Beyond Infinity
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Author Description
Even small children know there are infinitely many whole numbers - start counting and you'll never reach the end. But there are also infinitely many decimal numbers between zero and one. Are these two types of infinity the same? Are they larger or smaller than each other? Can we even talk about 'larger' and 'smaller' when we talk about infinity? In Beyond Infinity, international maths sensation Eugenia Cheng reveals the inner workings of infinity. What happens when a new guest arrives at your infinite hotel - but you already have an infinite number of guests? How does infinity give Zeno's tortoise the edge in a paradoxical foot-race with Achilles? And can we really make an infinite number of cookies from a finite amount of cookie dough? Wielding an armoury of inventive, intuitive metaphor, Cheng draws beginners and enthusiasts alike into the heart of this mysterious, powerful concept to reveal fundamental truths about mathematics, all the way from the infinitely large down to the infinitely small.
Menrva's Summary
THE THESIS
The book investigates the nature and paradoxes of infinity, exploring its different sizes and implications. Eugenia Cheng, an acclaimed mathematician, uses accessible metaphors and intuitive examples to demystify the concept of infinity for a broad audience. The book delves into scenarios like Hilbert's paradox of the Grand Hotel and Zeno's paradoxes to illustrate the counter-intuitive properties of infinite sets. Cheng aims to reveal fundamental mathematical truths by examining infinity from the infinitely large to the infinitely small.
THE SCOPE MAP
- Explanation of different sizes of infinity, including countable and uncountable infinities.
- Exploration of Hilbert's paradox of the Grand Hotel to demonstrate infinite capacity.
- Analysis of Zeno's paradoxes, such as Achilles and the Tortoise, in the context of infinity.
- Use of inventive metaphors and intuitive examples to explain complex mathematical concepts.
- Discussion of how infinity applies to both the infinitely large and the infinitely small.
- Introduction to fundamental mathematical truths through the lens of infinity.
- Accessible explanation for both beginners and enthusiasts in mathematics.
THE AUTHORITY PERSPECTIVE
Eugenia Cheng's 'Beyond Infinity' is lauded for its ability to make the abstract concept of infinity understandable and engaging for a general audience. Reviewers frequently highlight Cheng's skillful use of analogies and clear explanations, which demystify complex mathematical ideas without oversimplifying them. The book is recognized for its intellectual rigor combined with a playful and accessible tone, making it a valuable resource for anyone curious about the nature of numbers and the infinite. It successfully bridges the gap between complex mathematical theory and everyday comprehension.
Page Count:
0
Publication Date:
2018-01-01
ISBN-10:
1781252866
ISBN-13:
9781781252864
Science
Non-Fiction
Popular Science
Logic
Mathematics
