Miracle Learning Center

# Big Numbers

## 04 Feb Big Numbers

Today, we are going to talk about big numbers – really really really big numbers. So, you have been taking math tuition for a while now. What is the biggest number that you can think of that you have ever used? A million? A billion? A trillion? The numbers that we are going to talk about today are much bigger than probably what you have ever used.

Googol
Most of you probably have heard the story from your maths tuition teacher about how our favourite website “google” was named. For those of you who have not heard the story, the founders had the plan of naming it as “googol”. However, due to a spelling error, the website was registered as “google”. The word “googol” is not just any word – it is the name of a number. A very big number. “Googol” is the name given to the number which is 1 followed by 100 zeros i.e. 10100 in exponential form. How big is the number? The number of atoms in the universe is approximately 1080 – way too small when compared to “googol”.

Googolplex
“Googolplex” is a humungous number and the “googol” is just a tiny little blob when compared to this giant of a number. A “Googolplex” is 10(googol) i.e. 1010100. This number is enormous even when compared to “Googol”. It is a number which starts with the digit 1 followed by a “googol” zeros. However, googolplex is not the biggest number that we are going to discuss today. The size of the next number that we are going to discuss next is a sheer jaw dropper.
Graham’s Number

Mathematician Ronald Graham used this number in one of his papers and this number remains the biggest number which has been used in a published paper till date. How big is this number? This is much much much bigger than the “Googolplex”. Graham’s number is humongous; enormous. It is so big that it cannot be written in the normal exponential notation and an all new technique – known as the up-arrow notation is used to express this number. You have probably never heard your maths tuition teacher mentioned this number before. Who do you think may use these numbers?

TREE(3) and SCG(13)
Next we are going to discuss about TREE(3). The number TREE(3) was derived by Harvey Friedman and in terms of size, TREE(3) is even bigger than Graham’s number. Harvey Friedman also devised another large number known as SCG(13) which surpasses TREE(3) in size.