Mysterious Numbers

Take any 3 digit number whose digits are not all the same. Numbers like 027, 889, and 534 are all valid examples. Now let us just start with 027. We are going to play a game. First rewrite 027 by ordering the numbers in descending order, 720. Then subtract from it the number made by […]

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The Pigeonhole Principle

  Imagine that two people are playing “Paper, Rock, Scissors” and one wins the first game.  Then the loser chimes in and declares “best two out of three!” This is a common phrase heard in win/lose games and it utilizes a very important and subtle principle known as the pigeonhole principle. We know that two out […]

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Paradoxes: Gabriels Horn

Gabriel’s horn is the function on the interval rotated around the x-axis. Intuitively, it should require less paint to fill the horn than to paint the surface (imagine painting a box or a ball). With Gabriel’s Horn this is not the case. In fact, There is an infinite surface area and only a finite volume. […]

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Paradoxes: Zeno of Elea

Zeno of Elea was a Greek philosopher famous for paradoxes which assert that motion is nothing but an illusion. It is assumed that Zeno created the paradoxes in support of Plato’s Parminedes.  We will present two of these paradoxes along with a refutation.   1. Achilles and the Tortoise Achilles was challenged to a race by […]

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The Road to Larger Infinities

Georg Cantor was a German mathematician responsible for the invention of set theory. Before him, the concept of infinity was not well studied or considered by mathematicians. The importance of Cantor’s development of set theory is very clear as it is the basis for much of modern mathematics. We will take a look at Cantor’s […]

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