The first time a variable appears whether in the initial statement of what you are proving or in the body of the proof you must state what kind of variable it is for example a scalar an integer a vector a matrix and whether it is universally or existentially quantified. Direct indirect contradiction and contrapositive and know the thought process behind why each are used. With these tools in place students then learn logic and problem solving as a further foundationNext various proof techniques such as direct proofs proof by contraposition proof by contradiction and mathematical induction are introduced.
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The math proofs that will be covered in this website fall under the category of basic or introductory proofs. At the very least mathematical-type reasoning is a powerful addition to anyones critical thinking toolbox applicable in a wide variety of settings. It is a creative reasoning process to build up substantiated argument. These proof techniques are introduced using the context of number theory.