You're on the money in both this post and the grandparent. However, I'd urge you to examine your style. There's no need to condescend. In particular:
> I just proved it. If you didn't understand the above proof, read it again.
> I can't believe you aren't getting this.
Plenty of otherwise rationally minded people have a hard time reasoning about this stuff. If I had a dollar for every time someone suggested that you can beat the house by playing a Martingale... gosh! You'll have a much easier time persuading people if you don't insult them.
I agree with your point, but in the 21st century, I have a hard time accepting that many people ignore basic scientific principles -- in particular, the null hypothesis, which in essence says that a given proposition is assumed to be false until there's evidence for it.
> Plenty of otherwise rationally minded people have a hard time reasoning about this stuff.
Rationality is what rationality does. There's a devious investment scam that, once explained, seems obvious, but most people fall for it unless forewarned. I call it the "Miracle Man" scam. Here it is:
I would like to live in a world where a scam like "Miracle Man" couldn't work, because people would say "It seems too good to be true, therefore chances are it's not true."
> I can't believe you aren't getting this.
Plenty of otherwise rationally minded people have a hard time reasoning about this stuff. If I had a dollar for every time someone suggested that you can beat the house by playing a Martingale... gosh! You'll have a much easier time persuading people if you don't insult them.