In idle moments, I used to wonder what I would do in the Faustian scenario ("anything for your soul"). I mean, scouts honor their word, and their motto is "Always Prepared", right?
So, one day, the Nameless One did show up, just as you might imagine. The deal was the same as ever. My response was to ask for the Infinite, and offer to double the dealer; that is, double the price for double the benefit. The Devil loves a better, so naturally, he was intrigued, and agreed to my deal.
And now? Now, I know precisely how the tangent can have the value of positive and negative infinity simultaneously. The down side is, I desperately need a new pair of shoes.