A cool thing I learned a long time ago is that 0.99999… = 1. And I mean exactly equal. Not just “very close to”. EXACTLY equal. Behold the proof! Let a = 0.111111… Then 10a = 1.11111… 10a – a = 1.11111… – 0.11111… 9a = 1. But 9 times 0.11111… is 0.99999…. So 0.999999…. [...]

Some years ago, when I first learned about imaginary numbers, I asked myself the inevitable question – “What’s the square root of i?” Okay, so i is the square root of -1. I had come to grips with that concept. But after that, when you start thinking about it… surely the square root of i [...]