Even getting to Graham’s number is mind-boggling. Of course it’s nothing compared to infinity. But that’s a topic for another entry. What’s your favorite gigantic number?

I love the Googolplex: a 1 followed by a Googol zeroes! A Googol is a 1 followed by a hundred zeroes, which can be written thus:

10,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000.

With a Googol

*plex*, there are less particles in the universe than there are 0s following the 1; like Graham's number, you couldn't write it down or even store it in a computer. It's smaller than Graham's number though.

Speaking of infinity, I've learned in recent years that there are different

*types* of infinity, and whilst they are labelled in all sorts of ways, the two that make the most sense to me are these:

**Divergent Infinity** - an infinite series in which the individual elements have a finite limit. For example:

1, 2, 3, 4, 5, 6, 7, 8, 9... (a finite difference of 1 between each number)

2, 4, 6, 8, 10, 12, 14, 16... (a finite difference of 2 between each number)

1, 3, 5, 7, 9, 11, 13, 15... (a finite difference of 2 between each number)

**Convergent Infinity** - an infinite series in which the individual elements have an undefined limit which tends towards zero or infinity. For example:

1, 1, 2, 3, 5, 8, 13, 21... (each number is the previous two added together, providing differences between each number which tend towards infinity)

0.1, 0.01, 0.001, 0.0001, 0.00001, 0.000001... (the difference between the numbers in this series gets infinitely smaller, tending towards zero)

0.1, 0.11, 0.111, 0.1111, 0.11111, 0.111111... (the difference between the numbers in this series gets infinitely larger, tending towards infinity)

It helps to explain why there is an infinite series of whole numbers (1, 2, 3, 4, 5, 6, 7, 8, 9...) but there is

*also* and infinite number of subdivisions between each whole number (0.1, 0.11, 0.111, 0.1111, 0.11111...)

A thought I've always found interesting is: where do you start counting between 0 and 1?

0.0000000000000000000000000000000000000000000000000000000000000000000000000000001? Well, why not

0.00000000000000000000000000000000000000000000000000000000000000000000000000000001?

0.(0 recurring) is one of my favourite infinite numbers, for this reason. It never even

*starts* counting towards 1, it just exists in all its glory as a divergently infinite number.