am having major probs with proof in maths can any one help?

Question

i am finding it hard to prove statements using contradiction, direct argument and counter examples. is there a way i can learn them easily without doing my head in (Alevel maths by the way)

Answer 1

I don't know what you mean by "without doing my head in," but look at mathworld.com. They should have examples of these. If not, they are easy
For example, say someone says, "given the equation f(x) = x , then f(x) is positive for all x." You can prove any 'always' statement wrong by finding only one counterexample. So
f(-1) = -1, thus f(x) is not positive for all x.

Answer 2

For proving or disproving some mathematical statement you first assume that something is true. Then you proceed a few steps on basis of the assumption and arrive at a result which violates a fundamental axiom of Mathematics or contradicts your assumption. This means that whatever you had assumed to be true is actually is incorrect and hence the opposite is true.

Answer 3

Hey cool cool..
Its nothing ya... jus do some trial and error methods at first
in quiet easy prob..
then go to the assumptions which you know it is right or wrong and solve the prob.. Now if you arrive at a wrong answer then your assumption is contradicting and if you arrive at the right answer then it is true.. Tat's so simple..Practice makes you perfect in these..

Answer 4

As Euclid told the pharoah of Egypt, there is no royal (easy) road to mathematics.