This is true, but much of math understanding comes from analogies. Summation over an infinite set is like mechanical summation over a finite one, etc. As a tea

This is true, but much of math understanding comes from analogies. Summation over an infinite set is like mechanical summation over a finite one, etc. As a teaching tool I think it's valuable. But it's important not to identify the math with the analogies that are used to teach it.