There are a greater number than googolplexian


Gogool + 1

After common sense, a largest number doesn't make sense. Even the number of atoms in the universe is smaller than a googol: 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. But Gogool is of course not the highest possible (meaningful) number either. Because there is also a Gogoolplex, i.e. 1 Googol ^ 100. There is also a googolplexplex and a googolplexian. And that's still tiny when you compare it to other numbers in mathematics. A googol is still very easy to write on. I even wrote it just now. If that is too strenuous for you, a Googol with the prime factors 2 and 5 represents.

Higher than you can write.

Graham's number is even greater. Until recently, it was the largest number ever defined in a mathematical proof. Of course there is also Graham's number +1 and (Graham's number +1) +1. When it comes to numbers like this, everything works a little differently. Usually numbers are part of formulas, but this time a formula describes a number! I can of course make up the number Graham's number + n, but that is still no achievement. Of course, Graham did not name any large number of Graham's number. He was concerned with how many different ways you can combine a certain number of objects. Graham's number is an upper limit. But that does not mean that this is the largest number, because in some thought experiments even significantly larger numbers appear, for example in Kruskal's tree theorem.

Why the greatest number is impossible

Each number can be added with 1. The largest number is probably obtained by adding the current largest number with 1. The new largest number is now obtained by adding the current largest number with 1, etc. A scheme is used to name numbers, which names every imaginable number. The “number line” is known from school. It is not called a number line for nothing and not a number range. A ray has a beginning and no end, just like the series of numbers. The question of the largest number is therefore much more a philosophical than a mathematical question.

Posted in physics tagged Grahams number, greatest number, Kruskal by Jason vJ2 comments