Nobody downloaded yet

Math paradoxes - geometric series - Speech or Presentation Example

Comments (0) Cite this document
Though this might sound like another colorless joke, it is indeed a deep paradox in mathematics. David Hilbert, the great German mathematician pointed out that if there were to be a hotel with an…
Download full paperFile format: .doc, available for editing
GRAB THE BEST PAPER96.5% of users find it useful
Math paradoxes - geometric series
Read TextPreview

Extract of sample "Math paradoxes - geometric series"

Download file to see previous pages The key concept here is that there are an infinite number of rooms, so that our logic – which would terminate in the ‘real world’- can go on forever. This is called ‘Hilbert’s infinite hotel paradox’ and the famed hotel is often jokingly referred to a “Hilberts” analogously to “Hiltons”!
Infinity is a very hard concept to understand and possess the most absurd properties of any mathematically definable object. Cantor was the first mathematician to study the properties of infinite sets in greater detail. Suppose you group together all the even numbers (2, 4, 6, 8, 10…) and all the perfect squares (1, 4, 9, 16…) separately into two groups. Which group has more members? If selection was from a small set, say from the first 100 numbers, then the answer is fairly obvious. There are 50 even numbers in the list from 1 to 100 while there are only 10 perfect squares. As the set grows larger, we expect the ratio to remain the same. However, if the grouping is from the entire set of integers, then lo and behold, we find the rather unusual result that both the groups have exactly the same number of members! This is because, for every even number from the first set we can find a perfect square in the other set. Thus, since for every element in the first set there is a corresponding element in the next set, we have to conclude that no set has more members than the other; as if this were to be so, some even number would have no perfect squares to relate to.
Series’ show the remarkable properties of “Convergence and “Divergence”. These properties happen to be very well studied as they find applications in most branches of engineering. Take an apple pie and cut it in half. Cut one of these halves in half again and repeat the process. Initially you have 1 object (in this case a pie). It then becomes . The third iteration reduces it to . It is easy to see where we are going. ...Download file to see next pagesRead More
Cite this document
  • APA
  • MLA
(“Math paradoxes - geometric series Speech or Presentation”, n.d.)
Math paradoxes - geometric series Speech or Presentation. Retrieved from
(Math Paradoxes - Geometric Series Speech or Presentation)
Math Paradoxes - Geometric Series Speech or Presentation.
“Math Paradoxes - Geometric Series Speech or Presentation”, n.d.
  • Cited: 0 times
Comments (0)
Click to create a comment or rate a document

CHECK THESE SAMPLES OF Math paradoxes - geometric series

College Math Math Problem

...Math Problem a) I constructed the first linear function based on the municipal solid waste data for 1970 and 1997 and the second linear function based on the data for 1980 and 1997. A dependent variable is the annual production of municipal solid waste in million tons. An independent variable is the number of years after 1960. Based on the municipal solid waste data from the graph, I received such numbers for independent and dependent variables for the models. Model 1 Model 2 Dependent Variable Independent Variable Dependent Variable Independent Variable 121 10 152 20 217 37 217 37 Model 1: 121 = a + b*10 217 = a + b*37 The solution is a=85.4, b=3.56. Therefore, the first linear function is: Annual MSW =...
2 Pages(500 words)Math Problem


...Derivatives of sine functions Investigate the derivative of the function Figure Graph of function and for Figure shows the graph of function (red curve) and it derivative (gradient) (green curve). From graph it can be seen that the gradient of the function behaves similarly as original function, however it shifts left side by (or shift right side by). = or From above, it is obvious that the graphs of the sine and it derivative cosine functions are sinusoids of different phases1. The derivative is also a sine function with a phase-shift of (or). Conjecture: The graphs of the sine function, and its derivative cosine function, are sinusoids of different phases i.e. the derivative is also a sine function with a phase-shift... of sine...
4 Pages(1000 words)Essay


...SSQ-CH4 Start     26 Sep 2008 at 02:00 PM Due     28 Oct 2008 at 01:00 AM Access after Due    Yes. Mark Late Graded:    No Post-Lecture, Question 1 To enter a net income for the period into a work sheet requires an entry to the: balance sheet debit column and the balance sheet credit column. income statement debit column and the income statement credit column. income statement debit column and the balance sheet credit column. income statement credit column and the balance sheet debit column. Post-Lecture, Question 2 Income Summary has a credit balance of $12,000 after closing revenues and expenses. The entry to close Income Summary is: credit Income Summary $12,000, debit the owners drawing account $12,000. debit Income Summary... Start    ...
1 Pages(250 words)Speech or Presentation

Cubism and Geometric Abstraction

...Cubism and Geometric ion (20th Century Art History The Bicycle Race by Lyonel Feininger The given picture is Lyonel Feininger’s The Bicycle Race, which attracted great mass attention as a work in Cubism. It is a work that makes one clearly understands what Cubism is and the peculiarities of this movement. The artist has skillfully used his talent that even an ordinary viewer can identify the effective use of different colors and geometrical forms. Feininger’s picture mainly consists of triangles which form the outline figure of the bicycle racers. Along with triangles, squires and circles also have been used. The cave and convex— the most important feature of Cubism, has expertly utilized in this picture...
1 Pages(250 words)Assignment


...Death Penalty Thesis ment: The statistics used in death penalty cases can be used to argue for or against the practice, but rarely are all of the real statistics given. Outline I. Introduction II. Pro Death Penalty Statistics a. Victims b. Death Row Inmates with Prior Convictions III. Anti Death Penalty Statistics a. Race b. Education Level of Death Row Inmates IV. Real Death Penalty Statistics a. Race b. Number of Executions since 1930 V. Conclusion The statistics used in death penalty cases can be used to argue for or against the practice, but rarely are all of the real statistics given. Pro death penalty advocates generally state crime statistics, while anti death penalty advocates cite the cost... Penalty Thesis ment: ...
5 Pages(1250 words)Essay


... XXXXX Number: XXXXX XXXXX XXXXXX XXXXX of XXXXX XX – Jun - 2010 Mathematics - Assignment A. What kind of correlation do you expect to find between annual income and amount spent on car? Will it be positive or negative? Will it be a strong relationship? Base your answer on your personal guess as well as by looking through the data. The two variables, annual income and amount spent on car are expected to have a positive correlation. The main reason is that when the income is higher, people tend to spend more on their cars. Moreover, the relationship between the two variables is expected to be strong. Based on the data given, it is evident that the annual income and the amount spent on car are directly proportional to one... XXXXX Number:...
4 Pages(1000 words)Essay


...Chapter 5 & 6 Questions Find the prime factorization of 191 or if the number is prime.  (Format: prime or not prime)  prime 2. Determine whether 580 is divisible by 2, 3, or 5. State your answer as a single number or two or three numbers divided by a comma, i.e., 2,3 or 2,5, etc.  (Format: Whole numbers separated by commas such as 4,7 or as a single number such as 4)  580 = 2*290 580 = 5*116 Divisible by: 2, 5 3. Find the LCM of 12,15, and 20.  (Format: Whole number such as 4)  12 = 2*2*3 15 = 3*5 20 = 2*2*5 LCM = 2*2*3*5 = 60 4.  Use the LCM determined above to add: 1/12+ 1/15 + 1/20. State your answer in fraction form and reduced to the lowest common form.  (Format: Fraction such as 1/6) (1/12) + (1/15) + (1/20) = (5 + 4 + 3)/60...
4 Pages(1000 words)Speech or Presentation


... Mathematics The first button used is obviously the ‘Home’. This button includes the summary of all the contents of the My Math Lab. Second button is ‘Temporary Access’, this button leads to the temporary access page to my assignments and course work by providing a temporary access code. The ‘HOMEWORK’ button enables access to homework and tests and other things related to the course work. Quizzes and test button contains details of test that were conducted and upcoming test details. Study Plan button contains practice test and quizzes tabs and score of each completed quiz. Grade Book button contains grades of the completed quizzes and tests. Expand Chapter content button it populates more tabs with the heading of the chapters... such info...
1 Pages(250 words)Lab Report


...Assignment al Affiliation: Assignment Find the indicated values. (a)  =   (b)  =  2.List all of the combinations of {a, b, c, d} when the elements are taken two at a time. (Select all that apply.) {a, b} {a, c} {b, b} {b, c} {b, d} {a, a} {c, c} {d, e} {d, d} {c, d} {a, e} {a, d} 3.A committee of four is to be selected from a group of 15 people. How many different committees are possible, given the following conditions? (a) There is no distinction between the responsibilities of the members.   (b) One person is the chair, and the rest are general members.   (c) One person is the chair, one person is the secretary, one person is responsible for refreshments, and one person cleans up after meetings. 4.An English class consists of 26...
5 Pages(1250 words)Speech or Presentation


...and ascribing symbols to smaller unequal parts of the cube, children even memorized algebraic formula for cube of a trinomial. Thus, it was revealed that children can remember quantity and order through visual memory of objects. 6. How sensorial and practical life activities relate to Montessori Math curriculum, control of error, direct and indirect Aim of Montessori Math Materials Sensorial activities includes geometric materials such as cubes, prisms and rods, which aim at refinement of child’s senses and stereognostic skills. The activities help the child in discriminating and identifying objects in relation to properties such as size, shape, color, texture and smell. These...
2 Pages(500 words)Essay
sponsored ads
We use cookies to create the best experience for you. Keep on browsing if you are OK with that, or find out how to manage cookies.

Let us find you another Speech or Presentation on topic Math paradoxes - geometric series for FREE!

Contact Us