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Mathematics

The p-adic Numbers and Their Surprising Topology

Quick fact

In the p-adic world, the infinite series 1 + p + p² + p³ + ... converges to a surprising but finite value: 1/(1-p), even though the terms are getting larger in the usual sense.

Why this is interesting

We all know that on the number line, numbers get closer as they get closer to each other. But what if we changed the meaning of 'closeness' entirely, and a large number could be considered 'closer' to zero than a small one?