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**[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?