I came up with a proof that 0.999... = 1 so that we can finally put this thing to bed.

1) Pick any number from the interval between zero and one (zero and one are included in the interval) with the criteria that it is not equal to one

2) Trivially 0.999... will always be greater than the number you picked, no matter which number you picked according to 1)

3) 0.999... is not greater than one for obvious reasons

4) Therefore 0.999... is in the same interval

5) Conclusion is that 0.999... cannot be equal to anything else but one exactly