# Non-differentiable functions defined in terms of classical representations of real numbers

## TL;DR

This paper studies a subclass of non-differentiable functions defined via s-adic and nega-s-adic representations of real numbers, offering a simpler modeling technique based on digit transformations.

## Contribution

It introduces a novel, simplified method for modeling non-differentiable functions using digit modifications in s-adic and nega-s-adic representations.

## Key findings

- Provides a new approach to model non-differentiable functions
- Simplifies the analysis of functions based on number representations
- Highlights the role of digit transformations in function behavior

## Abstract

The present article is devoted to functions from a certain subclass of non-differentiable functions. The arguments and values of considered functions represented by the s-adic representation or the nega-s-adic representation of real numbers. The technique of modeling such functions is the simplest as compared with well-known techniques of modeling non-differentiable functions. In other words, values of these functions are obtained from the s-adic or nega-s-adic representation of the argument by a certain change of digits or combinations of digits.