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# Beyond Infinity: An expedition to the outer limits of the mathematical universe

by

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, interna
...more

Paperback, 304 pages

Published
March 1st 2018
by Profile Books
(first published March 9th 2017)

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## Community Reviews

Showing 1-30

Cantorian Sets: "Beyond Infinity - An expedition to the outer limits of the mathematical universe" by Eugenia Cheng

“If this be not that you look for, I have no more to say, but bid Bianca farewell for ever and a day.”

In “The Taming of the Shrew” by William Shakespeare (quoted by Cheng in the book)

Eugenia Cheng starts by saying right at the beginning of the book, "Infinity is not a number," and I think it really helps to get that mis ...more

**Maths As Art Form**

If you find it hard to tell your reals from your naturals or can’t remember why infinitely repeating decimals aren’t irrational, then this may be the book for you. A charming sortie into the poetry of mathematics, a guided tour of what they didn’t teach you in school: how numbers work and what it means to say that there are an infinite number of them. Cheng knows how to make a narrative with a beginning, middle and end, and with just the right touch of humour.

*Beyond Infinity*is ...more

Nov 23, 2017
Jose Moa
rated it
it was amazing
·
review of another edition

Shelves:
mathematics,
science

There are to day a lot of good popular books about mathematics that those of some age and fond of maths would like have read when young,this one is one of theese books.

Here Eugenia Cheng explains in a masterful way for the layman concepts of advanced mathematics,as the infinite series of infinite cardinals and ordinals,the concept of infinite countable sets is to say those that one can put in a one to one correspondence with the natural numbers and the uncountable sets where one cant ,as for exa ...more

Here Eugenia Cheng explains in a masterful way for the layman concepts of advanced mathematics,as the infinite series of infinite cardinals and ordinals,the concept of infinite countable sets is to say those that one can put in a one to one correspondence with the natural numbers and the uncountable sets where one cant ,as for exa ...more

Apr 01, 2019
Corey Thibodeaux
rated it
really liked it
·
review of another edition

Shelves:
non-fiction,
numbers

I had nothing but the best intentions.

This book is the mathematical equivalent of asking a meteorologist why the sky is blue. When answered comprehensibly, the answer is much more than any simple patron would necessitate. Just say "because of tiny molecules in Earth's atmosphere," or something to that effect. Anything more would make me feel like a dummy.

So in my good intentions, I, a writer and wordsmith, wanted to broaden my mind by accessing the mathematical lobe left dormant after my freshm ...more

This book is the mathematical equivalent of asking a meteorologist why the sky is blue. When answered comprehensibly, the answer is much more than any simple patron would necessitate. Just say "because of tiny molecules in Earth's atmosphere," or something to that effect. Anything more would make me feel like a dummy.

So in my good intentions, I, a writer and wordsmith, wanted to broaden my mind by accessing the mathematical lobe left dormant after my freshm ...more

On the other hand, algebra is a must in the world today, and sooner children get the concepts, the better.

"I was helping two six year olds to understand symmetry." That killed me, haha, now I can understand why so ...more

Sep 07, 2017
Paul
rated it
liked it
·
review of another edition

Shelves:
royal-society-prize,
books-read-2017

There are some big numbers out there, footballers earn a jaw dropping amount per year, for what I am not entirely sure… The global economy is around US$107.5 trillion, there are approximately seven quintillion, five hundred quadrillion grains of sand on the earth and it is thought that there are 10 times as many stars as that. All of these numbers are frankly huge, enormous, gargantuan even, but compared to ∞ they are a mere drop in the ocean. In this book, Eugenia Cheng takes us on a journey to
...more

Apr 11, 2017
Jeremy S
rated it
it was amazing
·
review of another edition

Shelves:
owned,
big-thinking

This book was fascinating. I truly believe if I'd had a math teacher like Cheng I would have been fully engaged.

I loved algebra growing up, and I have fond memories of a friend of my mom who used to print off algebra equations for me to do while I was waiting for my mom to get off work. I'd anxiously look forward to them.

I look back at my time in school and wonder where the shift happened? It's frustrating for me as I am now so interested in physics, biology, and math, three things I avoided lik ...more

I loved algebra growing up, and I have fond memories of a friend of my mom who used to print off algebra equations for me to do while I was waiting for my mom to get off work. I'd anxiously look forward to them.

I look back at my time in school and wonder where the shift happened? It's frustrating for me as I am now so interested in physics, biology, and math, three things I avoided lik ...more

But in a way, she writes, this book is not about infinity. It’s about a journey into the abstract unknown. This book tells how abstract thinking works and what it does for us. For Cheng, the usefulness of math is about mathematical thinking and how it sheds light on the thinking process.

“We use science to study the world abstractly,” writes Cheng. We use ...more

*This review has been hidden because it contains spoilers. To view it, click here.*

I loved Cheng's explanations and metaphors and talking about cake and cookies when actually conveying complex topics (even though sometimes I just wanted to tell her: "Stop calling yourself fat, your weight doesn't measure you"). I'm certa ...more

Most view infinity as simply a number so large it is like an endpoint. This book talks about how it is more than that and delves in to what infinity means. It also comes with refreshing reminders of basic mathem ...more

"In life and in mathematics there is a trade-off between beauty and practicality, along with a contrast between dreams and reality, between the explicable and the inexplicable. Infinity ...more

Digressions on food, music and sports help her confront her task with rigor without seeming to go on forever. She fondly recalls the two-line programming loop she wr ...more

One of the things I have a new appreciation for is number theory. It does seem rather amazing that we can generate the natural numbers (0, +1), integers (-ve), or even the reals (a/b, irrationals), with a few rules, and given only these simple rules the ...more

At the very least, I'm glad I don't have to move people from a one floor hotel with an infinite number of rooms, to a two floor hotel, each of which has an infinite number of rooms, and that's something prior to reading th ...more

I thought I'd give a math book a try. I haven't done any math since high school. Let's see what happens if I go into it out of curiosity. The title sounds interesting.

Turns out I wasn't interested. I read really closely for the first several chapters, but had trouble giving a damn about any of it. There's a lot of talk about different infinities and trying to be precise about close differences between things ...more

Also, some examples seem more convoluted than they need to be, like the one demonstrating why the real numbers are more infinite than the natural numbers. The style is right for a popular science book, but I feel the examples could have been picked a little better.

She keeps the subject of infinity interesting and almost fully comprehensible -- within my limited ability to comprehend. I may even read another math book!

*Innovation Hub*:

http://blogs.wgbh.org/innovation-hub/...

(She wasn't there to promote this book, but I liked the conversation.)

Update 5/10/18: she popped up in another podcast today! This time, actually talking about infinity:

https://www.npr.org/sections/money/20...

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