Back when I was a freshman in high school, and had an inadequate grasp of higher mathematics, I came up with an algebraic “proof” that I thought violated, well, something in math. I had “proved” that 0 = -1 using infinity. It was pretty basic. I don’t know why I remembered this today, but I thought it would be amusing to post.
It’s like this:
The symbol ∞ represents, well, infinity. So, you whittle infinity down to a simple variable and start with:
∞ = ∞
Nothing earth-shaking. But infinity being infinity, you could also say that infinity minus one (∞ – 1) is also infinity, since it still goes on forever. Then you’d have:
∞ = ∞ – 1
Then, following the rules, drop out the variable ∞ from the equation by subtracting it from both sides of the equation:
∞ – ∞ = ∞ – ∞ – 1
Which of course leaves you with:
0 = -1
Then, of course, you could further apply various equality rules and come up with all sorts of non-zero results equalling zero.
I remember being pretty disappointed when it turned out to be appallingly wrong. Fortunately, I still went on to the Advanced Math and then Calculus courses…