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.