2adics
2-adics, or the 2-adic numbers, are the completion of the rational numbers with respect to the 2-adic absolute value. They form the field Q2, with its ring of integers Z2. Z2 can be described as the inverse limit of the system Z/2^n Z, or equivalently as the set of all infinite series sum_{i=0}^∞ a_i 2^i with digits a_i ∈ {0,1}.
Every nonzero 2-adic number x can be written uniquely as x = 2^k u with k ∈ Z and
Topological and algebraic properties: Z2 is a compact, totally disconnected ring; Q2 is a locally compact field.
Arithmetic and analysis: computation in 2-adics follows non-Archimedean rules, with convergent sequences determined by their 2-adic