Set Theory Explained


While I was using the communal computer in my mother’s senior residence. I got involved in a background conversation.

“What’s a google?” a resident asked one of the young staff mambers.

“It’s an Internet search engine,” she replied.

I just had to butt in. “It’s also a number. A very large number. A google was a number before it was a search engine.”

I should have googled the google right then and there rather than admit my ignorance of exactly how big a google was. I knew it was bigger than a million, billion or trillion. But how much bigger?

The question continued to bug me, so eventually I went looking for the answer.

A google is a one followed by a hundred zeros. Actually, that’s not entirely accurate. A GOOGOL is a one followed by a hundred zeros. However, the google search engine spelling is having a serious impact on the stability of spelling of the number googol.

If that isn’t enough to count whatever your want to quantify, there is the GOOGOLPLEX – a one followed by a googol of zeroes, not to be confused with the googleplex, a physical structure built by the google people.

Despite its staggering size, a googolplex is just as far from infinity as the lowly ONE. If you add one to a googolplex, you increase its size without decreasing its distance from infinity. If somebody feels the need to invent a larger number, it still won’t be the largest possible number, because you will always be able to add one more.

My first source of information for this piece was a delightful article, written in 1999, about infinity, set theory, and inconceivable numbers on the Bucknell University site. It was written in 1999. I should have copied and pasted it somewhere, because that site has disappeared from cyberspace, like googols of others.

All this is enough to make me wish I had pursued post-secondary mathematics instead of French and Latin. Numbers clearly have more pizzaz and versatility than irregular verbs. But, thanks to the Internet, I don’t have to remain mired in ignorance. I can google GOOGOL or any other topic I want.