Finite Sets and Natural Numbers
This course on set theory and finite structures is an attempt to better understand certain questions on the foundations of mathematics including Benacerraf's Identification Problem and Hilbert's 24-th Problem. A Canonical Set Theory is proposed for a simple and transparent construction of natural numbers. This set theory also gives new results that tie together set theory, finite mathematics, group theory, number theory and analysis.
Course Material
Video Lectures
Finite Sets and Natural Numbers
Course Notes
Supplementary Material
The supplementary material includes examples, problem sets, extra topics, detailed proofs and external references to complementary books, videos, reviews, essays and more. The bibliography will include academic references and recomendations for relevant books, articles, etc.
Examples and Problem Sets
Bibliography
Juan Pablo Ramirez. (2023). Canonical Set Theory with Applications from Parallel Addition of Multiple Inputs to Matrix Multiplication and Data Structures. Qeios. doi:10.32388/G6KRQE.2
Additional Links
“The Nature of Numbers”. Logic and Foundations Special Session, 52 Mexican Congress of Mathematics, Monterrey, Nuevo León, 2019. (Click here for VIDEO)
“Simple Representation of Natural and Real Numbers”. Logic and Foundations Special Sessions, 55 Mexican Congress of Mathematics, Guadalajara, Jalisco, 2022. (Click here for VIDEO)
"A Pseudo Measure on the Space of Finite Functions and Permutations”. Algebra Special Sessions, 56 Mexican Congress of Mathematics, San Luis Potosí, 2023. (Click here for VIDEO)
"Canonical Block Form for Finite Groups". Algebra Special Session, 55 Mexican Congress ofMathematics, Guadalajara, Jalisco, 2022. (Click here for VIDEO)