well now i see that there are alot of ways of proving things, but there is one way in which I dont understand at first sight, and that is proof by contradiction, is there anyway general way of understanding it? I have worked on so many proofs but these are the only ones i most likely to have trouble with.

I now normally assume that if i cant do the question then it must be a proof by contradiction, but see i dont understand how would such a proof be structured and how is it really proving something, the last proof i came across that i cant do is this one and I believe that it must be another proof by contradiction? so here we go

let f:[a,b]->R be a continuous function. let M>0 and f(x)<M for all x an element of [a,b]. define g:[a,b]->R by

[tex]g(x)=\frac{1}{M-f(x)}[/tex]

then show that g is bounded