I almost feel like ranting about it. It's a simple error of overlooking that you're conflating two distinct cases. But explaining it would take an entire thread, and I'm too tired to do it. But I had a math teacher friend get it entirely wrong and then get mad at me for daring to disagree with him.
Haven't thought about it in years. No idea why it popped to mind again and is rattling around what's left of my brain.