2Fast2Finite: Breaking the natural speed limit of finite numbers

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In a previous video, we used infinite ordinals to prove that certain finite number sequences called Goodstein sequences were necessarily finite. Now, let's take this one step further and derive a formula for computing the precise length of these sequences! This will also give a bit of insight to why the previous video delved into a language of "infinities" even though the problem is purely of finite nature.

Prerequisite:
   • Solving a finite number problem using infi...  

References:
[Cai07] A.E. Caicedo. 2007. "Goodstein's function."
[Cic83] E.A. Cichon. 1983. "A short proof of two recently discovered independence results using recursion theoretic methods." Proc. of the Am. Math. Soc. 87(4), 704--706.
[Wai70] S.S. Wainer. 1970. "A Classification of the Ordinal Recursive Functions." Arch. Math. Logik 13, 136--153.

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Timestamps:
00:00 - Introduction
01:15 - Recap
02:36 - A closer look at each term's shape
03:26 - omega minus one
04:04 - Wainer fundamental sequences
06:43 - Ordinal "predecessor"
08:48 - The main focus
09:41 - Fast-growing hierarchy
11:25 - The main theorem
12:19 - Induction base case
12:38 - Induction step
15:03 - Formula for Goodstein sequence length
15:50 - Thx 4 watching
16:00 - Epilogue

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