Why a double negative makes a positive. (Mathematics)

[Zhalentine]

Since we agreed that any positive number multiplied by negative 1 is the negative form, and that (-1)(-1) = -1, we can further simplify this:

(-1)(0) = -1 + -1

So:

0 = -2???

If we place any other number (apart from +1) as the answer to the calculation (-1)(-1) = ?, the same thing happens. This is why two negatives make a positive in mathematics.

Reproduced for your enjoyment from http://mathforum.org/dr.math/faq/faq.negxneg.html

I don't think we did agree that (-1)(-1)= -1. Were you just trying to show that if (-1)(-1) = -1, then 0 = -2? You never mentioned you were doing that and when you said "For example, let's assume (-1)(-1) = +1." maybe you meant (-1)(-1) = -1.

Anyways, here is a math problem for you

"proof" that 0 = 1.
We compute the indefinite integral of (1/x dx) by parts. Set u = 1/x and
dv = dx, so that du = -1/x^2 dx and v = x.

We get:
indefinite integral of (1/x dx) = uv - indefinite integral of (v du)
= x/x + indefinite integral of (x/x^2 dx)
= 1 + indefinite integral of (1/x dx)

Subtracting indefinite integral of (1/x dx) from both sides, we get 0=1