Logical Dichotomy and Structural Reconstruction of Finitude and Infinity

This book represents the fruit of the author's years long research and reflection. While accompanying his child through growth, the author started from the doubts the child encountered when learning mathematics. Gradually, he perceived certain biases within the foundational concepts of the existing mathematical system. Through continuous sorting and deduction, a revised theoretical framework has been developed. The objective of this book is to repair the conceptual loopholes mentioned above, rather than constructing an entirely separate system from scratch. The proposed theory remains compatible with wellestablished mathematical results validated by practice. Admittedly, as an emerging theory, though internally selfconsistent, numerous details still require refinement and improvement via further research. It is worth noting that the theory in this book cannot be adequately tested by presentday AI tools. Current mathematical reasoning performed by artificial intelligence is built upon traditional mathematical paradigms. This observation illustrates that AI lacks genuine original speculative capacity and cannot replace human creative thinking. The book would not have come into being without the author's son. As a middleschool student, he spotted inconsistencies in standard mathematics during his coursework and kept raising thoughtful questions. Those youthful inquiries prompted the author to examine fundamental problems earnestly. The intellectual exchange between father and son ultimately gave rise to this work.