Proof

Let's assume that you have two unknown values, x and y. Let's also assume that x = y. Therefore, if x = 1, then y = 1, or, if x = 2 then y = 2. Let's start with that:
x = y
Then, let's multiply both sides of the equation by x (this keeps both sides equal):
x² = xy
Subtract y² from both sides:
x² - y² = xy - y²
There is an algebraic property that says (x + y) * (x - y) = x² - y². Another property says that y * (x - y) = xy - y². Let's use that here:
(x + y)(x - y) = y(x - y)
Now, we'll divide both sides by (x - y):
((x + y)(x - y)) / (x - y) = (y(x - y)) / (x - y)
This cancels out the (x - y) values on either side, so we get:
x + y = y
If we set x = 1, then this means that:
1 + 1 = 1
How does this work if math is supposed to be perfect?

This doesn't actually work, and there's a reason why.