> Peluse answered that question in a counterintuitive way — by thinking about exactly what it would take for a set of numbers not to contain the pattern you’re looking for.

Proof by contradiction isn't that counter intuitive.

And it's utterly bizarre that this article doesn't explain that this technique is proof by contradiction, or give an example of what it is. The proof that the square root of two can't be expressed as a ratio of integers (hence is not-ratio-able, or irrational) is approachable by highschool freshmen, and would add so much to the article.