 The completion can in this case be constructed also from the "p"-adic absolute value on Q.The "p"-adic absolute value on Q is a map formula_206 from Q to R given by formula_207 where formula_208 denotes the exponent of "p" in the prime factorization of a nonzero integer "n" into prime numbers (we also put formula_209 and formula_210).It defines a distance function on Q and the completion of Q as a metric space is denoted by Q"p".