Numbers

Unlike a lot of mathematicians, I'm actually rather fond of numbers.

We have an infinite number to play with. One of the big ones is Graham's number - a number so huge that even the number of digits is inconceivable.

A considerably smaller but still vast number is the number of monkeys required to produce Hamlet.  Very roughly this is 200000 zeroes with a 1 at the beginning.  More real world, or at least real universe numbers - atoms in the universe; somewhere around 100 000 000 000 000 000 000 000 000 000 000 000 000 000 000 000 000 000 000 000 000 000 000 000 000 000 000.  

As long as you have enough time, you can count to every single one of these. 

There are many numbers that have never been used.  783 932 912 375  has in all probability never been used until just now.  1 000 000 000 000 has been used many times, as have a smattering of the numbers between those two. 

Smaller numbers are used much more frequently.  595567 is my parents' old phone number.  It's used 44 thousand times the internet.  It is the phone number of dozens of people, the unique user Id of various people in dozens of databases, probably the bank balance of a lot of accounts.  

There is a number somewhere that has never been used, and is smaller than every other number that has never been used. 

You could theoretically find out what this number is.

And if you did that, it would no longer have never been used.