[SOLVED] I know this has been hammered out before, but ... When I was in high school, my math teacher showed us that 0.99999... is equal to 1. He went through the fraction proof and I was literally amazed; however, I've also wondered why 0.99999... can't be considered an irrational number. My first guess is that there is a least upper bound which is 1. I always thought that irrational numbers never have a least upper bound. But then I thought that the only definition is that an irrational is a number that can't be expressed as a fraction of integers. Any other thoughts?