Question

Difference between all even integers and all positive even integers?

Answer 1

Any even number takes the form x=2n
x
=
2
n
where n
n
is an integer. So, two even numbers
a=2n
a
=
2
n
and b=2m
b
=
2
m

a−b=2n−2m
a
−
b
=
2
n
−
2
m

a−b=2(n−m)
a
−
b
=
2
(
n
−
m
)

since integers are closed under subtraction n−m
n
−
m
is a new integer p
p
, and
a−b=2p
a
−
b
=
2
p

an even number