makes direct reference to Auguste Rodin’s sculpture “Adam”. The sculpture is a giant bronze cast from 1881 inspired by Michealangelo’s “Creation of Adam” Ceiling Fresco in the Sistine Chapel. “The Academy” by Canadian painter, Kent Monkman was commissioned by the AGO in 2008. The piece was created as a visual commentary on the “injustices and oppression Aboriginal people have suffered” (Filgiano) However different they may appear to be, Kent Monkman ‘borrows’ the theme of Rodin’s “Adam” sculpture to create an analogy between Adam’s banishment from paradise and the Aboriginal’s loss of paradise through colonization.
In order to understand the concept of Moore’s Paradox, we must first assess and understand the behavior of logical and performative contradictions. Credited for devising and examining this paradox, George Edward Moore, a British philosopher who taught at the University of Cambridge and studied ethics, epistemology, and metaphysics describes the paradox in its omissive and commissive forms in which we will discuss thoroughly. I will then express my standpoint on which solution is the most optimal choice for Moore’s Paradox in order to analyze and explain why I believe my solution is superior to other solutions. I will also discuss any issues that arise
In probability theory, The Birthday Paradox serves as a proposal that in a room of twenty-three people, there is a 50% chance that two or more people within that room share the same birthdate. The legendary source of this paradox claims to be discovered and first practiced by Richard von Mises, who posed the theory in 1939, However, the first practicing of The Birthday Paradox is, in all originality, Harold Davenport, who discovered this theory in 1927, making it the earliest discovery of this paradox. Another practice of the theory was taken into account by Philip J. Erdelsky, a computer programmer of over twenty years as well as a research and development engineer for eight. Erdelsky tested the paradox in his college years. Within his discovery, Erdelsky hypothesized that no person was born on February 29th, although birthdates were equally apportioned throughout 365 days of an average year. In conclusion to his college experimentation, Erdelsky found this theory on the recurrence of birth dates in a select group to be true.
...ion. Hempel’s solution provides to give a reason as to how induction can lead to confirmation and how the logical gap can be filled through the use of logically equivalent statements. However, his view and answer to the paradox prove to be a stretch and lead to the issue of common sense being broken and illogical observations being made to confirm the hypothesis. Good successfully brings attention to this rather blatant error on the part of Hempel to eventually lead to the Raven paradox being invalid. Not only is Good effective in highlighting errors within Hempel’s solution, but Popper, Scheffler, and Goodman are all equally successful in negating individual parts of Hempel’s argument as well. In the end, it is the addition of all these counterarguments that prove to exhibit that Hempel is unsuccessful in trying to come up with a valid answer to the raven paradox.
Are you part of a community and you don’t even know it? A community is a feeling of fellowship with others because one shares common attitudes, interests, and goals. In the remix text “It Takes a Tribe” David Berreby talks about how college students make “tribes” within their school and tribes against other schools. This text relates to my community because the One Direction fandom could be considered a “tribe” full of fans who are against other fandoms of other artists because they all think they 're the best.One direction is a very popular boy band thats known all over the world and very successful. This community meets everywhere , concerts, schools, and social media etc., since one directions fans are everywhere .In the One Direction
as John Anderson explained: "I did not want to marry a girl belonging to my own place because I knew I could not bear to see her ill-treated." Moses Grandy agreed he wrote: "no colored man wishes to live at the house where his wife lives, for he has to endure the continual misery of seeing her flogged and abused without daring to say a word in her defense." As Henry Bibb pointed out: "If my wife must be exposed to the insults and licentious passions of wicked slave-drivers and overseers. Heaven forbids that I should be compelled to witness the sight."
In The Pursuit of Holiness the author, Jerry Bridges, shows the Christian what it looks like to be truly holy. Holiness is to live a life of conformity to God’s will. Holiness is a joint effort between God and his people, it is not something God just gives us when we accept him into our lives. Many times Christians neglect the responsibility we have of moving towards God and pursuing holiness. Holiness is not something that is fully attainable, it is a constant pursuit to be like God. Holiness is expected by God. Not only is it expected, it is a part of our birthright as Christians. God specifically calls us to holiness, “I am the Lord your God; consecrate yourselves and be holy, because I am holy” (Leviticus 11:44a). God is perfectly holy. Therefore, to be holy is to conform to the character of God, and not to this world. Since God is perfectly holy we can have confidence that when dealing with us he is just and perfect. Bridges explains that holiness is God’s greatest attribute. Since he is holy, that makes all his other attributes good, holy, and just. God, being all of these things, cannot hold us to a standard of any less than holiness.
One example of this in relation to Bundy’s case is how it allowed him to apply for an appeal over and over again. There was fairness in his trails by moving the trail location, by moving the location it gave Bundy a fail trial with an impartial jury. Also, with the theory of the X or Y model you could say that Bundy could have had an extra X chromosome since he was a person who lived in a life of crime and had an uncontrollable urge to keep killing, but you can’t exactly confirm that the theory is right since it’s never been proven to be 100% true, hence the term to why its called a
The image you have taken effectively demonstrates the consumer society in which so many of us have fallen into. Multinational corporations such as Apple have effectively weeded themselves into our idea of a comfortable living shown by the number of people in the store who wish to associate with the brand. The photo, paired effectively with the quote, raises awareness of those who fall into the traps of temptation to fulfil our wants of “comfort” while disregarding our call to duty with others. The number of individuals with their heads down in the phot0 shows how common a practice it has become to allow our devices to separate us from others. As George Faludy states in “Arming the Spirit”, we owe it to ourselves to “rise above evil and mindlessness.”
The Four Color Theorem was one of the first major theorem that was proved by the computer. It is the proof that can not be verified by many mathematicians. But the independent verification had convinced people that the theorem was finally proved. I believe because of the new technology, the proof of Four Colo Theorem will be improved in later time.
The principle of “explosion” in classical Logic consists that anything can be inferred from a contradictory proposition. In other words, we could conclude anything we want out of a contradictory proposition.
Ronald Lewis Graham is an American mathematician who comes from California, and who was born in 1935. His work revolves around looking for patterns in chaotic systems, and so he pursued a pattern involving joining up four points with six lines, all red or all blue, in a tube of many dimensions. This pattern is repeated many times in an all-blue cube, but Graham changed the color of individual edges, trying to avoid the pattern in just one color. His aim was to see if avoidance of the pattern in blue would force it to pop up in red. This doesn't happen in three, four, or even five dimensions. The number of dimensions required to guarantee this pattern turns out to be Graham's number. This part of mathematics is called Combinatorics, and Graham started looking into a more specific field of it, called Ramsey’s Theory. This theory could be explained the following way; this is an example of where complete disorder is impossible. In any large system, you've got to have a smaller set that has a lot of structure to it....
Neale, Vicky. "Theorum11the pigeonhole principle." Theorem of the Week. Cambridge Maths Tripos, 25 March 2009. Web. 8 Dec 2013. .
There are therefore absolute distinctions between what is true and what is false in such fields where a distinction matters and is significant, but circumstances also arise when truth must be relative to a certainty continuum where one may find a middle ground.
Because they occur so frequently, there is an infelicitous propensity to invoke mundane distributions in situations where they may not be applicable. As Lippmann verbally expressed, "Everybody believes in the exponential law of errors: the experimenters, because they cerebrate it can be proved by mathematics; and the mathematicians, because they believe it has been established by observation"