"can you give us the counterexample?" they asked.
"sure," i said. "take the closed interνal $[0,\infty)$ and then .."
".. wait, that's a closed interval?" one asked, shrilly.
i blinked; oh no ..
so i said yes. they inquired further, and we looked it up in the textbook.
"so is $\mathbf{R}$ an open interval?" another asked.
"actually, it's both open and closed," i pointed out. "there are no endpoints to test, so it has to be both."
"what?!?"
[sighs]
i thought that was one of the first things that anyone ever teaches students: open vs. closed, neither or both ..
oh well. i'll just grade the exams generously.
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