Adics

Some articles on adic, adics:

0.999... - In Alternative Number Systems - p-adic Numbers
... The p-adic numbers are an alternative number system of interest in number theory ... Like the real numbers, the p-adic numbers can be built from the rational numbers via Cauchy sequences the construction uses a different metric in which 0 is closer to p, and much closer to pn ... The p-adic numbers form a field for prime p and a ring for other p, including 10 ...
Hasse Principle - Intuition
... solution, then this also yields a real solution and a p-adic solution, as the rationals embed in the reals and p-adics a global solution yields local solutions at each prime ... or rather, asks what the obstruction is when can you patch together solutions over the reals and p-adics to yield a solution over the rationals when can ... For number fields, rather than reals and p-adics, one uses complex embeddings and -adics, for prime ideals ...