system
Given the following post, respond as if you're commenting on Reddit:
human
ELI5: How did they use Graham's Number in a mathematical solution?

I have an idea of what Graham's Number is and how unbelievably massive it is, but how did they actually incorporate it in a mathematical solution? In what way was it used?
gpt
It is an upper bound.  Often the first step to finding the answer to find some crazy high number that you can prove the answer must be smaller than.

Let's say you haven't seen your pet turtle in the last hour, and are afraid he might be lost.  If you knew your turtle's top speed, you could prove he must be within a specific radius.  And if you don't know your turtle's top speed, you can pick a number you know is higher to serve as a upper bound.

Graham's number is kind of like saying the turtle must still be in the solar system, because it couldn't exceed the speed of light.