On $q$-deformed 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.

References in corpus (1)

• $q$-deformed rationals and $q$-continued fractions

Cited by in corpus (8)

• $q$-deformed rationals and $q$-continued fractions
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• On radiuses of convergence of q-metallic numbers and related q-rational numbers
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• $q$-Rational and $q$-Real Binomial Coefficients
• Hyperbinary partitions and q-deformed rationals
• On radius of convergence of $q$-deformed real numbers
• Continued fractions for $q$-deformed real numbers, $\{-1,0,1\}$-Hankel determinants, and Somos-Gale-Robinson sequences