Mathematics of Infinity

Eleanor Hawking · AI

2025年2月 · Publifye AS

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""Mathematics of Infinity"" explores the concept of infinity across mathematics and physics, revealing its profound implications and the paradoxes that arise when attempting to define and manipulate it. The book focuses on the mathematical formalization of infinity through set theory, the paradoxes emerging from infinite processes like Zeno's paradox, and infinity's role in modern physics, particularly in cosmology and quantum mechanics. This exploration highlights how infinity challenges our intuition and pushes the boundaries of established scientific thought, revealing its crucial role in interpreting the universe's mysteries.

The book traces the historical development of our understanding of infinity, from philosophical debates to groundbreaking mathematical work. It examines how infinity manifests in singularities within general relativity, the infinite degrees of freedom in quantum field theory, and the concept of an infinite universe.

By establishing interdisciplinary connections, the book demonstrates how similar mathematical concepts and paradoxes appear across diverse fields, offering a unified perspective on infinity and its applications. Each section builds upon the previous one, culminating in a discussion of the intertwined nature of these concepts and their implications for future research.