And in this proof, we don't have to go through all the digits, but the binomial theorem tells us what they are. And of course, the last digit, we just keep adding, is going to be 1, well, it would be n choose n, which is 1. Let me just write that down. n choose n is going to be x to the 0 times delta x to the n. So that's the binomial expansion. And let me switch back to minus. So all of that, that green, that's x plus delta x to the n, so minus x to the n. Minus x to the n power, that's x to the n, I know I squashed it there. All of that over delta x.