Makes sense. The fact that e^(ipi) = -1 seems crazy at first, but no one has a preconceived notion of what it should equal, so when you show a simple proof, of

Makes sense. The fact that e^(ipi) = -1 seems crazy at first, but no one has a preconceived notion of what it should equal, so when you show a simple proof, of course they'll accept it. But people's whole mathematical careers they've worked with decimals and developed firm ideas of how they work. So they idea that 0.999... = 1 seems to defy their years of decimal practice, which makes it hard to accept. Fun anecdote: In my calc BC class, we did an infinite series question that proved that .999... = 1 (it was an infinite series of 9/(10^n), so it was adding 9/10 + 9/100 + 9/1000 + ...), which blew the minds of half of our class. During the argument that ensued, our teacher said "Well, it doesn't actually equal 1. It'll never quite get there. It just gets infinitely close." Needless to say, what little respect for her I did have at that point in the year was gone after that.