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The "Reduction to Absurdity" approach

I remember (not fondly) the 2 years of engineering school prep-class I spent in Math. Sup M and Math. Spe M*, more than 13 years ago now. We were fed, or rather filled, with mathematical and physics theories 40 hours per week. These theories had hardly any application in our everyday’s world, for most of them. And then, there were the gems; these approaches so universally applicable that they balance two years of painful learning conjectures that had no other direct application than the exam we would pass every other week, as one of our professors put one day. Some of the most applicable lessons were a set of very general approaches to resolving problems.

Today, I will just touch on one of these methods: The resolution of problems by “reduction to absurdity”. This approach is basically saying, because we know that a statement cannot be true and false at the same time, if a situation can only be either A or B, and I can prove to you that it cannot be B because fundamental theories would , then it is A.

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