Question

When working with proofs and theorems is there a simple way to determine when to use contradiction? I understand HOW contradiction works, but not really WHEN I need to use it. Any tips or pointers would be incredibly helpful.

Answer 1

Yes we should not use contradiction as a proof always. So we have to find such conditions where we can use contradiction or other method equally and the other condition where we can use contradiction much stronger than other proofs and the last condition where we must have to use contradiction.

See if the proofs involving something like this that prove x cannot be equal to y. Then this is the condition where we must use contradiction, here we assume that x = y and do some calculation and comes on a condition where it is not possiy, hence x not equal to y.

For example prove that is irrational is equivalent to prove that

for any integers m and n.

So we assume that for some m and n. Then we contradict it.