EXPLAIN

"Proof": 2 = 1

a = b
a² = ab
a² - b² = ab-b²
(a-b)(a+b) = b(a-b)
a+b = b
b+b = b
2b = b
2 = 1

OR

"Proof" that 1 + 1 = 1
a = 1
b = 1
a = b
a² = b²
a² - b² = 0
(a-b)(a+b) = 0
(a-b)(a+b)/(a-b) = 0/(a-b)
1(a+b) = 0
(a+b) = 0
1 + 1 = 0
2 = 0
1 = 0
1 + 1 = 1

Good Luck ;)