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What’s the biggest possible number?

The simple answer is infinity but in the 1870s, the mathematician Georg Cantor produced ingenious arguments revealing the existence of lots of different infinities- some of which are much bigger than the others. The “smallest” type is the one simply obtained by counting forever: 1,2,3… and so on. This is aleph-null (named after the first symbol of the Hebrew alphabet) ans is the first of what Cantor called the transfinite numbers. Such numbers have some decidedly odd properties. For example, adding aleph-null to itself produced aleph-null, so does multiplying it by itself. This is just the start; Cantor also showed that there are other, even larger, infinities starting with aleph-one- a number so big that it cannot be reached even by counting for an infinite amount of time. It turns out that there an infinite number of more infinities, each bigger than the previous, until one arrived at the biggest of them all, known as Absolute Infinity, denoted Omega. This number is so vast that it is literally indescribable: indeed, its definition is based on the idea that any attempt to describe it can only be describing something smaller.

-from the book Q & A, Cosmic Conundrums and everyday mysteries of science, Robert Matthews, Viva Books