This study summarizes the series of confusions that arise when studying calculus theory within the traditional limit-based frameworks. The study analyzes several questionable aspects of constructing calculus systems based on limits from eight dimensions: rules of the division operation, objective laws of partition, differential concepts, logical deduction, semantic connotations, learning and practice, the transition from quantitative to qualitative change, and numerical field operations. It argues that the limit is merely an outward manifestation of calculus rather than its essence, introduces the concepts of explicit and implicit real fields, explains the internal operation mechanism of differentiation and integration, and contends that calculus is an inherent natural property of real numbers, and is a mathematical discovery rather than a human invention, in order to construct a cognitive system of calculus that can be connected with elementary mathematical operation rules, and provide a new perspective for understanding the underlying logic of calculus.