There are three basic properties of equality. These are known as the reflexive, symmetric and transitive properties. Let’s take a look at each of these. Reflexivity: This means that any object or number is equal to itself. Let’s draw an…
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In a paper published in 1924, Stefan Banach and Alfred Tarski proved a theorem which has sparked a great deal of controversy since. As improved over the years, the theorem roughly states that a solid ball in 3-dimensional space (actually,…
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November 16, 2013 Physical Science
The Josephson Effect and Josephson Junction The British physicist Brian David Josephson postulated the existence of a current which could traverse two superconductors separated by an insulator of miniscule dimensions in 1962. His prediction has allowed the development of quantum…
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November 16, 2013 Physical Science
While twenty first century Quantum mechanics is highly abstract and counter-intuitive it’s not that difficult to glean a fundamental understanding of this branch of modern physics by following its history. If we alter our usual ways of thinking that is…
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Understanding the quadratic equation can be confusing and difficult for the beginner. With so many terms and possibilities, the frustration often is overwhelming. This usually leads to the problem solver to giving up. But with any mathematical problem, it can…
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Manipulatives are any various objects designed to be moved or arranged by hand as a means of developing motor skills or understanding abstractions, especially in mathmatics. Children can use these manipulatives to get concret pictures of abstract concepts. Research indicates…
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I like logical explanations of dividing by zero, which we’ve all been told is “against therules.” I was sitting there in my apartment the other day with my math club buddies. Four of us in all. We decided you could…
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When dividing a number by zero, lets stay practical. Say, I have ten apples. I need to divide them between ten same size families (10 member each). It is usually understood, that dividing has to be in equal portions, very…
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Well well, are we racking our brains over this issue? Ladies and gentlemen, please allow me to put this issue to rest! I am a professor of mathematics with lifelong studies in foundational systems of analysis. The answer to this…
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How Long is a Piece of String? My English daughter in law sent me a recipe for Summer Berry Yoghurt Ice Cream. She adapted it from the internet, adding cream as a refinement. I wanted to publish it in our…
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