Question

Prove that adding two even numbers together makes an even number always?

Answer 1

it is pretty obvious that adding two evens together always makes and even, but how can this be proved to be true for all numbers?

Answer 2

let m and n be those 2 even numbers

so they can be written in the form, m= 2k, and n=2r
where k and r are any numbers, even or odd

agree?

Answer 3

if you agree to that
then their sum m+n = 2k+2r = 2(k+r)
because of the presence of 2 there,
m+n is always even!
whatever be the value of k or r

Answer 4

ah, thank you!

So, as the definition of even numbers being that they have a factor of 2, as m+n can be written as 2(k+r) this means that the sum also has a factor of 2 (due to the 2 in the equation) and thus must also be even?

Answer 5

correct! :)

Answer 6

Is there a name for this sort of proof?

Answer 7

not that i know of...

Answer 8

ok then, just wondering. Thanks for your help :)

Answer 9

welcome ^_^