On Some Features of the Implementation of the Proof by Contradiction Method in the School Course of Mathematics and Physics
in the School Course of Mathematics and Physics
Nikoghosyan Gagik
Summary
Key words: statement, negation, set, addition, stage, creative thinking
The following paper is devoted to highlighting some of the possibilities for the effective application of the proof by contradiction method in the school course of mathematics and physics. To begin with, the article outlines the essence of the proof by contradiction method, the tools for its implementation. The article begins by briefly outlining the essence of the method as one of the main approaches to indirect proof. It then explains the method in more depth, first using the tools of propositional logic and later employing set theory. Following this, the article clearly presents and distinguishes the main stages involved in effectively applying the method. It emphasizes that the key challenge lies in the second stage: deriving a contradiction through logical reasoning. The other stages are generally more straightforward and primarily formal or procedural in nature. Finally, the paper examines various problems of proof and/or refutation encountered in the school mathematics course, as well as various statements encountered in the school physics course, in the solution and/or proof of which the method of contradiction is directly applied.