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Euclid Releases his proof of the existence of the irrational numbers.
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The Egyptians and Babylonians were first recorded in 3000 BC using the natural numbers and rationals. Egyptians used base 10 while the Babylonians used base 60.
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The Pythagoreans(a sect of Greek Philosophers) suppress evidence that irrational numbers exist by murdering Pythagoras. Pythagoras had proof of irrational numbers.
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The Arabic Number System begins. This is a place value system that uses base 10, including zero.
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Arabic Number System Becomes Prevalent in Europe. Negative Numbers are defined.
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Imaginary Numbers are first used to give notational solutions.
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Compley Arithmetic is defined as part of Mathematics(arithmetic that used the imaginary number "i"). This leads to the development of the Argand Diagram and much, much more.
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The Euler Equation is used to define the natural logarithm of negative numbers.
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Cantor and his Diagoal Argument define the real numbers absolutely and defend them rigorously. The argument also establishes countable and uncountable infinities.
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Godel's Incompleteness Theorem(as expressed by the Liar's Paradox) rules out total completeness of mathematics. Consisency is not affected.