Since university mathematics is founded on proof, developing your ability to construct and analyse logical arguments is critical. Often in a school mathematics context the proofs encountered are reasonably straightforward to check and verify. It is important to start to think about difficult proof issues as soon as possible
It is easy to underplay the prevalence of the logical traps that abound in advanced mathematics and this is often the cause of error in proofs constructed by mathematics students. Frequently, a step in a proof which seems to follow 'obviously' from the previous step contains a subtle trap for the unwary.
This problem will help you to develop your clear, logical reasoning skills. It involves a set of (clearly incorrect somewhere!) proofs of seemingly absurd statements, such as 1=0. Trying to pin down the precise points where the proofs break down will give many insights into proof and will help you to develop your mathematical reasoning.