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To Graham's number and beyond

Past few days I have tried to show you some big numbers and math to go even bigger. It's pretty much all the preparation I could give before getting into the actual topic the Graham's number.

Before we start I would like to reiterate a few things: our insanely huge number that expands all of the multiverse, the Knuth's up-arrow notation and how adding just a single arrow launces the number to a completely new magnitudes. And finally the fact that mere 3↑↑↑↑3 is already much bigger than that multiverse-spanning meganumber.

Higher order calculus

In order to reach those truly big numbers like Graham's number the ordinary math isn't enough. The rate of growth is an important part of this process as it lets us get to the bigger numbers faster. Even though the exponential growth is a common term and is indeed pushing our ability of comprehension It's like staying in place compared to where we are aiming for. 

So there are the addition, multiplication and exponentiation everybody is familiar with. But it doesn't stop there. After those come the hyperoperations like tetration, pentation and so forth.

Even bigger numbers

We've already reached the limits of our universe to express these big number so we need to look beyond that. Enter the multiverse theory. The idea of having multiple possible universes gives us some more room to continue expanding the boundaries of big numbers.

Big numbers

Graham's number is big. So big that it's hard to even grasp how big it actually is. So maybe it's better to start with some "smaller" numbers first to truly realize the magnitude of such numbers.

As a kid thousand things was already a lot and million was the biggest thing ever. Coming up with even bigger numbers always involved just adding more zeroes to the end of the numbers. Million millions and so forth.

Graham's pie

Graham's number is one of those mathematical curiosities that always blows my mind. It's so perplexing that for a moment I think I have grasped it, but then the next time I'm again as awestruck as before. 

Graham's number is one of the biggest known numbers. Yes, it's insanely big number. The known universe isn't big enough to write out the amount of digits it has. And yet, there are even bigger numbers known.