Out of curiosity, were you perhaps taught with some other seemingly-intuitive explanation? The one given here was the first (and, really, only) such explanation

Out of curiosity, were you perhaps taught with some other seemingly-intuitive explanation? The one given here was the first (and, really, only) such explanation that I received in grade school. It was also my first real exposure to the concept of infinity and limits in math class (although my brother had stumbled upon and explained to me the concept of a derivative in his head one day while sitting in church, way before either of us would be exposed to calculus).