I actually found mblase's explanation to be just as inaccurate as the one in the original story. "Infinity is not a number and you can never get there" is never

I actually found mblase's explanation to be just as inaccurate as the one in the original story. "Infinity is not a number and you can never get there" is never a good defence in well-formed arguments about limits. It just sidesteps the question and says that it is meaningless, incidentally doing the same to all of mathematical analysis. "Just because a series of curves tends to a limit curve doesn't mean that the series of lengths of those curves tends to the length of the limit curve" is the whole of the explanation.