What is an Infinity

Infinity Symbol

Infinity (represented mathematically as 8) is simply the concept of endlessness: an infinite object is one that is unbounded. It is hard to do mathematics without encountering infinity in one form or another. Many mathematical arguments and techniques involve either choosing something from an infinite list, or looking at what happens if some process is allowed to tend to infinity, continuing toward its infinite limit.

Infinite collections of numbers or other objects, called infinite sets, are a key part of mathematics. The mathematical description of such sets leads to the beautiful conclusion that there is more than one sort of infinite set, and hence there are several different types of infinity.

In fact there are infinitely many, bigger and bigger, kinds of infinite set, and while this may seem counter intuitive, it follows from the logic of mathematical definitions.