1. If 0.999...=1, then ...999.0=-1
2. If 0.999...=1, then 2=1
3. You can construct a set for a number that is infinitely close to 1 but is still less than 1. Not sure what the speaker means by 0.999...=1 in some math systems and not in others. It's not like 2=1 in some math systems and not in others.
Disclaimer: I had nothing to do with the making of any of the videos I cited here, they were created by mathematicians on YouTube. I don't own those videos.