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I recently volunteered to help with a summer math program at a local high school for which I thought would be a breeze. As it turns out, it isn't a program for those catching up (summer school) like I thought, it's a small group of kids that have strong math skills and seem to have an endless desire for knowledge. I have been able to keep them reasonably in check intellectually, but I'm nearing the end of my bag of tricks.
For better or worse, they love mathematical fallacies. Of course they were familiar with showing $0=1$ (all numbers equal all other numbers fallacy), and after I showed them $1=-1$ through complex numbers I was out of ideas. I knew of the, all triangles are isosceles triangles fallacy, but couldn't remember it at the time. Does anyone have any interesting fallacies that I can show them? Their math knowledge goes through most of calculus but fallacies outside of that are fine too.
If this is a ridiculous question, I apologize. I figured there were more fallacies out there than what I could find on wikipedia and a few of the other top search results.
Thanks in advanced.
Note: I have another 3 weeks with them so no major rush.