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

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III.70 π

What makes one number more fundamental and important, mathematically speaking, than another? Why, for instance, would almost everybody agree that 2 is more important than Image? One possible answer is that what really matters about a number is its properties, and in particular any interesting properties it might have that distinguish it from all other numbers. Of course, we now have to decide what counts as an interesting property: for example, why do we not regard it as interesting that Image is the only number that gives you when you double it? ...

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