So there is a proof that the sum of any two even numbers is an even number. 2k + 2l = 2(k +l) We have written the sum as 2 times an integer. Therefore the sum of any two even numbers is an even number. An essential part of this proof is that k + l is an integer. How do we know this? Is it an assumed property of integers, an axiom, or is there a proof out there that this is true?