I particularly emphasize that infinity is not a (real) number, so any arithmetic I see them doing with infinity will be automatically wrong I agree with you fo

I particularly emphasize that infinity is not a (real) number, so any arithmetic I see them doing with infinity will be automatically wrong I agree with you for the purposes of teaching undergraduate beginning level courses that involve mostly the real number system (and only incidentally the complex number system). That said, our learned fellow participant impendia here on HN, a professor of mathematics, has strenuously disagreed with me by pointing out the specialized number systems that do treat infinity somewhat like a number. On my part, for the students I encounter, I stick to discussions like "All about Infinity"[1] (formerly titled "Infinity Is Not a Number - It's a Free Man") Katherine Körner, another astute mathematician. I have frequently seen discussions of infinity as a (real) number here on HN that essentially boil down to the error of treating the quotient upon dividing by zero as a real number. [1] http://nrich.maths.org/2756 http://nrich.maths.org/2756