Catatan terhadap Turunan Fungsi Bernilai Real pada Ruang Metrik Diskrit

Abstract

In these notes, comments will be provided on the paper by Herdiana et al. (Jurnal Ilmiah
Matematika dan Pendidikan Matematika: 15(2), 2023). In that paper, a definition of the derivative
of a function in a metric space is given, along with properties involving discrete metric spaces. The
purpose of these notes is to comment on the section involving discrete metric spaces, specifically
where a derivative is defined for functions in a discrete metric space, despite that discrete metric
spaces do not have limit points. Additionally, if certain modifications are made to the definition of
the derivative to accommodate discrete metric spaces, it would result in the derivative values not
being unique. This makes the discussion of the derivative of functions in discrete metric spaces
meaningless.