Do you think the dismissive nerd thing is, like, a goal people set out to do?

You seem to have spent your time around sufficiently many unpleasant people that you see their behavior everywhere, even when explicitly corrected. I'm sorry for that.

Could I have independently gone through and rigorously deconstructed my solution? Sure, and we would all be poorer for it. See, there's another, valuable reason people say what I said beside the "classic dismissive nerd thing".

For every person with a question, there's probably 5 more with the same question who didn't ask. By writing down questions like I did, and inviting their answer to be written down, that provides education not only to me but to anyone who reads it after having similar thought.

I consider that sufficiently valuable to create, that I am willing to accept a handful of people criticizing me for "doing the dismissive nerd thing".

So yes. I knew the thing I wrote was wrong, I didn't know why/how, and I wrote it down as is rather than just going off on a personal side quest to come up with some generalized proof. And I would do it again.