As near as I can tell, he's just redefining what division means when the divisor is zero. That is, creating a special case. And yes, I get that it's a useful hack in programming.

So anyway, IANAM. What I learned was that 1/0 is infinity. And in software, that generally means a divide-by-zero error. But I also learned the utility of making approximations and exploring behavior at limits. And 1/x obviously increases exponentially as x approaches zero.

So how, then, can 1/x all of a sudden be zero when x is zero? It makes no sense to me. Call it undefined if you like. But it's obviously not zero.