Beyond Infinity is a captivating book that takes readers on a mind-expanding journey into the outer realms of mathematics. With her engaging storytelling style, Eugenia Cheng delves into various mathematical concepts, shedding light on the complex idea of infinity and unraveling its mysteries.
Through clever analogies and thought-provoking examples, Cheng guides readers through the exploration of natural numbers, rational numbers, and real numbers, ultimately showing that infinity defies classification as a “normal type” of number. Along the way, we encounter fascinating topics such as Hilbert Hotels, Cantor’s diagonalization argument, and the different sizes of infinities, all brought to life with vivid storytelling and relatable scenarios.
Once we grasp the concept of infinity, Cheng takes us on a captivating journey into the realms of the incredibly large and the infinitesimally small. We explore growth rates through the lens of folding puff pastry and song shuffles, delve into the idea of dimensions and infinite dimensions, and catch a glimpse of category theory. We also ponder infinite sums of diminishing numbers and the mind-bending paradoxes they create. Cheng expertly fills gaps in our understanding of the real number line, shedding light on the irrational numbers and bringing us closer to a comprehensive definition of the real numbers.
This book is a must-read for anyone curious about infinity, whether they are beginners or seasoned mathematicians. It offers a fascinating introduction to the concept of infinity while showcasing the creative and playful nature of mathematical thinking. Beyond Infinity is an enjoyable and enlightening read that will leave readers longing for more.