__
Proof__

In this topic we look
at how to prove that something is ALWAYS TRUE - so simply giving an example is
not sufficient

Prove that "even +
even = even"

2a + 2b
*this could represent any "even + even" if a and b are integers*

*=2(a+b)
twice any integer is always even and (a+b) is an integer hence the original
statement is always true*

Prove that "odd^{2}
= odd"

2n
* n is an
integer and twice any integer is always even*

2n + 1
*must be odd since "even + odd = odd"*

(2n + 1)^{2}
*now we square our odd number*

= 4n^{2} + 4n
+ 1

=2 (2n^{2} +
2n) +1 *this is an odd number since 2(integer) + 1 is always
odd*