What does it mean to prove something? What are logical deductions and inferences? What kind of logic do we use every day? All maths depend on order, so we can begin by proving 1> 0. Contradiction, counterexample, proof by induction. Proving irrationality of sqrt(2).
Resources
- Exercise lists
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- Videos
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- TOK
- Mathematics vs Faith (Pythagoreans and irrationality). How is it possible to construct a never-ending irrational number just from two side lengths of 1?
- Group work
- Here's a proof (some assembly required). Students are given steps to a proof and they must cut them out and assemble them in a logical order
- Toolkit
- Methods of proof (examples of accepted proofs by brute force using computer simulations. Four colour theorem, checking primarily of large numbers)