2013/05/14 by Jerzy Dydak, Dydak, Jerzy
Computer Science · #54C15 #Advanced Algebra and Logic #FOS: Mathematics #General Topology (math.GN) #Geometric Topology (math.GT) #Logic (math.LO) #Logic, Reasoning, and Knowledge #Primary 01A72 #Secondary 55M15
paper · pdf · doi:10.48550/arxiv.1305.3283
openalex publication_date 2013/05/14 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
The purpose of this paper is to outline a simple set of axioms for basic set theory from which most fundamental facts can be derived. The key to the whole project is a new axiom of set theory which I dubbed "The Law of Extremes". It allows for quick proofs of basic set-theoretic identities and logical tautologies, so it is also a good tool to aid one's memory. I do not assume any exposure to euclidean geometry via axioms. Only an experience with transforming algebraic identities is required. The idea is to get students to do proofs right from the get-go. In particular, I avoid entangling students in nuances of logic early on. Basic facts of logic are derived from set theory, not the other way around.