proof by contradictionWatch
Not too sure on propf by contradiction
For example, you can use contradiction to prove that the square root of 2 is irrational.
Assume that the square root of 2 is rational. Then it can be expressed as p/q, where p and q are integers. Let p and q be co-prime, otherwise divide by their common factors.
So 2 = p/q squared. Rearrange this into p^2 = 2q^2. Therefore p^2, and p, divides by 2.
Because p divides by two, we can let p = 2r, where r is an integer.
Therefore 4r^2 = 2q^2, or 2r^2 = q^2. Therefore q divides by 2.
So p and q divide by two. But we said that they shared no common factors in the beginning! This is a contradiction, so the square root of 2 cannot be rational. QED.
what do the terms "proof by contradiction" and "disproof by counter-example" mean and has anyone gt any examples i can try ??
Proof by counter-example - you're given a statement to prove, alongside some conditions that should be given/obvious. All you need to do is find an example satisfying the conditions but not the statement.
Disproof by counter-example is like exhaustion except you're proof is that you can't exhaust the solutions because the one you use does not work for the proof