Hey Brilliant users,
I haven't been on here in a while, I've been really busy with school lately. I have, however, found time to write a few original proofs in the past few weeks. At some point I'll put the better/more interesting ones up here. However, I'm having a somewhat annoying problem with one of my proofs. I probably won't post the proof on here for many reasons, one being the proof's actual length and the other being the originality of it. My problem is, the entirety of the proof rests on the fact that the function I'm considering is infinitely differentiable. Assuming this is true, the remainder of the proof is complex but manageable. For some reason, I'm having trouble proving that this function is infinitely differentiable. I know that it is, it wouldn't make sense for it not to be, but I'm having trouble applying full rigor to the problem. I don't want a direct answer, as I'd rather prove it myself, but I would like some advice if anyone can offer it. In short, my question is: How do you prove that a function is infinitely differentiable?