My Googology Notation

Hello! I recently got into Googology - hence the website - and I figured I’d make a notation that explains things a bit easier than these notations. I’ve also transferred some numbers from https://googology.wikia.org/wiki/Googology_Wiki into my notation, so as soon as I find a way to transfer my pdf onto here, I will do so.

But here’s the standard Letter notation:

Ax = 10^x. A1 is 10, A2 is 100. A googol, one of the most popular large numbers, is AA2.

For example, A5 = 100000. AA5 = A(A5) = A100000.

B(x) is A(A(A(...A(1))))...)) with x copies of A. B(1) is 10, B(2) is 10^10.

(We can also get rid of the parentheses as they are not needed here.)

As another example, B2 = AA1.

A(A1) = A10 = 10^10.

C(x) is BBB...B1 with x copies of B. C1 is 10, C2 is 10^10^10^10^...^10 with 10 10’s.

C(2) = BB1 = B10

And so on, and so forth.

This is the condensed version of the Hyper-Extended Letter Notation, which goes as follows:

A(w, x) = w^x

(and yes, we do need the parenthesis on this one.)

B(w, x, y) = AAA...(w A’s)...AA(x, y).

C(w, x, y, z) = BBB...(w b’s)...BB(x,y,z)

Anyways, there’s the notation, here are some examples of numbers with this system:

10 >> A1.

100 >> A2.

Googol >> AA2 >> B(2,10,2)

Googolplex >> AAA2 >> B(3,10,2)

Here are some numbers that have C.

1. Tetrataxis (C4)

2. Pentataxis (C5)

3. Hexataxis (C6)

4. Heptataxis (C7)

5. Octataxis (C8)

6. Ennataxis (C9)

7. Dekataxis (CA1)

8. Dodekataxis (C12)

9. Hecta-taxis (CA2)

10. Chilliataxis (CA3)

11. Myriataxis (CA4)

12. Googoliataxis (CAA2)

13. Tetralogiataxis (CB4)

14. Googolduplexiataxis (CB(4,2))

15. Pentalogiataxis (CB5)

16. Hexalogiataxis (CB6)

17. Heptalogiataxis (CB7)

18. Octalogiataxis (CB8)

19. Ennalogiataxis (CB9)

20. Dekalogiataxis (CB10 / CBA1 / CBB1 / CC2 / D(2,2))

21. (Endekalogiataxis) (CB11)

22. Toomolplex (CCA3)

Here are some with D.

1. Tria-petaxis (D3)

2. Tetra-petaxis (D4)

3. Penta-petaxis (D5)

4. Hexa-petaxis (D6)

5. Hepta-petaxis (D7)

6. Octa-petaxis (D8)

7. Enna-petaxis (D9)

8. Deka-petaxis (D10 / E2)

Etc etc.

Now, this notation, by itself, does run into some limitations, i. e. at Z, but the Googology Wiki doesn’t have a number for a number with Z, like Z(10), yet, so I’ll reference a number called the Icosagol, which is TA2. I’m working on a notation that encompasses this one and also extends it to numbers beyond Z(x), but I’ll post that when it’s ready.

Hope you enjoyed this blog post! I’m MatthewNotebook, find me on Wikia, and hopefully we’ll meet again.