Example
To prove: For all whole numbers, if is even then is even.
A direct proof is difficult, so a proof by contrapositive is preferable.
Suppose is not even; that is, is odd. Then, for some whole number .
So which is odd.
Thus we have proved: if is not even, then the square of is not even.
So by contrapositive: if the square of is even, is even.
Read more about this topic: Proof By Contrapositive
Famous quotes containing the word example:
“Our intellect is not the most subtle, the most powerful, the most appropriate, instrument for revealing the truth. It is life that, little by little, example by example, permits us to see that what is most important to our heart, or to our mind, is learned not by reasoning but through other agencies. Then it is that the intellect, observing their superiority, abdicates its control to them upon reasoned grounds and agrees to become their collaborator and lackey.”
—Marcel Proust (1871–1922)