1. Sep 8, 2009

Hi guys, Im looking to find some exercises, preferably online to practice Mathematical Proof by Contradiction.

I have just finished my A-levels in the UK doing Maths and Further Maths and very little is done in the way of mathematical proof. The is only a single chapter on proof by induction, with a short bit explaining the concept of Proof by induction and then many questions asking you to proove by induction. The question ask either to proove that and inequality is correct, proove that the solution to a reccurence relation is correct or prove that the general formula to a series is correct.

Now logic in the sense of propositional logic or otherwise actually is not discussed at all or even required as a prerequisit to doing this (true mathematical logic isnt disscused at all in the maths A-levels in the UK), everything is done in "Plain english" as it were :D. And Im really looking for a similar thing to practice proof by contradiction. I am currently reading "100% mathematical proof", which is really enjoyable, but proof is approched from a completely logic standpoint with the first half of the book really didicated to familiraising the reader with propositional and predicate logic, and in truth I know that is the way it should be done, other wise youll end up with unrigourous proofs, which arnt really proofs then. And it seems that all the material I can find that includes exercises for contradiction take the completely logical standpoint, presented in with logic maths text or philosiphy texts.

Can anyone suggest something similar to what I have found in my A-level for induction, without all the logic shrouding it, Im sure most would advise against it but I really have thought about it and would love to find some exercises that I can do without the need to learn basic logic theory first. Any help, suggestions or advise would be really appreciated, thanks alot guys :D