This is probably one of those matters that depends upon the text you're using. If your textbook uses this definition, some students might actually read it (wouldn't that be nice!) and being consistent with that content could be pedagogically worthwhile. I don't think there is likely to be any unwanted or unexpected consequence from simply overlooking that usage if your text doesn't push it. My first post on this topic was not to suggest that this usage is somehow superior, but to show that there might be a reasonable rationale behind choosing to go that way.
Jon Graetz wrote:
I need to think, then, about how (and if) to press the distinction onto students