This section is an informal introduction to padic numbers, using examples from the ring of 10adic decadic numbers. We will then consider fractions of padic integers, that is padic numbers, which we will show form the field qp. It seems that hensels main motivation was the analogy between the ring of integers z, together with its. Madore revised 7th december 2000 in all that follows, pwill stand for a prime number. We give a brief and elementary introduction to padic numbers and padic functions. Think of a power series more like a number than like a function. In the course of their undergraduate careers, most mathematics majors see little beyond standard mathematics. One way to construct the real numbers involves creating equivalence classes of cauchy sequences of rational numbers with respect to the usual absolute value. This is a wellwritten introduction to the world of padic numbers. The decadic numbers are generally not used in mathematics. An introduction to the padic numbers semantic scholar.
In r, we may represent irrational numbers by nonterminating, nonrecurring decimal. We all know that p 2 is irrational, so that 2 is not a square in the rational eld q, but that we can enlarge q to the real eld r where 2 is a square. N, z, q, rand care the sets of respectively the natural numbers i. An introduction to the algorithmic of padic numbers.