The field of p-adic numbers

Joseph Mullaney

Friday 29th May, 2009 16:00-17:00 Mathematics Building, room 516


Informally the real numbers can be constructed by taking the rational numbers and `adding in' limits of all Cauchy sequences. In an analogous way we can build, for a fixed prime p, the field of p-adic numbers by `adding in' limits of Cauchy sequences in Q with respect to the p-adic norm rather than the usual absolute value. I will discuss this con- struction and explain how each p-adic number can be represented as a (possibly infinite) sum of powers of p.

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