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 the outer reaches of the mathematical universe to contemplate the slightly abstract concept that is infinity. In it she poses various questions about this number, asking if 1 + ∞ is larger than ∞ + 1, are some infinities larger than others, can you fit an infinite number of people in Hilbert’s Hotel and when does a number start becoming irrational.
Thankfully this book has lots of diagrams as Cheng sets about explaining the concepts of infinity, from the very simplest right up to the most detailed. I found most of it straightforward, but occasionally it was fairly tough going. When trying to get your head around infinity has challenged mathematicians for ages so it is not going to be easy for us mere mortals. Cheng endeavours to keep the prose readable, however, someone who has not picked up a maths book since school might struggle with this, but most of the time she gets the concepts across clearly. Overall a good introduction to infinity.