> To me, this pretty much captures what people understand the numbers to be used for outside of college math (so no transfinite, cardinals etc.)
I'm in my fourth year of mathematics right now. I guess I'm not in the target group of articles such as these :P
To be fair, it's kind of upsetting, but maybe there's no way to help it... some mathematical proofs can be "dumbed down" to the point that people with very little background can understand them. The proof of sqrt(2) being irrational might be one of those. But, what's given in the article feels like either the author didn't really understand the subject, or she couldn't explain what she understood in simple terms. But, it's really rare that there's such an easy to understand proof or concept. So, I don't blame her.