Deformed Mathematical Objects Stemming from the q-Logarithm Function

Generalized numbers, arithmetic operators, and derivative grouped in four classes based on symmetry features, are introduced. Their building element is the pair of q-logarithm/q-exponential inverse functions. Some objects were previously described literature, while others newly defined. Commutativity, associativity, distributivity, also a linear/nonlinear derivatives, observed within each class. Two entropic functionals emerge from formalism, one them nonadditive Tsallis entropy.