One of the main applications of method of contradiction in our syllabus is proving irrationality of square root 2. But it also done without mentioning the most important infinite decent method which was used by Sir Andrew Wiles in proving Fermat’s last theorem in 1994 ( Very long period of around 350 years after Fermat conjectured it .) Not only that, method of contradiction can be applied to prove principle of mathematical induction ( according to our syllabus we are mainly focusing on one particular type of mathematical induction but pretending as the full idea related to the principle) and all of the problems proven by mathematical induction can be proven by method of contradiction . There are many applications of method of contradiction where mathematical induction can not be used. If so, you can realize which one is the most powerful, then by giving much priority to mathematical induction over method of contradiction actually what kind of mathematics skill development we can expect from our students?
(This post is for meaningful discussion)

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