10 votes

# Pictures of Ultrametric Spaces, the p-adic Numbers, and Valued Fields

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This is a paper on how we can think about drawing the p-adic numbers, which are a set of number systems formed by extending the rational numbers in a different way than we extend them to make our...

This is a paper on how we can think about drawing the p-adic numbers, which are a set of number systems formed by extending the rational numbers in a different way than we extend them to make our normal real numbers. I think this is a reasonably accessible paper even if you don't have much higher math experience, the only background you really need is the concept of a metric space, which is simply a set equipped with a metric, that is, a way of measuring distance that follows a few rules. Copying from wikipedia, informally:

the distance from a point to itself is zero,
the distance between two distinct points is positive,
the distance from A to B is the same as the distance from B to A, and
the distance from A to B (directly) is less than or equal to the distance from A to B via any third point C.

2 votes