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Sequences and Numbers: The Formation and Evolution of the Concept of Number

Author: FENG Qi
Subject:Humanities & Social Sciences
Publication Date:2023.07.01
Page Count:344

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This book is a treatise in mathematical philosophy, addressing fundamental ontological and epistemological issues related to natural numbers. Starting from the phenomenon of order in the natural world and integrating the wisdom of ancient Chinese predecessors in applying order, this book attempts to illustrate how this almost ubiquitous “ordered structure” is the source of human understanding derived from life experiences like the widely seen “geometric structure.” It argues that the understanding of natural numbers and their arithmetic principles, also like the understanding of geometric knowledge, stems from the perception of the objective world. The book strives to use rigorous mathematical methods to demonstrate the natural and typical path of the concept of natural numbers to be abstractly divorced from the original source it relies on to become what Plato referred to as “eternity,” as well as the typicality of the fundamental developmental path from natural numbers to real numbers. Thus, it presents convincing insights into specific epistemological questions related to the concept of numbers.

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