I understand why physicists and mathematicians get tired of crackpots and such. Heck, I get tired of them because when I’m researching subjects they are all over the place.

No, motherfucker, you can’t disprove Cantor’s diagonal argument or relativity in your basement using two shot glasses and a laser pointer. And that you “feel like” bijection doesn’t work or that the irrational numbers aren’t uncountably infinite doesn’t mean jack shit because these are firmly proved. There is not a room for debate here. There is nothing to discover or argue about. This is simply how the universe is and that’s it.

Sure, I’d feel more comfortable too if the rational numbers weren’t utterly swamped (to a degree that is impossible to comprehend) by a vast and endless sea of uncomputable irrationals. That makes me uncomfortable because it implies something about the universe that I don’t quite understand. Nevertheless, it is what is true. There is not a basis for dispute here. It’s not like arguing about what your favorite soft drink is.

When I can see the obvious wrong logic and assumptions in your “proof” that the rational and irrationals are equal in measure, then damn, you have truly failed.