Catatan terhadap Turunan Fungsi Bernilai Real pada Ruang Metrik Diskrit

Syamsuddin Mas’ud

Jurnal Diferensial
Vol 6 No 2 (2024): November 2024

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