Infinity. Inconceivable! Agreed. Inscrutable! Nope. 

The infinite is hard to grasp. Does the universe extend without bound beyond what we can observe? Would we want to be immortal? Will this boring movie go on forever? Infinite time, space, wealth, love … none of these are easy to grasp by our finite minds. 

An exception is how infinity appears in mathematics. Mathematicians engage infinity on a daily basis. Infinity can be handled with no more angst than numbers such at 8, –5, or π. This Guide to Infinity takes readers on a tour of a variety of ways in which infinity appears in mathematics. Indeed, variety is a key message of the book. Infinity is not one thing in mathematics. 

There are many different concepts of infinity. The simplest idea is to append ∞ to the real numbers and extend the definitions of basic operations in a way that is consistent with the rules of algebra. Infinity may also refer to an idealized line at the horizon where parallel lines meet. Infinity is also the answer to a “How many?” question. In this context, readers will be delighted to see that some infinities are bigger than others. And in yet another setting, we find that ∞+1 and 1+∞ are not the same.