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We associate a formal power series with integer coefficients to a positive real number, we interpret this series as a $q$-analogue of a real. The construction is based on the notion of $q$-deformed rational number introduced in arXiv:1812.00170. Extending the construction to negative real numbers, we obtain certain Laurent series.
We study analytic properties of $q$-deformed real numbers, a notion recently introduced by two of us. A $q$-deformed positive real number is a power series with integer coefficients in one formal variable~$q$. We study the radius of convergence of th
We explain the notion of $q$-deformed real numbers introduced in our previous work and overview their main properties. We will also introduce $q$-deformed Conway-Coxeter friezes.
This work is a first step towards a theory of $q$-deformed complex numbers. Assuming the invariance of the $q$-deformation under the action of the modular group I prove the existence and uniqueness of the operator of translations by~$i$ compatible wi
Nonextensive statistical mechanics has been a source of investigation in mathematical structures such as deformed algebraic structures. In this work, we present some consequences of $q$-operations on the construction of $q$-numbers for all numerical
We described the $q$-deformed phase space. The $q$-deformed Hamilton eqations of motion are derived and discussed. Some simple models are considered.