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posted by  adam-for-you on 9/6/2008 4:11:11 AM  |  status: Live  

Introduction to proof

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2. Use a direct proof to show that the sum of two even integers is even?
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Sage
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posted by Sullest on 9/6/2008 4:17:43 AM  |  status: Live
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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 x + y = 2a + 2b = 2(a + b). 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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