The Shape of Data

Data is a large part of our everyday lives. We personally take in all kinds of data everyday. Things such as weather, political polls, meal costs, and much much more make up most of our daily lives. Companies collect data as well. Medical, consumer, weather, and other kinds of data have been collected for years. […]

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Axioms: Sets (ZF and ZFC)

In a previous post Axioms: Sets (Russell’s Paradox) we discussed axiomatic systems and we explored an example of why we might need one. Here we will view the axiomatic system that “fixed” naive set theory. This material will be a little heavy so in between each axiom We will see a little intuition to better help understand the […]

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Axioms: Sets (Russell’s Paradox)

Bertrand Russell (1872-1970) It isn’t too often that we think about or even explore the fundamental building blocks of mathematics. These building blocks are called axioms. Axioms are statements taken to be true, i.e. they cannot be proven. This causes mathematicians, whether they know it or not, to take a lot of things on faith. All of […]

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Banach-Tarski Paradox

It is a common occurrence in mathematics that when something does go wrong, it goes terribly wrong. This exact phenomenon occurs with the Banach-Tarski Paradox. Informally, it says that one can take a sphere (in 3 or more dimensional space)  can be split into finitely many pieces and, using only rigid motions, can be rearranged […]

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Pythagoras and the Square Root of 2

Pythagoras of Samos (569-500 BCE) was an actual person, but was also the founder of the Pythagoreans. He was a political figure and a mystic. Beyond this, he stood out in his time as he involved women as equals in his activities. The Pythagorean society focused on mathematics, but also had some religious properties which include […]

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The Prisoner’s Dilemma

The prisoner’s dilemma is a very popular situation in crime fiction, and can be found in many areas of real life. It originated from Merrill Flood and Melvin Dresher, however Albert Tucker is credited for formalizing it into its current form. So let us take a look. Two criminal partners, A and B, are arrested […]

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The Volume of a Sphere (without Calculus)

This is the third and final post on the volume of a sphere. The other two can be accessed by the following links, “Coordinates in 3-Space” and “The Volume of a Sphere with Calculus” As the title suggests, this will be a derivation without the use of Calculus. This proof is Greek in origin, in […]

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