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The Princeton Companion to Mathematics by Imre Leader, June Barrow-Green, Timothy Gowers

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II.1 From Numbers to Number Systems

Fernando Q. Gouvêa

People have been writing numbers down for as long as they have been writing. In every civilization that has developed a way of recording information, we also find a way of recording numbers. Some scholars even argue that numbers came first.

It is fairly clear that numbers first arose as adjectives: they specified how many or how much of something there was. Thus, it was possible to talk about three apricots, say, long before it was possible to talk about the number 3. But once the concept of “threeness” is on the table, so that the same adjective specifies three fish and three horses, and once a written symbol such as “3” is developed that can be used in all of those instances, the conditions ...

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