How do we prove that subtracting an even number by 2 still gives an even number?

Question

anonymous · Answer

I asked a similar question earlier and based on that have made an attempt similar tot he answer I was given. Can somebody check that I am right?...

anonymous · Answer

Lets say that the starting even number is x.

x = 2k where k can be any integer, even or odd.

x - 2 = 2k - 2

x - 2 = 2(k-1)

As this is still dividable by 2, it is an even number still

anonymous · Answer

Am I correct?

mary.rojas · Answer

10-2=8 8 is even
is that what you mean?

anonymous · Answer

well yes, but algebraic proof for all even numbers

anonymous · Answer

Proving that [Even number 1] - 2 = [even number 2]

i.e. it will never be odd

jhonyy9 · Answer

so you know that every even has a form of 2n and 2 is even too

so 2n-2 = 2(n-1)  so note (n-1=k 

than 2(n-1)=2k 

what mean that 2k will be allways even

hope that you understand it now sure

mary.rojas · Answer

oh sorry lol, am not sure but good luck

jhonyy9 · Answer

and yes you are right

anonymous · Answer

So my proof was right?

anonymous · Answer

Thanks :)

jhonyy9 · Answer

good luck

jhonyy9 · Answer

my pleasure