Generating the Primitive Recursive Functions
In this video, I review the proof from Mazzanti's 2002 paper "Plain Bases for Classes of Primitive Recursive Functions" that the primitive recursive functions are generated by the modular remainder function and the hyperoperations under composition. Please let me know in the comments what you learned from this video and if you have any questions! My previous video on Jones and Matijasevich's "Exponential Diophantine Representation of Recursively Enumerable Sets": • Singlefold Unary Exponential Diophantine I... My playlist on primitive recursive functions: • What is Primitive Recursion? My playlist on the MRDP Theorem: • Some Lucas Sequences My video on Kummer's Theorem: • Kummer's Theorem 00:00 Primitive Recursion 04:54 Proof Outline 09:19 Monus is Generatable 11:20 Division is Generatable 12:40 Binomial Coefficients are Generatable 14:15 GCD is Generatable 19:53 exp_2 is Generatable 24:51 MRDP Theorem 28:32 Counting the Value of P 33:17 Digit Stabilizer Function F 36:43 Concatenating Tables of Values 40:35 Example: Integer Square Root 45:21 Cleaning up 54:18 Summary
What is Primitive Recursion?
Primitive Recursive Arithmetic
Singlefold Unary Exponential Diophantine Inequalities with Two Intermediate Variables
the famous goat problem
Bending Space itself | The Jacobian
How C Really Works
Defining continuity of real functions of real variables in Calc 1 textbooks
Primitive Recursive Functions are Pure Iterative: Simplifications of the Recursion Scheme
Richardson's Theorem
Something strange happens when you "bump the base"
A Hyperbolic Take on the Fibonacci Sequence
Arithmetic Notation for Sets
Stabilizing an Unseen Triple Pendulum
Is Reality Really Real? With Donald Hoffman
Smooth-Maximum, the most useful function
Kummer's Theorem
Saunders Mac Lane: "Mysteries and Marvels of Mathematics"
Casey Muratori – The Big OOPs: Anatomy of a Thirty-five-year Mistake – BSC 2025
Limitations of Primitive Recursive Functions
