Example
What follows is a simple, direct proof that the sum of two even integers is itself an even number.
Consider two even integers x and y. Since they are even, they can be written as x=2a and y=2b respectively for integers a and b. Then the sum . From this it is clear x+y has 2 as a factor and therefore is even, so the sum of any two even integers is even.
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“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.”
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