An Introduction to ZG Geometry (Zhi Ziqi Geometry): A Discrete Calculus Framework at the Planck Scale

(The content of this article was originally handwritten by the author and transcribed by DeepSeek AI, so there may be errors. The translation was also performed by DeepSeek Harness; please point out any mistakes.The 'ZA' in the two accompanying figures refers to the comparison between discrete calculus and traditional calculus)1.3 Physical motivation and the continuum limitTo address extreme physical problems that classical calculus cannot resolve analytically, such as theblack-hole singularity, the fundamental step a is taken to be the Planck length (other values may bechosen as needed). The Planck length is the smallest physical scale and never becomes exactly zero,which removes the division-by-zero divergence of classical calculus at its root. In the limit a fi 0 thesystem reduces to classical calculus.