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Whilst Archimedes may not have viewed fractions as we view them, this doesn't mean that they didn't have the concept of a fraction. This is in part, because there is more than one way to view the concept of a number. One of the viewpoints put forward by category theory is that the natural integers (the strictly positive integers, that is not including zero) ...


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No, Archimedes, and ancient Greeks generally, did not see fractions as numbers, and they did not use fractions as we use them today, they did not use them at all. What they used was ratios of magnitudes. Despite some superficial similarities, ratios were not fractions, and they were not single entities, numbers or otherwise, they were relations between ...


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