Studying limits again, this time a pair was finding a limit that they said got very small, but then wrote negative infinity instead of zero. When I acknowledged the difficulty of this question, one student mocked me “It’s not like I asked you a touchy subject!” I laughed and explained that negative infinity has large absolute value, so it is a large negative number. His partner protested “but negative numbers are small!” so I countered with “If you owe someone 100 dollars is that a lot?” They both concurred that it is, so maybe my explanation was valid. The original student wanted a non-economic example though, and he proposed toothpicks (this kid cracks me up all the time). Then I was stuck talking about the non-existence of negative toothpicks, unless we return to the concept of owing someone. The entire conversation was amusing and I think I was moderately convincing this time.

How do you differentiate between small numbers and negative numbers? We didn’t even include “less than” in our discussion…