However I find this argument curious (emphasis mine):
But isn't that also an argument that contradicts the whole thing? I can reword the last sentence to an equivalent sentence that puts things in a different perspective: "There is always a real number between 0.999... and 1 (no matter how many 9's you choose, I choose one more 9)."Originally Posted by MacNilly
This is at the core of the concept of infinity. Where you wish to establish you know what happens when we reach infinity, I wish to establish we actually don't. Where you wish to establish you can prove it, I wish to establish you can't. And my own proof for that theory is exactly the contradiction that the proofs we have seen so far present when we consider that for any real number we can't think of, 0.999... is never equal to 1.
This is the basis of my thesis that you can't prove 0.999... equals 1. You can only establish it through an unproven rule that serves the purposes of limits and that gives consistency to the Real number system (that unproven rule being that there is no distance between 0.999... and 1).
I can certainly accept the ruling. But cannot accept that as a proof.