Discuss the properties of the mysterious number 0.999... and its elusive relationship with one. Not much is known about 0.999... and I hope to encourage civil discussion to push the limits of our collective knowledge on this topic.

>Isn't 0.999... already proven to be equal to 1?
There are many naive proofs circulating online that 0.999... = 1. But there is still a lot of debate on this topic, so the issue is not settled. Many of these naive proofs have been debunked.
>You can obviously tell 0.999... is less than 1, just by the way it's written.
Numbers are not necessarily as they seem. 1.0 is equal to 1, even though they are written differently. There are easy ways to show that 1.0 = 1, but the case of 0.999... is not so trivial.
>I have a proof that 0.999... equals/does not equal 1!
Feel free to share your results here, and your peers will debate the validity of your argument.