Titlebook: p-adic Numbers; An Introduction Fernando Q. Gouvêa Textbook 19972nd edition Springer-Verlag Berlin Heidelberg 1997 Algebra.absolute values

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0172-5939 methods borrowed from calculus and analysis for studying such problems. More recently, p-adic num­ bers have shown up in other areas of mathematics, and even in physics.978-3-642-59058-0Series ISSN 0172-5939 Series E-ISSN 2191-6675

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Textbook 19972nd editionfford a natural and powerful language for talking about congruences between integers, and allow the use of methods borrowed from calculus and analysis for studying such problems. More recently, p-adic num­ bers have shown up in other areas of mathematics, and even in physics.

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Foundations,ce a different absolute value function on the field of rational numbers. This will give us a different way to measure distances, hence a different calculus. Once we have that, we will use it (in Chapter 3) to construct the .-adic numbers.