Well they certainly exist in our imagination, which is not to say anything of their import. However, examples of infinite sets are not represented in the material aspect of existence to my knowledge. Examples of 1 are represented materially. So, when we equate a materially grounded concept to a...
Clarification: I am not implying that the equation is wrong. Rather, I am re-interpreting the common student response. The equation is logically consistent in a mathematical system that happens to rely upon a concept--infinity--that is rather imaginary. The student's rejection is a result of...
I was searching the web for some perspective on this non-intuitive equation, 0.999...=1. The consensus is that if a student rejects it as a "parlor trick" there are a handful of reasons to explain the student's "confusion." One reason given is that the student cannot help but see the number as a...