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What is the biggest number in the universe? What is the biggest number that any human has ever conceived of, or used in a proof, or been able to write down? In this video we are going to explore the fascinating world of googology, the study of unbelievably big numbers. We will begin near the bottom with "tiny" number like a googol (10^100) and a googolplex (10^googol) before realizing we will really need to do introduce better notation. We will then see Knuth’s up-arrow notation that let’s us form power towers of numbers, repeated exponentiation called tetration that is much like how exponentiation is repeated multiplication and multiplication repeated addition. And it goes up and up from there! We will see Graham’s number which infamously got the googology ball rolling when it was used as an upper bound for a problem in graph theory and finally we will the unimaginable Tree(3) which comes out of a simple to state problem in graph theory and amazingly results in this incredible number.
You can check our Ron Graham himself introduce how Graham’s number comes about over on Numerphile here: https://www.youtube.com/watch?v=HX8bihEe3nA. You might also like to check out the googology wiki here: https://googology.wikia.org/wiki/Googology_Wiki
0:00 Intro to Googology
1:13 Googol and Googolplex
2:40 Towers of Exponents
3:58 Knuth’s up-arrow notation
9:00 Graham’s Number
11:21 Tree(3)
18:18 Brilliant.org/treforbazett
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