section_path: Extensions of the concept/p -adic numbers
section_name: p -adic numbers
paragraph_text: p -adic numbers
  
  The p -adic numbers may have infinitely long expansions to the left of the decimal point, in the same way that real numbers may have infinitely long expansions to the right. The number system that results depends on what base is used for the digits: any base is possible, but a prime number base provides the best mathematical properties. The set of the p -adic numbers contains the rational numbers, but is not contained in the complex numbers.
  
  The elements of an algebraic function field over a finite field and algebraic numbers have many similar properties (see Function field analogy). Therefore, they are often regarded as numbers by number theorists. The p -adic numbers play an important role in this analogy.