# On $q$-deformed real numbers

## TL;DR

This paper introduces a novel $q$-deformation framework for real numbers using formal power series, extending previous rational deformations to all real numbers, and explores their properties and interpretations.

## Contribution

It develops a new $q$-deformation approach for real numbers, extending rational deformations to negative reals and Laurent series.

## Key findings

- Defined a $q$-analogue for positive real numbers.
- Extended the construction to negative reals resulting in Laurent series.
- Provides a new perspective on $q$-deformations of real numbers.

## Abstract

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.