Generally speaking, it can be said that Kurt Godel showed via his Incompleteness Theorems that any formal system based on axioms that are sufficient for arithmetic can be manipulated in such a way as to make the following like statement…
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Scalars and vectors are used in science to mathematically describes certain quantities (e.g. temperature, or velocity) in order to know what sort of mathematical operations can be properly done on them to give real results. The important phrase is “mathematically…
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Al Karaji enjoyed fame as a mathematician and engineer in his lifetime. Born around 980, he died in 1030. Some dispute exists as to whether his actual name was al-Karaji or al-Karkhi. If his name was al-Karanji, then he is…
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I am going to be using multiple number systems so I will explain a few terms to keep this as simple as possible. When referring to a system I will spell out the number (base ten, base eleven). When I…
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A prime number is any number that cannot be divided by any other number except one and itself. The twenty-five prime numbers below 100 are 2, 3, 5, 7, 11, 13, 17, 19, 23, 29, 31, 37, 41, 43, 47,…
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There were at least four self contractictory arguments concerning time and space that circulated around the philosophical schools in Athens during the fifth century B.C. The one that was most closely associated with Zeno of Elea is called the Paradox…
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Integral calculus is the mathematics of integration, which is used to calculate volumes and areas of complicated shapes. Whereas a rectangle or circle has a simple mathematic function for finding its area, an undefined, squiggly shape is not as straightforward,…
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On the subject of “Zero Division”, I would definitely agree that zero division is possible in a very general case. First, I would just like to give a short background to describe the motivation of my arguments. One can view…
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Around 300 BC, the Greek Euclid wrote “The Elements”, which stated five postulates upon which he based his theorems. These postulates form the basis of what is known as Euclidean geometry, and is the foundation of the geometry most of…
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In 1482, Euclid’s Elements was published, presenting the first clear and logical framework for a geometrical system. This Euclidean Geometry, which was known simply as ‘geometry’, is an axiomatic system, in which all theorems are derived from a smaller number…
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