For a prime number p, the field of p-adic numbers is a completion of the field of rationals. Together with the field of reals, the p-adic numbers form all completions of ℚ. In this chapter we discuss the notion of absolute values on fields and their completions. We give several useful descriptions of the field ℚ p of p-adic numbers and compute the additive and multiplicative Haar-measures, which are the equivalents of the Lebesgue measure in the case of the real numbers.
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