  We propose a one-parameter family \ $\mathbb{R}_q$ \ of deformations of the
reals, which is motivated by the generalized additivity of the Tsallis entropy.
We introduce a generalized multiplication which is distributive with respect to
the generalized addition of the Tsallis entropy. These operations establish a
one-parameter family of field isomorphisms \ $\tau_q$ \ between \ $\mathbb{R}$
\ and \ $\mathbb{R}_q$ \ through which an absolute value on \ $\mathbb{R}_q$ \
is introduced. This turns out to be a quasisymmetric map, whose metric and
measure-theoretical implications are pointed out.
