Weekend fun puzzle / experiment:
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This is the perfect kind of problem to troll people. Its statement can be understood by high school students or anyone who has learned about functions (that's in Math 001). It should be easy. But is it?
Here is where the experts will start to shake their heads knowingly, but I'm conducting an experiment to see if people, including & especially math majors, can solve it without already knowing the main lemma used in the proof. Maybe they can give a new solution too? Try your best, /sci/.