Zero Is Equal To One
Final exam day for my students is today. Dexter will love me a bit more in the coming days.
On the first day of this fall term, I told my classes that complaining is mouth-farting, proved to them that zero is equal to one, and then held up three fingers on my right hand and said “if you see me hold my fingers like this, I am telling you that I love you,” and the fall quarter term began on a day I discovered how much your upper lip can sweat through a mask.
A student in one of my classes did not like that I proved to him that zero equals one, so he asked “are you serious or are you joking?” I said “yes, I am.” I said there is much to learn, so i showed him that the sum of all the natural numbers is equal to -1/12.
A week into the course, the students became aware of three kinds of infinite sums: those that converge, those that diverge, and those that oscillate. Same student complained that I was not following the book. I reminded him to beware of mouth-farting.
On the first midterm, the last question was the hardest: it read “is there a problem you feel that is missing from this exam, one that you thought about or prepared to answer in your review? If so, describe this problem and its solution in such a way that a reader does not have to do any work to understand you.”
Student wrote “yeah, why you’re wrong that zero equals one and the sum of those numbers you mentioned aren’t negative. I think that’s a problem we need to solve.” I wrote on his paper”please notice my artistic rendering of your word “we” as you used it in this sentence”—I changed WE to I— “this will be a deduction of 90 + 9 + 0.9 + 0.09 + 0.009 + 0.0009 + 0.00009 + …. points, but I’ll give them back to you on the next exam if you think there is a problem there and can describe it and its solution.” I am happy to report that the student did an excellent job, and proved to me that 0.693147 is equal to 0.346573.
I was quite proud, so I passed along a joke from my father, who taught me there were three kinds of turds: mustard, custard, and… what is the third? (Hi siblings?)
