Gill's paradox

Gill’s paradox highlights a surprising situation in set theory: it claims there's a way to match each point on a line with an entire plane, yet still assign each point a unique position along just the line. This seems counterintuitive because we usually think of one-to-one matches as involving objects of similar size or complexity. In simple terms, it shows that, in mathematics, infinite sets can be compared in ways that defy our usual intuition—like pairing each point on a line with a whole plane, even though the plane has “more” points, but both are infinite and can be matched perfectly.