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## Finite: a tour of the finite numbers

Hi. I am putting together a YouTube video to celebrate the field of Googology and to give the public an introduction to the amazing range of large finite numbers as far as our present day knowledge allows.

The video is meant to be accessible to the average person, but the nature of the subject is mind-boggling, so it is hard to guess the level of interest out there.

## Corrections 7 Apr 2017

I finally got around to correcting some errors I made in the YouTube video. The following are displayed as captions:

29:06 f2(2048) is 'only' equal to 10^619 and is much smaller than 10^10^620

29:13 f2(f2(14)) = f2(229376) is bigger but only equal to 10^10^4

29:18 f2(f2(16)) is only equal to 10^10^5

29:21 f2(f2(24)) is only equal to 10^10^8

29:26 f2(f2(64)) is only equal to 10^10^20 but is bigger than Achimedes' Myriad numbers

29:33 f2(f2(f2(8))) = f^3 2(8) is the next bigger number and is equal to 10^10^619 which is bigger than the Bodhisattva number and Googleplex

40:38 fw+1^4(64) = fw+1(fw+1(fw+1(fw+1(64))))

46:58 fe1(3) = fe0^e0^e0(3)

48:50 f phi(1,1) (3) = fe0^e0^e0(3) = fe1(3)

## Update 7 Apr 2017

As of Jan 2017, the biggest named number is 'Little Bigeddon' by the author 'Emlightened'

Little Bigeddon is based on a further extension of the language of set theory.

## What is the highest named number ?

I plan to finish the video with the highest named number. At the moment, I plan to present the following 3 named numbers (only) at the end of the video. Appreciate your thoughts on the best way to explain these numbers (to the public) and whether any other numbers should be added, or should replace one of the below:

3rd last: TREE(3)

1. Harvey Friedman, an American logician, defined the TREE sequence, in 2002, as a fast-growing function arising out of graph theory.
2. TREE(3) may be comparable to $$f_{LVO}(3)$$ in the fast-growing hierarchy, but this remains unproven.
3. TREE(n) grows at least as fast as $$f_{\vartheta(\Omega^\omega\omega)}(n)$$ in the fast-growing hierarchy.
4. The weak tree(n) function grows at around the same rate as $$f_{\vartheta(\Omega^\omega)}(n)$$ in the fast-growing hierarchy.

2nd last: Rayo's Number

1. Rayo's number was coined in a large number battle, in 2007, between Agustín Rayo and Adam Elga.
2. Rayo's number is equal to Rayo$$(10^{100}) =$$ Rayo(Googol$$)$$. 'Rayo' function is uncomputable.

Last: BIG FOOT

1. BIG FOOT is currently the largest named number. It was defined in October 2014 by an author under the pen name "LittlePeng9", and named by Sbiis Saibian.
2. BIG FOOT uses an uncomputable language called 'FOOT' theory, which is an extension of first-order set theory.
3. BIG FOOT number is equal to FOOT$$^{10}(10^{100}) =$$ FOOT$$^{10}($$Googol$$)$$.

## Final Draft

The final draft of this video is on YouTube. Here is the link:

Happy to hear any feedback and suggestions from this community on this final draft.

## YouTube Country Blocking

YouTube Country Blocking no longer applies to this video.

Unfortunately, this video was produced around a specific piece of music:

Music for 18 Musicians by Steve Reich

The copyright owners have blocked the video in some countries. I have asked for a country blocking exemption on the grounds that the video is 'educational'. Will wait and see on the response to this.

In the mean time, there are good youtube bypass websites. One that seems to work well is:

This direct URL should get you to the video:

Otherwise, simply enter this youtube URL:

Please, leave any comments or suggestions on this issue if you have any. Much appreciated.

## Final Version

I don't plan to tinker with the video for much longer. There will be opportunities to make a few edits based on any feedback I receive. A final version will be uploaded to YouTube in about 3-4 weeks.

Hope you have the time to review and make a contribution.

Cheers B1mb0w.