I puzzled two high school Pre-calc math teachers today with a little proof (maybe not) I found a couple years ago that infinity is equal to -1:

Let x equal the geometric series: $1 + 2 + 4 + 8 + 16 \ldots$

$x = 1 + 2 + 4 + 8 + 16 \ldots$

Multiply each side by 2:

$2x = 2 + 4 + 8 + 16 + 32 \ldots$

Again from the equation in step 1, move the $1$ term to the left hand of the equation:

$x - 1 = 2 + 4 + 8 + 16 + 32 \ldots$

So the following appears to be true:

$2x = x - 1 \implies x = -1$

This is obviously illogical. The teachers told me the problem has to do with adding the two infinite geometric series, but they weren't positive. I'm currently in Pre-calc, so I have extremely little knowledge on calculus, but a little help with this paradox would be appreciated.