 The corresponding mapping to an additive group would be the logarithm of the absolute value, although this does not meet all the requirements of a valuation.According to Ostrowski's theorem, up to a natural notion of equivalence, the real numbers and formula_20-adic numbers, with their orders and absolute values, are the only valuations, absolute values, and places on the rational numbers.The local-global principle allows certain problems over the rational numbers to be solved by piecing together solutions from each of their places, again underlining the importance of primes to number theory.