On a number of occasions, we have caught students using reasoning that shows that they do not believe that zero is a number. There is a difference between saying that the value of a definite integral is zero and saying that the value of a definite integral is nothing.

(JT) Another example is the distinction between zero as an eigenvalue and there being no eigenvalue.

We will discuss this further when time allows. In the meantime, watch for it in your classroom! and send us your examples. It's much more common than you think.